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Difference and Differential Equations in Mathematical Modelling demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.
...
A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments.
way and using an easy to follow format, it will help boost your understanding and develop your analytical skills. Focusing on the core areas of numeracy, it will help you learn to answer questions without using of a calculator and...
This book makes quantitative finance (almost) easy! Its new
visual approach makes quantitative finance accessible to a broad
audience, including those without strong backgrounds in math or
finance. Michael Lovelady introduces a simplified but powerful
technique for calculating profit probabilities and graphically
representing the outcomes. Lovelady's "pictures" highlight key
characteristics of structured securities such as the increased
likelihood of profits, the level of virtual dividends being
generated, and market risk exposures. After explaining his visual
approach, he applies it to one...
Based on the award winning Wiley Encyclopedia of Chemical Biology, this book provides a general overview of the unique features of the small molecules referred to as "natural products", explores how this traditionally organic chemistry-based field was transformed by insights from genetics and biochemistry, and highlights some promising future directions. The book begins by introducing natural products from different origins, moves on to presenting and discussing biosynthesis of various classes of natural products, and then looks at natural products as models and the possibilities of using...
Quantitative Techniques: Theory and Problems adopts a fresh and novel approach to the study of quantitative techniques, and provides a comprehensive coverage of the subject. Essentially designed for extensive practice and self-study, this book will serve as a tutor at home. Chapters contain theory in brief, numerous solved examples and exercises with exhibits and tables.
...
The book is meant for an introductory course on Heat and Thermodynamics. Emphasis has been given to the fundamentals of thermodynamics. The book uses variety of diagrams, charts and learning aids to enable easy understanding of the subject. Solved numerical problems interspersed within the chapters will help the students to understand the physical significance of the mathematical derivations.
...
Applied Mathematical Methods covers the material vital for research in today's world and can be covered in a regular semester course. It is the consolidation of the efforts of teaching the compulsory first semester post-graduate applied mathematics course at the Department of Mechanical Engineering at IIT Kanpur for two successive years.
...
Economics, far from being the "dismal science," offers us valuable lessons that can be applied to our everyday experiences. At its heart, economics is the science of choice and a study of economic principles that allows us to achieve a more informed understanding of how we make our choices, whether these choices occur in our everyday life, in our work environment, or at the national or international level. This book represents a common sense approach to basic macroeconomics, and begins by explaining key economic principles and defining important terms used in macroeconomic discussion. It uses...The UK Clinical Aptitude Test (UKCAT) is used by the majority of UK medical and dentistry schools to identify the brightest candidates most suitable for training at their institutions.
With over 600 questions, the best-selling How to Master the UKCAT, 4th edition contains more practice than any other book. Questions are designed to build up speed and accuracy across the four sections of the test, and answers include detailed explanations to ensure that you maximize your learning.
Now including a brand new mock test to help you get in some serious score improving practice, How to Master the...
As advancements in technology continue to influence all facets of society, its aspects have been utilized in order to find solutions to emerging ecological issues. Creating a Sustainable Ecology Using Technology-Driven Solutions highlights matters that relate to technology driven solutions towards the combination of social ecology and sustainable development. This publication addresses the issues of development in advancing and transitioning economies through creating new ideas and solutions; making it useful for researchers, practitioners, and policy makers in the socioeconomic sectors....Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.
...
Praise for the Third Edition
"This book provides in-depth coverage of modelling techniques used throughout many branches of actuarial science. . . . The exceptional high standard of this book has made it a pleasure to read." —Annals of Actuarial Science
Newly organized to focus exclusively on material tested in the Society of Actuaries' Exam C and the Casualty Actuarial Society's Exam 4, Loss Models: From Data to Decisions, Fourth Edition continues to supply actuaries with a practical approach to the key concepts and techniques needed on the job. With updated material and extensive... | 677.169 | 1 |
Math Class Offerings
Monday, 03 January 2011 10:58 | Posted by Admin IT | |
Mathematics courses at Springfield High School address the Vermont Grade Level Expectations and the Vital Results, along with preparing students for the New England Common Assessment Program, college entrance, and S.A.T. Exams. The Mathematics Department offers a wide range of upper level courses, such as; Statistics, Algebra III, Pre-Calculus, and College Board Certified A.P. Statistics and A.P. Calculus.
375 Math Lab
This course provides support for beginning high school students. Participants will be required to stay organized. In addition to supplementary help in High School Mathematics, participants will work on areas of deficit, identified by their NECAP scores and their primary math teacher. Participants will develop skill sets and gain confidence as they experience sustained success with math.
344 Algebra I (CP)
1 credit
Open to: grades 9-12
Prerequisite: none
This course provides the student with a strong foundation for High School mathematics. Problem solving and mastery are emphasized through whole class, small group, and individual explorations. In addition to algebra and functions, statistics and probability, Geometry and discrete mathematics concepts are developed. A scientific calculator is suggested.
354 Geometry (CP)
1 credit
Open to: grades 9-12
Prerequisite : credit of Algebra I
Scheduled: all year
Plane355 Geometry CATS (CP)
1 credit
Open to: grades 9-12
Prerequisite : credit of Algebra I
Scheduled: all year
In coordination with the Arts academy, plane362A Algebra II A (CP)
A brief review of Algebra I naturally extend to the following topics: equations in three variables, quadratic equations and functions, irrational numbers and polynomials. Students are expected to have a scientific calculator.
362B Algebra II B (CP)
1/2 credit
Open to: grades 10 - 12
Prerequisite: credit in 362A
Topics studied this term will include: complex numbers, triangle trigonometry, an introduction to circular functions and quadratic relations. Students are expected to have a scientific calculator.
333 Applied Algebra II
This course employs an interactive, applied approach to teaching advanced topics in high school mathematics. Students build upon their algebra and geometry foundations as they learn abstract concepts through concrete experience. This course is ideal for the technical center student who has completed Algebra I and Geometry or two years of an integrated high school level math program. Students are expected to have a scientific calculator.
361A Advanced Algebra II A (AC)
This challenging option is specifically designed for the Advanced Placement intending student. A review of the real number system leads to the study of first and second degree equations in both one and two variables. Exponential and logarithmic functions will be introduced. Students are expected to have a scientific calculator.
361B Advanced Algebra II B (AC)
1/2 credit
0pen to: grades 10-12
Prerequisite: credit in 361A
The study of relations and functions will continue with the exploration of the properties of conic sections, polynomial and rational functions, and an introduction to the trigonometric functions. Students are expected to have a scientific calculator.
calculator.
325 Integrated Math II (CP)
1 credit
Open to: grades 10-12
Prerequisite: credit of Integrated I
Scheduled: all Year
This second course in the Integrated series continues the study of Algebra and Geometry, probability, statistics, and discrete math. The underpinnings of trigonometry are established. Students who successfully complete both Integrated Math I & II will have the foundation of Algebra I and Geometry needed for Algebra II or Integrated Math III. A TI-83, or TI-84 calculator is suggested.
326 Integrated Math III (CP)
Students will continue collaborating to explore and solve problems with algebra and geometry. They will use multiple-variable, symbolic, and discrete models along with patterns and families of functions as preparation for college math. A TI-82, TI-83, or TI-83+ calculator are suggested.
334 Finance I
1/2 credit
Open to: grade 12
Prerequisite: none
Students will develop a long-range view of budgeting, exploring investment options and debt management strategies with an eye toward financial independence. Areas of study include stocks, mutual funds, credit, insurance and retirement. A scientific calculator is required.
335 Finance II
1/2 credit
Open to: grade 12
Prerequisite: none
Students will develop a long range view of budgeting, exploring investment options and debt management strategies with an eye toward financial independence. Areas of study include stocks, mutual funds, credit, insurance and retirement. A scientific calculator is required.
371A Algebra III A (CP)
This course will focus on refining skills with functions, including linear, quadratic, polynomials, rational, exponential, logarithmic, and the trigonometric functions. Students are expected to have a scientific calculator.
371B Algebra III B (CP)
1/2 credit
Open to: grades 11 and 12
Prerequisite: credit in 371A
This course will include an introduction to counting theory, probability and statistics as well as matrix algebra and mathematical vector and analysis. Students are expected to have a scientific calculator.
379A Statistics A (CP)
This course is a non-AP level introduction to statistics. The course covers statistical methods and reasoning as they apply to such fields as medicine, environmental science, sports, politics and entertainment. Students will produce and organize data and will then analyze their findings using measures of central tendency and statistical tests.
379B Statistics B (CP)
1/2 credit
Open to: grade 11-12
Prerequisite: credit in 379A
This course is a continuation of 379A. The focus is on developing and evaluating inferences and predictions that are based on data. Students will understand and apply basic concepts of chance and probability
381A Pre-Calculus RF (CP)
This is a college preparatory course designed for the student with above average interest and ability in mathematics. Topics include polynomial functions, rational functions, and exponential functions. Students are encouraged to have a TI-83+ or TI-84 graphing calculator.
381B Pre-Calculus TD (CP)
1/2 credit
Open to: grades 11 and 12
Prerequisite: credit in 381A
This college preparatory course includes a thorough study of elementary trigonometry. Other topics introduced include combinations, probability as well as sequences and series. Students are encouraged to have a TI-83+ or TI-84 graphing calculator.
380 Statistics AP
This is a college level introduction to probability and statistical analysis. The material covered in this course will be sufficient to prepare students to take the Statistics Advanced Placement Examination. A TI-83+ or TI-84 graphing calculator is required for this course.
390 Calculus AP
This is a college level introduction to differential and integral calculus. The material covered in this course will be sufficient to prepare students to take the AB Calculus Advanced Placement Examination. A TI-83+ or TI-84 graphing calculator is required for this course. | 677.169 | 1 |
[
Calculus Essentials For Dummies
Publisher: For Dummies ,Wiley Publishing, Inc.
Mark Ryan
English
2010
196 Pages
ISBN: 0470618353
PDF
22.1 MB
Just the key concepts you need to score high in calculus
From limits and differentiation to related rates and integration, this practical, friendly guide provides clear explanations of the core concepts you need to take your calculus skills to the next level. It's perfect for cramming, homework help, or review.
Test the limits (and continuity) — get the low-down on limits and continuity as they relate to critical concepts in calculus
Ride the slippery slope — understand how differ-entiation works, from finding the slope of a curve to making the rate-slope connection
Integrate yourself — discover how integration and area approximation are used to solve a bevy of calculus problems
[/color][/quote][/b] | 677.169 | 1 |
M145 Math Grade 9 - Algebra I
$40.00
Algebra I is built logically,
moving smoothly from one concept to another. Letters are used to
represent numbers in expressions and equations. Expressions are
simplified and equations are solved. As they work with the axioms,
rules and principles of algebra, students are encouraged to use their
reasoning ability. Revised 2007. | 677.169 | 1 |
1. Course
Description. This yearlong course provides continuation to the mathematics
concepts and processes introduced in Integrated Mathematics I. The intend of
this course is to provide additional algebraic concepts and processes to the
student and demonstrate how they are utilized in the workplace. Topics include
quadratics, linear systems, probability, statistics, and higher level
measurements.
2.Grading. Grades will be
collected from tests, quizzes, and daily work. Daily work will include study
guides, lab activities, and problems. Grades will be determined by the
following plan:
Tests: 50%
Quizzes: 25%
Daily Assignments: 25%
Late assignments
will be accepted but will only receive 50% for what is correct upon the
assignment. The handbook, pg.7 explains the grading scale. Your book number is
your identification number for the posted grades. If you do not want people to
know your grade do not tell them your number.
3.Retest Policy. If a
student scores less than 80% upon a test, he/she has the option to retake the
test. A retestís maximum score will be 80% and must be retaken before the next
unitís test. | 677.169 | 1 |
Interpreting Distance – Time Graphs A6 pictures of situations rather than abstract representations. In addition, they also find it difficult to interpret the significance of the
gradients of these graphs. In this session, students begin by discussing a question that is
designed to reveal common misconceptions about distance–time graphs. They then work in pairs and threes to match descriptions, graphs and tables. As they do this, they will interpret their meaning and begin to link the representations together. (GCSE grades A - D | 677.169 | 1 |
GOOD COURSES
CONTENTS
I. Undergraduate mathematics
A discussion of what a good undergrad programme in
mathematics should be about can be found here.
The book concerns mathematics in the American system, where applied
mathematics was
rarely taught in maths departments (at the time of writing). It also
discusses the content often presented in four-year American liberal arts
colleges, and two-year community colleges, and criticises the specialist
nature of the topics
chosen. The courses offered to students of science and engineering by
departments of mathematics are also panned, one point being that the
professor doing this job knows no science or engineering at all.
The author, Morris Kline, talks of the research professor, who hates
teaching undergraduates of any sort, and also mentions the wide use made
of graduate student tutors, who have neither training nor
experience. Scarce mention is made of full, associate and assistant
professors, who form (in my experience) the bulk of the academic staff in
most departments of mathematics in American universities, and who do a
very professional job in their teaching, as well as research and admin.
Some of the criticism of present methodology is way off centre. For
example, Kline objects to the teaching of applied mathematics by using
over-simplified models. He argues that there is no point teaching the laws
of falling bodies as if there were no air friction: tell that to a
parachutist, he quips. In this he fails to capture the essence of
science: we must study models, and compare with experiment, so that we may
shoot them down, and revise them. More, we can usually find a range of
applicability of
the simple model, outside of which it is no longer a good one. But
worse: he seems to be saying that only a fully developed, correct model
should be taught. This goes against the teaching of Picasso: a teacher
should mix a little bit of what we do not know with a lot of what we do
know. I taught physics at Virginia Tech., a course in which the technician
had prepared the "Galileo Bench". This was an inclined plane on an air
cushion, in which Galileo's laws of falling bodies, s = s(0) + vt + 1/2 at2,
was true, to within the experimental error. Some of the students
found these laws hard to understand, even without friction. When they had achieved
that, we went on to the refinements coming from friction. To start with
the full theory, would place them in a similar position to Galileo... who
had to cope with Aristotle's dictum that a force was needed to keep a
body moving; when Galileo had abandoned this, he broke the 2000 year stalemate
in science.
Most of the points made about the limited syllabus of a maths degree do
not apply to the UK, where applied
mathematics traditionally forms half of the degree in
mathematics. However, with the possible replacement of A-levels with a
bacc., our school programme might become more like the American one. We
should then think about whether the university course might also move in
that direction. Should we have four-year degree courses in mathematics, with
the first year devoted to maths, physics, chemistry and computing? These
could cover the four subjects to replace the omitted parts of A-level. The
mathematics course
could cover analytic geometry with calculus, trig, probability and
statistics,
complex numbers, and vectors, with a little theory of matrices.
Physics could include Newton's laws, with examples from one
dimension, such as motion under constant gravity, friction,
simple damped oscillator, sinusoidal wave
motion, interference of waves, the laws of thermodynamics, Eulerian fluid equations,
and electricity and magnetism (before Maxwell). Chemistry might contain
the Bohr atom, the Mendeleev table, the inorganic chemistry of
acids and bases, salts and metals. Some physical chemistry such as the law
of mass-action, and some organic chemistry, should be
included. Lab work in physics and chemistry should be at the
level now done in schools in the UK. Computing might introduce a useful
language such as Java, Maple or Mathematica, and should give a general
competence in Windows.
Kline suggests that scholarship in mathematics would serve a purpose,
to reduce the number of pointless and empty papers, by critical reviews.
This used to be the job of Mathematical Reviews, until it changed its
policy, and now bans controversy in the reviews. Kline suggests that a new
degree of high status, Doctor in Arts, should be awarded, which would not
require
original theorems, but would be readable and deep. We have something
similar, in
the M. Phil., which however has not got the status of the Ph. D.
III.Abstract Algebra
IV. Graph theory
V. The Kentucky Archives on
Mathematics
The site of the University
of Kentucky hosts a list of free material on mathematics, of which
III. above is just one. I found the course on partial
differential equations very useful. The course
on Hilbert Space Methods for Partial Differential Equations, by
R. E. Showalter, is very pleasant indeed. It is slightly informal in its
definition
of distributions, but this is all that is needed for partial
differential equations at this level.
VI.Wikipedia
Wikipedia is a free internet
encyclopaedia, written by its viewers. There
is quite a large set of mathematics pages, as well as pages on physics and
other sciences, and all other subjects. Some pages are sketchy, and others
are literally empty,
awaiting the first volunteer. I found a mistake in Wightman's
biography: it said he was British. I was able to edit that page and
correct it. The statement of the Navier-Stokes equations could not be
right, as the terms do not all have the same physical dimension.
The site is worth a browse, and might become more reliable as time
passes. | 677.169 | 1 |
eBook Ordering Options
DescriptionExamining how information technology has changed mathematical requirements, the idea of Techno-mathematical Literacies (TmL) is introduced to describe the emerging need to be fluent in the language of mathematical inputs and outputs to technologies and to interpret and communicate with these, rather than merely to be procedurally competent with calculations. The authors argue for careful analyses of workplace activities, looking beyond the conventional thinking about numeracy, which still dominates policy arguments about workplace mathematics. Throughout their study, the authors answer the following fundamental questions:
What mathematical knowledge and skills matter for the world of work today?
How does information technology change the necessary knowledge and the ways in which it is encountered?
How can we develop these essential new skills in the workforce?
With evidence of successful opportunities to learn with TmL that were co-designed and evaluated with employers and employees, this book provides suggestions for the development of TmL through the use of authentic learning activities, and interactive software design. Essential reading for trainers and managers in industry, teachers, researchers and lecturers of mathematics education, and stakeholders implementing evidence-based policy, this book maps the fundamental changes taking place in workplace mathematics.
Contents
Acknowledgements
1. Introduction
1.1 New Demands on Commerce and Industry
1.2 Information Technology and the Changing Nature of Work
1.3 Background to the Research
1.4 A Description of Key Ideas
1.5 Aims and Methods
2. Manufacturing 1: Modelling and Improving the Work Process in Manufacturing Industry
2.1 Process Improvement in Manufacturing
2.2 Workplace Observations of Process Improvement
2.3 Learning Opportunities for Process Improvement
2.4 Outcomes for Learning and Practice
2.5 Conclusions
3. Manufacturing 2: Using Statistics to Improve the Production Process
3.1 Process Control and Improvement Using Statistics
3.2 Workplace Observations of Statistical Process Control
3.3 Learning Opportunities for Statistical Process Control
3.4 Outcomes for Learning and Practice
3.5 Conclusions
4. Financial Services 1: Pensions and Investments
4.1 The Techno-Mathematics of Pensions and the Work of Customer Services
Related Subjects
Name: Improving Mathematics at Work: The Need for Techno-Mathematical Literacies (Paperback) – Routledge
Description: By Celia Hoyles, Richard Noss, Phillip Kent, Arthur Bakker. Improving Mathematics at Work questions the mathematical knowledge and skills that matter in the twenty-first century world of work, and studies how the use of mathematics in the workplace is evolving in the rapidly-changing context of new technologies...
Categories: Adult Education and Lifelong Learning, Educational Research, Post-Compulsory Education, Teaching & Learning, Education Policy, Work-based Learning, Operational Research / Management Science | 677.169 | 1 |
Discovering Geometry Intro
Discovering Geometry began in my classroom over 35 years ago. During my first ten years of teaching I did not use a textbook, but created my own daily lesson plans and classroom management system. I believe students learn with greater depth of understanding when they are actively engaged in the process of discovering concepts and we should delay the introduction of proof in geometry until students are ready. Until Discovering Geometry, no textbook followed that philosophy.
I was also involved in a Research In Industry grant where I repeatedly heard that the skills valued in all working environments were the ability to express ideas verbally and in writing, and the ability to work as part of a team. I wanted my students to be engaged daily in doing mathematics and exchanging ideas in small cooperative groups.
The fourth edition of Discovering Geometry includes new hands-on techniques, curriculum research, and technologies that enhance my vision of the ideal geometry class. I send my heartfelt appreciation to the many teachers who contributed their feedback during classroom use. Their students and future students will help continue the evolution of Discovering Geometry. | 677.169 | 1 |
Math e-Books for $0
[29 Aug 2011]
Most of the following free (or low cost) math e-books are PDF versions of ordinary math books.
You probably won't find your assigned text book here, but you'll find something that is pretty close. And for the millions of keen students who cannot afford the high price of math text books, this will be a valuable list.
Copyright information: It's not clear if copyright permission has been granted in some of these collections. In some cases, the business model involves advertising throughout the book (but the quality tends to be higher). In Google Books' case, for many of the books, they've been given permission to show selected pages only.
Google Books
Google wanted to digitize every book in the world, but not surprisingly, they ran up against copyright issues. Many of these books are not complete, but can still be very useful for that nugget of information you're looking for. | 677.169 | 1 |
This is a course in the algebra of matrices and Euclidean spaces that emphasizes the concrete and geometric. Topics to be developed include: solving systems of linear equations; matrix addition, scalar multiplication,
and
multiplication, properties of invertible matrices; determinants; elements of the theory of abstract finite dimensional real vector spaces; dimension of vector spaces; and the rank of a matrix. These ideas are used to
develop
basic ideas of Euclidean geometry and to illustrate the behavior of linear systems. We conclude with a discussion of eigenvalues and the diagonalization of matrices. For a more conceptual treatment of linear algebra,
students
should enroll in MATH223.
MAJOR READINGS
To be announced.
EXAMINATIONS AND ASSIGNMENTS
Two midterm exams, homework assignments, final exam for most sections, various problem sets and occasional quizzes for some sections. Students will take midterm exams at 7:30 p.m. on Monday, October 10 and Wednesday,
Novmber 16.
ADDITIONAL REQUIREMENTS and/or COMMENTS
MATH121, 122 or the high school equivalent is strongly recommended as background, but not required. | 677.169 | 1 |
A Level Maths Core 2 Collins Student Support Materials for Edexcel AS Maths Core 2 covers all the content and skills your students will need for their Core 2 examination, including: * Algebra and functions * Coordinate geometry in the (x, y) plane * Sequences and series * Trigonometry * Exponentials and logarithms * Differentiation * Integration * EXAM PRACTICE * Answers | 677.169 | 1 |
,
Title Description:
The Trachtenberg Speed System of Basic Mathematics
Author : Jakow Trachtenberg adapted by Ann Cutler and Rudolph Mcshane
Bibliography : None
PaperBack : ISBN : 0285629166
Price: 24.95
Price: US $ 24.95
Details
The Trachtenberg Speed System of Basic Mathematics
Price: US $ 24.95
Book Background
Jakow Trachtenberg created the Trachtenberg system of mathematics, whilst a political prisoner in Hilter's concentration camps during the Second World War To keep himself sane whilst living in an extremely brutal and harsh environment, Trachtenberg immersed his mind in a world of mathematics and calculations. As concentration camps do not provide books, paper, pen or pencils nearly all of his calculations had to be performed mentally. This forced Trachtenberg to develop methods and shortcuts for performing calculations mentally. Trachtenberg developed his discoveries into a complete system of mathematics.
After the Second World War, Trachtenberg started teaching his system of mathematics. He started teaching the more backward children to prove that anyone could learn his system. In 1950 he founded the Mathematical Institute in Zurich, where both children and adults were taught the system.
The system has been thoroughly tested in Switzerland and is found to produce an increase in self confidence and general aptitude to study, as the students prove to themselves what they are capable of, by their accomplishments in calculating results to computations.
The Trachtenberg system is based on a series of keys which must be memorized. There is no need for multiplication tables or division as the system only relies on the ability to count. The system also places an emphasis on getting the right answer and provides a number of methods for checking the answers achieved by the system.
Research on the system, indicates that the system shortens time for mathematical computations by twenty percent and produces correct results, ninety nine percent of the time, due to the checking method used as part of the system. | 677.169 | 1 |
This course aims to introduce the basic concepts and techniques of linear algebra and single variable calculus which are necessary for undertaking subsequent courses in the Mechanical Design and Electronic themes. It is aimed at students without A Level Pure Mathematics (or its equivalent). The course will help students develop skills in logic thinking.
Course Intended Learning Outcomes (CILOs) Upon successful completion of this course, students should be able to:
No.
CILOs
Weighting (if applicable)
1.
explain concepts from basic linear algebra and single variable calculus.
develop simple mathematical models through linear systems of equations, derivatives and integrals, and apply mathematical and computational methods to a range of problems in scientific and engineering applications involving basic linear algebra and single variable calculus.
2
5.
the combination of CILOs 1-4
3
Teaching and Learning Activities (TLAs)
(Indicative of likely activities and tasks designed to facilitate students' achievement32 hours in total
Learning through tutorials is primarily based on interactive problem solving allowing instant feedback.
2
2 hours
3
2 hours
1
1 hour
4, 5
2 hours
Learning through take-home assignments helps students understand basic mathematical concepts and techniques of linear algebra and single variable calculus, and apply mathematical methods to some problems in scientific and engineering applications.
1--5
after-class
Learning through online examples for applications helps students apply mathematical and computational methods to some problems in scientific and engineering applications.
4
after-class
Learning activities in Math Help Centre provides students extra help.
2
70, 2
15-30%
Questions are designed for the part of linear algebra to see how well the students have learned basic concepts and techniques of linear algebra.
Hand-in assignments
1-4
0-15%
These are skills based assessment to see whether the students are familiar with basic concepts and techniques of linear algebra and single variable calculus and some applications in science and engineering.
Examination
5
70%
Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student's versatility in linear algebra and single variable calculus.
Formative take-home assignments
1--4
0%
The assignments provide students chances to demonstrate their achievements on linear algebra and single variable calculus learned in this course.
Grading of Student Achievement: Refer to Grading of Courses in the Academic Regulations
Part III
Keyword Syllabus
Vectors and coordinate geometry in space. Matrices and determinants. Complex numbers. Sequences and series. Differential calculus and integral calculus. System of linear equations. | 677.169 | 1 |
Basic Business Statistics
Berenson's fresh, conversational writing style and streamlined design helps students with their comprehension of the concepts and creates a thoroughly readable learning experience. Basic Business Statistics emphasises the use of statistics to analyse and interpret data and assumes that computer software is an integral part of this analysis.
Berenson's 'real world' business focus takes students beyond the pure theory by relating statistical concepts to functional areas of business with real people working in real business environments, using statistics to tackle real business challenges. Read More
Business Statistics
Berenson's fresh, conversational writing style and streamlined design helps students with their comprehension of the concepts and creates a thoroughly readable learning experience. Business Statistics emphasises the use of statistics to analyse and interpret data and assumes that computer software is an integral part of this analysis.
Business Statistics covers the key content in first year business statistics courses as well as further coverage of topics such as decision making, statistical applications, Chi-square tests and nonparametric tests. Read More
Numeracy in Nursing and Healthcare: Calculations and Practice
Australian Edition
Do your students find maths and medications challenging?
Would you like to be able to give your students more personalised support and feedback?
Would you like to provide more support for students with varying mathematical ability?
Numeracy in Nursing and Healthcare Australian Edition with MyMathLab is the perfect package to help your students prepare for their nursing program. Read More
MyMathLab Global, Australia/New Zealand Edition
MyMathLab Global is a powerful online homework, revision and assessment tool to help students and instructors.MyMathLab Global engages students in active learning—it's modular, self-paced, accessible anywhere with internet access and adaptable to each student's learning style.
Independent of any textbook, it has been designed so instructors can easily customise MyMathLab Global to better meet their students' needs. | 677.169 | 1 |
Probability : An Introduction - 87 edition
Summary: Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, and other key concepts and methods essential to a thorough understanding of probability. Designed for use by math or statistics departments offering a first course in probability. 360 illustrative problems with answers for half. Only high school algebra needed. Chap...show moreter bibliographies | 677.169 | 1 |
A very thorough introduction to some now classical topics can be found in James D. Murray's
now two-volume book published by Springer. Expect lots of ODE's and PDE's in that one.
As far as more exotic math is concerned, a complete overview would be difficult: it seems people throw everything they have and see what works. I've seen some interesting talks involving combinatorics, others involving algebraic geometry. | 677.169 | 1 |
Question 565853
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You are kidding, right? Which one of several hundred math books in use today, each of which costing in excess of $75, shall I pull off of my shelf of all possible math books so that I can see the diagram? This is Algebra.com. It is NOT the Psychic Hot Line | 677.169 | 1 |
Here is a new site that has some nice dynamic calculus tutorials. and here is a link to another good tutorial site called Visual Calculus TI Calculator Guide.. Here is a great link that lets you look up functions on your calculator in an alphabetical list, and then shows you how to do it... simply Great.
HEY, WAY COOL, FREE SOFTWARE
This link will download the WINPLOT program. The file is a self extracting compressed file, just double click to expand. It will create a new file called winplots that is the execute file you want to run when you run the program. And if that didn't convince you, you can also download a Discrete Math software program that is also a great tool.
Another graphing software program which is FREE is called GraphCalc.
You will find it at
Here is another great interactive Algebra and Geometry software, and it is also free. They call it GEOGEBRA.
Lots of Middle Grade teachers have asked about interesting math games for their students which are both educational and entertaining. This link will download a set of Arcade games including John Conway's Game of Life, the 15 puzzle, ghost mazes, and several others. Here are the links to documents I have written about assorted topics.
And for the stats TEACHER a FREE demo of FATHOM my very favorite software for statistics and probability simulations. Students can order a student version for less than $40.
Here is an index of DISCOVERY UNITS using the GEOMETER'S SKETCHPAD that I have written. Some are about GEOMETRY, and some are about ALGEBRA. I hope to have more added soon, so keep checking back. If you do not have Geometer's Sketchpad you can get a FREE DEMO | 677.169 | 1 |
Mathematics
SCC offers a wide variety of mathematics courses to prepare students for work in the fields of mathematics, science, health, education, business and more. Courses offered range from basic developmental mathematics through calculus, differential equations, linear algebra and transition to theoretical mathematics. SCC offers traditional, hybrid and online courses.
Mission Statement
To make mathematics accessible, to provide quality mathematical content with concerned instruction and to provide a broad range of courses so that students may acquire the necessary mathematical skills to meet their career and personal goals. | 677.169 | 1 |
Author:
Hao Wang, Wenlong Wang
This is a free textbook from BookBoon.'Algebra is one of the main branches in mathematics. The book...
Type: Open Textbook
Date Added: Jan 29, 2013
Date Modified: Jan 29, 2013 | 677.169 | 1 |
...
More About
This Book
Study quickly and more effectively; Get the big picture without spending hours poring over dull texts Schaum's Outlines give you the information teachers expect you to know in a handy and succinct format—without overwhelming you with unnecessary details. You get a complete overview of the subject—and no distracting minutiae. Plus,you get plenty of practice exercises to test your skill. Compatible with any classroom text,Schaum's lets you study at your own pace and reminds you of all the important facts you need to remember—fast! And Schaum's is so complete it's the perfect tool for preparing for graduate or professional exams! Students of mathematical economics apply complex formulas—a challenging task that even the best students find daunting. But this Schaum's guide demystifies tough problems and gives you plenty of fully worked examples! Chapters include: Review. Economic Applications of Graphs and Equations. The Derivative and the Rules of Differentiation. Uses of the Derivative in Mathematics and Economics. Calculus of Multivariable Functions. Calculus of Multivariable Functions in Economics. Exponential and LogarithmicFunctions. Exponential and Logarithmic Functions in Economics. Differentiation of Exponential and Logarithmic Functions. The Fundamentals of Linear (or Matrix) Algebra. Matrix Inversion. Special Determinants and Matrices and Their Use in Economics. Linear Programming: A Graphic Approach. Linear Programming: The Simplex Algorithm. Linear Programming: The Dual. Integral Calculus: The Indefinite Integral. Integral Calculus: The Definite Integral. Differential Equations. Difference Equations. Second-Order Differential Equations and Difference Equations. The Calculus of Variations
Schaum's Outlines contains hundreds of worked-out solutions to problems covered in any college | 677.169 | 1 |
Edie M. Brown / Academic Therapist
People often say that mathematics is a universal language. It is the essence of cognition - thinking with numbers, imagery, and language. For the people who understand mathematics, the language of numbers turns into imagery, letting them calculate and verify mathematics while seeing its logic. Through multisensory instruction, I integrate all of the senses to help create a mathematical picture of concepts and theories, forming the foundation of understanding.
Mathematics
Math literacy means having the mechanics and skills to perform calculations without looking them up and knowing what situations these skills may be appropriate. The true "math literate" is not someone who can successfully complete a test on recently acquired processes and techniques, but one who can apply those abilities to situations that occur in a variety of situations in the long term.
In secondary and postsecondary math, there should be a broad focus encompassing a wide variety of career choices. This includes common foundations of math ideas and applications. Students should be adept at the integration of mathematical concepts. These areas include algebra, geometry, probability, statistics, calculus, and discrete mathematics. | 677.169 | 1 |
Algebra - Wikipedia, the free encyclopedia Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. For historical reasons, the word "algebra" has several related ... | 677.169 | 1 |
Other Materials
Description
Calculus B introduces integration of functions, differential equations, and applications of integration. The student will�calculate antiderivatives using a variety of methods including substitution. The student will evaluate integrals using a variety of methods including numerical integration. Then the student will understand and apply Riemann sums, definite integrals, and the Fundamental Theorem of Calculus. In particular, the student will differentiate and integrate logarithmic, exponential, and inverse trigonometric functions. The student will solve simple differential equations, which can be solved by separation of variables, and�use the calculations�to solve applied problems. The student will use integration to determine the area between two curves, volume, and surface area. Finally, the student will apply integration to determine work, center of mass, and fluid force. | 677.169 | 1 |
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Tips to help make Math Simple
Frustration, stress and anxiety. Do these words come to mind when you hear the word "Math"? Well, for those of you who are experiencing trouble with Math, here are some tips to help make the subject an easier one.
Read the Book
Read the assigned sections over carefully and look closely at the sample problems. Decide if you benefit more by reading before or after the instructor covers the material.
Develop a Sound Math Foundation
Because most math courses are cumulative (in other words, new concepts are added to and build upon previous concepts), it is very important that the early material be mastered thoroughly. Similarly, mastery of material from previous courses makes success in later courses more likely, so continually review and practice concepts from prior math classes.
Time Management
Complete all readings – especially homework assignments – as soon after they are announced as possible. And definitely complete all assignments before new material is covered since math is cumulative. This ensures that the information is fresh in one's mind and linked to prior, more fundamental information. Do your assignments early enough that you can get help with the things you do not understand.
Calculator
Learn how to use your calculator effectively and efficiently, especially if exams are timed and you have trouble completing tests in the allotted time. Check with the instructor about suggestions for the appropriate calculator to purchase for a class. Be sure the machine comes with an instruction manual and read the manual. Learn how to use important function keys. Get in the habit of carrying the calculator with you. It is better in the long run to become proficient with your own calculator rather than borrowing other people's calculators.
Show Your Work
Avoid the temptation to skip steps when solving a problem unless you are quite clear about how to proceed. This is a good habit to get into with your math homework. And definitely don't skip steps on an exam no matter how well you know the material. Why take chances (unless you're running out of time)? Showing your work allows you to locate logical or calculation mistakes more easily, and sometimes partial credit is given for the correct portions of an answer.
Organise Your Work and
Write Legibly
Write all numbers and variables clearly so they may be easily distinguished. Pay particular attention to the distinguishing lines of the numbers 4 and 9, 1 and 7 and the letters x and y.
Spaces are as important in math equations as are the numbers and variables themselves. Allow enough space between different terms in an equation so it is easy to distinguish them.
Be sure to line up the terms in each step of the solution, and write steps one below the other rather than to the right or left. Use lined paper or graph paper to help organise the problems on your page. Don't scrunch! Use plenty of paper to work each problem. Recycle the paper at the end of the term if you are concerned about wasting paper.
Support Services and Materials
Find out about the support services and materials available to you. Support services include workbooks, study groups, self-help videos and cassettes, peer tutors, professional tutors, and instructors' office hours. Using the resources from the start of the course may help your confidence and get you off on the right foot. Minimally, make use of these resources as soon as you feel uncomfortable with the material; do not wait until it is too late!
Preparation and Supplies
• Being prepared for each course involves several important factors:
• Complete any previously assigned homework assignments
• Compile a list of questions about the previous assignments to ask the instructor | 677.169 | 1 |
Book Description
Release date: August 5, 2008 | Age Range: 11 and upEditorial Reviews
About the Author
Best known for her roles on The Wonder Years and The West Wing, Danica McKellar is also an internationally recognized mathematician. She was chosen as ABC World News Tonight's "Person of the Week" for writing Math Doesn't Suck and has recently been featured in Newsweek and The New York Times, and on the CBS Early Show, and NPR's Science Friday.
--This text refers to an out of print or unavailable edition of this titleThis funny math book teaches girls that it's OK to be smart, and that they are perfectly capable of kicking a little pre-algebra butt.
McKellar takes a lightweight approach to math, but is deadly serious about it. In the prologue, she writes that "lots of people change their majors and abandon their dreams just to avoid a couple of math classes in college." Girls in particular, she emphasizes, often use their fear of math to keep them from learning the skills they'll need to succeed in life, and they start backing away from the subject in middle school.
And it's not just fear. Girls often don't see how they'll use math once they get out of school. Testimonials in Kiss My Math fight this. Stephanie Perry, the finance director for Essence magazine, explains how she uses algebraic formulas to stay on top of the magazine's financial performance. Jane Davis, financial strategist at Polo Ralph Lauren, was hired as an assistant buyer because of her facility with math. She describes determining inventory over time by finding the mean of a list of numbers.
McKellar -- famous for playing Winnie Cooper in the "The Wonder Years" but also a summa cum laude math graduate from UCLA -- uses simple language and lots of illustrations to teach pre-algebra. Each chapter covers a single topic, such as the distributive property or exponents. She clearly explains each topic, and includes problems for the reader to solve (answers are in the back). The author is generous with helpful notes and shortcuts.
A lively, breezy writing style makes it seem as if McKellar is sitting next to the reader. She uses examples girls can relate to, like clothes shopping, working on the school play, blind dates, parties, kissing and breath mints. It's like having the perfect math tutor. (I'm not a middle school girl, of course, but I just got finished having one. My daughter is starting high school this month.)
Especially good are the entries called Danica's Diary, which are true stories from the author's life as a student, actress and mathematician. One is titled: Dumbing Ourselves Down for Guys: Why is it so Tempting? McKellar gives practical advice on how girls can avoid this common pitfall.
I can't think of a better book to buy for a girl taking pre-algebra.
Here's the chapter list:
Part 1: Number Stuff Chapter 1: Breath Mint, Anyone? Adding and Subtracting Integers (Including Negative Numbers). Chapter 2: The Popular Crowd. The Associative and Commutative Properties. Chapter 3: Mirror, Mirror, on the Wall... Multiplying and Dividing Integers (Including Negative Numbers!) Chapter 4: A Relaxing Day at the Spa. Intro to Absolute Value. Chapter 5: Long-Distance Relationships: Are They Worth It? Mean, Median, Mode. You Said: Most Embarrassing Moments in School Poll: What Guys Really Think... About Smart Girls Quiz: Are You a Stress Case?
Part 2: Variable Stuff Chapter 6: The Blind Date. Getting Cozy with Variables. Chapter 7: Backpack Too Heavy? Adding and Subtracting with Variables. Chapter 8: Something Just Went "Squish." Multiplying and Dividing with Variables. Chapter 9: Do You Like Him Like Him? Combining Like Terms. Chapter 10: The Costume Party. The Distributive Property. Chapter 11: Didn't That Guy Say He Was Going to Call? Using Variables to Translate Word Problems. More Than 20 Ways to Beat Stress Math... In Jobs You Might Never Expect!
Part 3: Solving for X Chapter 12: The Art of Gift Wrapping. Solving Equations. Chapter 13: Nope, She Never Gets Off the Phone. Word Problems and Variable Substitution. Chapter 14: Can a Guy Be Too Cute? Intro to Solving and Graphing Inequalities. You Said: Your Horror Stories About Procrastination Poll: What Guys Really Think... About Talented Girls Quiz: Do You Pick Truly Supportive Friends?
Part 4: All About Exponents Chapter 15: Champagne and Caviar. Intro to Exponents. Chapter 16: Excuse Me, Have We Met Before? Intro to Variables with Exponents. You Said: Well... That Didn't Work! Do You Sudoku?
I am a mother that went back to college later in life. One of my classes was algebra. I had math anxiety and tried to find way to wiggle my way out of this class. The algebra class was very difficult for me. I could not understand the instructor or the book. I went to tutors,family members and friends and I could not get algebra. I failed the class. I was embarrassed and angry with my myself. I needed something right away. So my boyfriend and I went to Barnes & Nobles and purchased Kiss My Math & Math Doesn't suck. (I do suggest that you purchase both). So I had a six week break before I had to take the algebra class again. I am happy to say that I passed the algebra class with a B and I am looking forward to starting MATH 209 which is the second part of algebra. Danica was easy to understand and the experiences from other young ladies helped a great deal too. Thanks Danica!
Danica McKellar is a beautiful actress who is probably very well off and successful. So why did she go to UCLA to study math after being a very successful child star on the wonder years and then bother to write a book entitled Math Doesn't Suck. Well it is because she wanted to prove she was more than just a good looking actress. She had a brain and could handle math. The attitude that math is not for the ladies was a horrible prejudice in my high school years and even in this enlightened age we haven't quite gotten over it and many a capable young lady lacks the confidence and courage to try to do math. Danica is a rol model who proves that they can. Her first book was so successful and helped young middle school girls overcome their fears and lkearn that math is not really hard and can be fun and interesting whenit is approached in the riht way. So math does not suck! But in addition to convincing young girls and boys that they can learn it she became encouraged to write another book based on the encouraging emails from young ladies who benefitted from the book. Well love of math should not end with middle school and algebra, geometry and calculus are very different form the kind of math you learn in the elementary and middle schools that a good series of lectures in pre-algebra is needed to help those who become discouraged again in high school. It bothers Danica to see a girlfriend of hers give up on medical school just because calculus is required. So in the same interesting style as her first book Danica interest the high schoolers with concepts like negative numbers, mathematical inequalities, exponential functions and much more. By uncovering the mysteries of pre-algebra Danica unlocks the door to advanced levels of mathematics that students in high school need. This book is good for high school teachers and anyone else with an interest in mathematics. But it is aimed at and can help most high school girls who are capable of doing well in math and nedd it for the careers they seek, like med school. | 677.169 | 1 |
Sometimes solve blocks cannot find a solution. Read on to see how to resolve some issues. Errors and Problems with No Solutions Sometimes there might be no solution, or Mathcad might not find a solution. In either case, Find displays the error message "No solution was found." The problem asks for numbers u and v that add to both 2 and 3, …
Easy Solutions and Visualizations: Exploring a System of Three Equations in Three Variables Using Mathcad In modern middle school and high school mathematics algebra is a gatekeeper course. Success in Algebra 1 in grade 8 is considered a prerequisite for college preparedness. My own first experience in Algebra 1 was at South Side Junior High School. At the time, a …
If you are visiting Boston this week for the American Mathematical Association of Two Year Colleges (AMATYC) Annual Meeting, stop by Booth 336 to meet the Mathcad Education Team and to learn more about Mathcad 15.0 and its role in PTC's STEM Education Programs. Ned Daniels and I have been working hard to prepare for the conference. We both have | 677.169 | 1 |
3: Communicate the breadth and interconnections of the
mathematical sciences
Every course should strive to:
Present
key ideas and concepts from a variety of perspectives;
Employ
a broad range of examples and applications to illustrate and motivate
the material;
Promote
awareness of connections to other subjects (both in and out of the
mathematical sciences), and strengthen each student ability to apply the
course material to these subjects;
Introduce
contemporary topics from the mathematical sciences and their
applications, and enhance student perceptions of the vitality and
importance of mathematics in the modern world.
Key
Ideas and Concepts from Varied Perspectives
Project Intermath
is an interdisciplinary mathematics project that is creating curricula at the
United StatesMilitaryAcademy, CarrollCollegeGeorgiaCollege & StateUniversity, HarveyMuddCollege, MacalesterCollege,
University of Redlands, and the Texas Southern
Consortium. By working with professors from science, engineering, mathematics
and computer science departments, the project aims to foster the creation of
interdisciplinary courses that demonstrate the interdependence of mathematics
and science. For example, at the United
StatesMilitaryAcademy , first semester students study the concept of change
from both a discrete and a continuous point of view. At the end of the
semester students must model and solve particular problems by using a
discrete dynamical system and by using a differential equation. Students then
compare and discuss the appropriateness and the results of the two
approaches. Within the four-course core program, students at the United
States Military Academy also examine mathematical topics from the
perspectives of linear versus nonlinear and stochastic versus deterministic.
At Carroll College, a 4-class core consisting of a total of 18 credit hours
covers many of the topics seen in the first two years of a traditional
curriculum, including differential and integral calculus, multivariable
calculus, differential equations, and linear algebra. The core also includes
topics not usually seen early, if at all: discrete dynamical systems, partial
differential equations, probability, and statistics. Concepts
are threaded together in and between classes to help students develop a
deeper understanding of how different branches of mathematics are
intertwined. The website contains complete texts for over 40 modeling
problems developed at the United
StatesMilitaryAcademy site.
Although a number of the textbooks produced during the calculus reform
movement are no longer in print, both mainstream and reform texts now
consider the concepts of calculus from a variety of perspectives: not only
the symbolic, but also the graphical, numerical, and verbal. The
Calculus Consortium at Harvard Newslettersdiscuss issues involved in teaching calculus. Many
calculus texts now come with software to enhance student understanding from a
variety of perspectives.
A good source of ideas on how to teach linear algebra from various
perspectives is Resources
for Teaching Linear Algebra, edited by David Carlson, Charles R.
Johnson, David Lay, Duane Porter, Ann Watkins, and William Watkins, MAA
Notes vol. 42.
The concept of function can be regarded from many different perspectives
and is important in all undergraduate mathematics courses. The editors of The
Concept of Function: Aspects of Epistemology and Pedagogy (Harel & Dubinsky, 1992) contributed to the body of
research on learning the function concept in order to assist in instructional
approaches. Key
Aspects of Knowing and Learning the Concept of Function by Marilyn
Carlson and Michael Oehrtman is a recent online
article that provides a broad view of the subject.
Victor Donnay, BrynMawrCollege, developed a
PowerPoint presentation
describing how computer visualization can be used to give an intuitive
understanding of complex ideas in modern mathematics.
Promote
Awareness of Connections between Mathematics and Other Subjects
Applications
Dan Maki (Indiana University Bloomington) and Bart Ng
(Indiana University-Purdue University Indianapolis) co-direct the NSF-funded
project Mathematics
Throughout the Curriculum. The website includes links to a prototype
course Analytical
Problem Solving and a set of Home Pages for
Developing Courses, which contain additional information about courses
that relate mathematics to the life sciences, business and economics, the
humanities and social sciences, and the physical sciences and engineering. A newsletter
provides additional information about the project.
The MAA'sJournal
of Online Mathematics and its Applications (JOMA) contains
peer-reviewed articles, class-tested, web-based learning materials, and
self-contained, dynamic, single-purpose learning tools. Many of these
illustrate a range of examples and applications and connections between
mathematics and other subjects. Some recent articles are Special
Relativity and Conic Sections, Designing Attribute Acceptance Sampling Plans,
and Art and Design in Mathematics.
DukeUniversity's
Connected Curriculum Project
collects and develops interactive learning materials for mathematics and its
applications, with applications to biology, chemistry, economics,
engineering, environmental sciences, epidemiology, and physics. Each
application is keyed to the level of mathematics used.
The MAA'sDigital Classroom Resources
provides a select collection of learning materials that are available without
charge through the site. These materials have been classroom tested and peer
reviewed. Many items in the library include editorial reviews and links to a
moderated discussion group focused on the materials.
The entry for the Consortium for Mathematics and Its Applications (COMAP)
in the bibliography contains additional information about incorporating
real-world applications into mathematics courses.
History
The MAA's online journal Convergence
is a new online magazine that provides resources to help teach mathematics
using its history. ReinhardLaubenbacher,
David Pengelley, Jerry Lodder,
and others at New MexicoStateUniversity
have developed a large collection
of instructional materials to teach mathematics using original historical
sources. Other books that link mathematical topics with their history
include William Dunham's Journey Through Genius: The Great Theorems of
Mathematics and The Calculus Gallery, Simon Singh's Fermat's
Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem
and The Code Book: The Science of Secrecy from Ancient Egypt to Quantum
Cryptography, Rudy Rucker'sInfinity
and the Mind: The Science and Philosophy of the Infinite, and Marcia Ascher'sEthnomathematics.
A Multicultural View of Mathematical Ideas. Judith Grabiner
of PitzerCollege developed two
general education courses with an emphasis on history: Mathematics,
Philosophy, and the 'Real World,' and Mathematics
in Many Cultures.
Art
In a note to Project NExT participants, Doris Schattschneider,
Moravian College, gave the following list of websites for courses linking
mathematics, art, and design:
* Survey course on mathematics in art
and architecture by Paul Calter at Dartmouth
College
* Course on Mathematics
in Art by HelmerAskalan
* Course in Mathematics
and Art by Marc Franz
* Jill Britton's website on Symmetry and
Tessellations, with annotated links to many other sites on these and related
topics
* Totally
Tessellated (can be accessed from Britton's site)
* A mini-site
on Escher's work and related math
* An exhibit
by artists whose work has been influenced by M.C. Escher featured at the
Escher Centennial Congress in Rome in 1998
* A website about harmony and
proportion by John Boyd-Brent, M.A, Royal College of Art
* This website,
related to a 'technical' paper by D. Schattschneider
and N. Dolbilin, has Java applets that allow users
to manipulate flexible tilings.
Most textbooks for general education mathematics
courses include sections that connect mathematics with other fields. For
instance, The
Heart of Mathematics: An invitation to effective thinking by Edward
B. Burger and Michael Starbird discusses the
mathematics of bar codes, cryptography, geometry and art, fractals and chaos,
and the likelihood of coincidences. A syllabus
for an interesting course that makes some use of this text is from Sarah
Greenwald, Appalachian State University. Another text, Using
and Understanding Mathematics by Jeffrey O. Bennett and William L.
Briggs, University of Colorado at Boulder, contains sections on financial
management, modeling a variety of real-world situations, mathematics and art,
mathematics and music, mathematics and politics, and mathematics and
business. See also the listings in this section under "Introduce Contemporary
Topics."
Introduce Contemporary Topics
Robert Devaney, BostonUniversity, is a leader
in promoting instruction in the contemporary topic of dynamical systems. In
addition to his books and articles, talks, and professional development
institutes, he has been director of the National Science Foundation's Dynamical Systems and Technology
Project since 1989. The goal of this project is to show students and
teachers how ideas from modern mathematics such as chaos, fractals, and
dynamics, together with modern technology, can be used effectively in the
high school and college curriculum.
The University of Maryland University College offers Mathematics
– Contemporary Topics and Applications as both an in-class and
distance-learning first-year course. The course is a survey of contemporary
topics in mathematics, centering on applications and projects. Topics include
measurements, rates of growth, basic statistics, the mathematics of political
power, the geometry of the solar system, and computer arithmetic. The goals
state that after completing this course a student should be able to cite
elements of good statistical design, undertake elementary statistical
analysis, and recognize and explain the shortcomings of unsound methods of
statistical analysis; mathematically analyze situations involving the
weighting of power in various voting structures and implement apportionment
of power strategies; and use the Pythagorean theorem and properties of
similar triangles to calculate sizes of and distance between objects,
including astronomical objects.
StetsonUniversity offers a wide variety of
courses that meet the general mathematics requirement, including many
that discuss contemporary topics such as chaos and fractals, game theory, and
cryptology.
Both of the popular texts For
All Practical Purposes, produced by the Consortium for Mathematics
and Its Applications, and Excursions
in Modern Mathematics by Peter Tannenbaum
and Robert Arnold aim to convey insight about topics in contemporary
mathematics and its applications to undergraduate students who have limited
mathematical backgrounds. Topics in these books include the mathematics of
voting, fair division, and apportionment, applications of graph theory to
management science, fractal geometry, and statistics.
At Mount Holyoke College George Cobb teaches a course on the Markov Chain
Monte Carlo method (MCMC), "a very general and powerful method for
computer simulation of situations that are too complicated to handle using
more conventional mathematical methods. MCMC has become a very active area of
research at the interface of computer science and statistics, and has had a
powerful impact on the practice of data analysis. As a method for computer
simulation, MCMC has very broad applicability. As a branch of mathematics,
MCMC offers a number of compelling surprises – structures that on a concrete
level seem quite different, but, viewed at the right level of abstraction, turn out to be different versions of the same
idea."
In the article "Geometric
Photo Manipulation" Tom Farmer shows how calculus and linear algebra can
be used to manipulate photographs, a contemporary application with which many
students have experience, thanks to currently available software.
G.H. Hardy once proudly asserted that number theory
would never be applied. Yet today number theory has a range of important
applications. Among these are cryptography (see, for example, lecture notes
from two cryptography
courses by Ed Schaefer at Santa Clara University, the RSA website,
and recent textbooks in number theory and discrete mathematics), and error
detection using check digits and error-correcting codes (see, for example, Numbers
and symmetry: An Introduction to Algebraby
Bernard L. Johnston and Fred Richman and Contemporary
Abstract Algebra by Joseph Gallian).
Enhance Perception of Vitality and
Importance of Mathematics
The World Wide Web provides a wealth of examples of the use and
applicability of mathematics, but searching for appropriate illustrations can
be time consuming. There are several sites that focus on providing good
examples for instructors: Plus,
an Internet magazine that aims to introduce readers to the beauty and the
practical applications of mathematics; Mathematical Moments,
an AMS program that offers a series of pdf files
and podcasts to promote appreciation and
understanding of the role mathematics plays in science, nature, technology,
and human culture; and the Math Forum,
a center that provides resources, materials, activities, person-to-person
interactions, and educational products and services to enrich and support the
teaching and learning of mathematics.
Chance
News is a monthly, on-line newsletter that provides abstracts of
articles from current newspapers, the media, and journals, and suggests
discussion questions for class use. It also includes links to related
resources at other web sites. Since 1992, Chance News has been
maintained by J. Laurie Snell of DartmouthCollege. The
examples are current and can be used for student motivation, for class
discussion, and as exercises in an introductory statistics course or
probability course. The website contains all issues of Chance News
as well as information on signing up for the newsletter by e-mail.
Additional Resources
Additional information and resources on communicating the breadth and
interconnections of the mathematical sciences are in Part 2, Section C.3. | 677.169 | 1 |
In this area we build the foundation of Algebra as we study the topic of Pre-Algebra. In this online math course, we will learn in detail about negative and positive numbers, exponents, order of operation, basic equations, and much more!
Section 1: Real Numbers and their Graphs
Section 2: The Number Line In this section, the concept of the number line is introduced and explained in detail. The concept of a negative number is illustrated by examples from everyday life and their relationship to positive numbers is shown on the number line. The student practices using the number line through numerous examples in this section, including basic addition and subtraction of integers. . . . View the lesson
Section 3: Greater Than, Less Than, Equal To In this section, the student learns how to properly use the greater than, less than, and equal to symbols in Pre-Algebra. Numerous problems illustrate how to compare positive or negative numbers with these symbols. The number line is used as a graphical reference to reinforce the concept. . . . View the lesson
Section 4: Adding Integers In this section, the student learns how to add two integers together and get the correct answer every time. Numerous examples of adding positive and negative numbers together are presented and by the end of the lesson the student will have memorized the simple rules for integer addition. The number line is also used to reinforce the concept. . . . View the lesson
Section 5: Subtracting Integers In this section, the student learns how to subtract two integers from one another and get the correct answer every time. Numerous examples of subtracting positive and negative numbers together are presented and by the end of the lesson the student will have memorized the simple rules for integer subtraction. The number line is also used to reinforce the concept. . . . View the lesson
Section 6: Multiplying Integers In this section, the student learns how to multiply two or more integers together. We begin the section by explaining the rules of integer multiplication. Next, we work numerous problems which give the student extra practice in multiplying negative and positive numbers together. . . . View the lesson
Section 7: Dividing Integers In this section, the student learns how to divide integers. We begin the section by explaining the rules of integer division. Next, we work numerous problems which give the student extra practice in dividing negative and positive numbers together. . . . View the lesson
Section 8: Powers and Exponents In this section, the student learns about the concept of an exponent and how it relates to pre-algebra. Numerous examples are provided to solidify this concept prior to moving on the the multiplication and division rule of terms that have exponents with the same base. . . . View the lesson
Section 9: Order of Operations In this section, the student learns about the concept of the order of operations in pre-algebra. This deals with understanding what order the student should perform calculations in an algebraic expression. . . . View the lesson
Section 10: Factors and Multiples In this section, the student learns how to calculate the factors of a number and the multiples of a number. These concepts will be central when we move into algebraic expressions later in this course. . . . View the lesson
Section 17: Adding Fractions In this section, the student will learn how to add fractions. We learn how to add regular fractions along with improper and mixed fractions and we learn to simplify the result. . . . View the lesson
Section 18: Subtracting Fractions In this section, the student will learn how to subtract fractions. We learn how to subtract regular fractions along with improper and mixed fractions and we learn to simplify the result. . . . View the lesson
Section 19: Multiplying Fractions In this section, the student will learn how to multiply fractions. We learn how to multiply regular fractions along with improper and mixed fractions and we learn to simplify the result. . . . View the lesson
Section 20: Dividing Fractions In this section, the student will learn how to divide fractions. We learn how to divide regular fractions along with improper and mixed fractions and we learn to simplify the result. . . . View the lesson | 677.169 | 1 |
The skills that students are practicing in related rates problems are:
Differentiating a known equation implicitly with respect to time.
Interpreting the time derivative of a quantity as a rate of change.
The main reason that related rates problems feel so contrived is that calculus books do not want to assume that the students are familiar with any of the equations of science or economics. Every related rates problem inherently involves differentiating a known equation, and the only equations that the calculus book assumes are the equations of geometry.
Thus, you can find related rates problems involving various area and volume formulas, related rates problems involving the Pythagorean Theorem or similar triangles, related rates problems involving triangle trigonometry, and so forth. A few of these problems are compelling -- for example, computing the speed of an airplane based on ground observations of its altitude and apparent angular velocity -- but most of them do feel a bit contrived.
The reality, of course, is that students are familiar with many of the basic equations and concepts of science and economics, and there's no rule against using these in problems. For example, you can make up all sorts of compelling related rates problems by starting with any physics or chemistry equation and imagining a situation where you might want to take its derivative:
The kinetic energy of an object is $K = \frac{1}{2}mv^2$. If the object is accelerating at a rate of $9.8 \text{m}/\text{s}^2$, how fast is the kinetic energy increasing when the speed is $30 \;\text{m}/\text{s}$?
An ideal gas satisfies $PV = nRT$, where $n$ is the number of moles and $R \approx 8.314\;\; \text{J}\; \text{mol}^{-1} \text{K}^{-1}$. Give the rate at which the temperature and volume of the gas are increasing, and then ask about the rate of change in pressure when the volume and temperature reach certain amounts.
The total energy stored in a capacitor is $\frac{1}{2} Q^2 / C$, where $Q$ is the amount of charge stored in the capacitor and $C$ is the capacitance. Give the value of $C$ and the rate at which $Q$ is decreasing, and ask about the rate at which the capacitor is losing energy when the energy is a certain amount.
In astronomy, the absolute magnitude $M$ of a star is related to its luminosity $L$ by the formula
$$
M \;=\; M_{\text{sun}} -\; 2.5\; \log_{10}(L/L_{\text{sun}}).
$$
where $M_{\text{sun}} = 4.75$ and $L_{\text{sun}} = 3.839 \times 10^{26} \text{watts}$. (Note that, by convention, brighter stars have lower magnitude.) If the absolute magnitude of a variable star is decreasing at a rate of $0.09 / \text{week}$, how quickly is the luminosity of the star increasing when the magnitude is $3.8$?
It's easy to make these up: just think of any equation in science or economics whose derivative might be interesting. Wikipedia and/or science textbooks can be helpful for finding equations from a wide variety of fields. | 677.169 | 1 |
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What's inside... Feature Math and Science Magnet Prepares Students for Algebra and Beyond What's New
Math and Science Magnet Prepares Students for Algebra and Beyond Algebra is an important foundation for building the critical thinking skills we need for solving everyday problems. Picture yourself at the local video rental store getting ready to pay for your selection. The clerk tells you that you have a choice of paying a $25 annual membership fee, plus $1.50 per rental, or paying no membership fee and $2.75 per rental. Would you have imagined that an understanding of algebra and linear equations could help you decide which is the better deal? Or perhaps you have a job offer that requires you to move across the country from Buffalo, N.Y. to San Francisco, Calif., but you would have to cover the cost of gas for approximately 2600 miles in a moving van. If the national average for gasoline is $3.25 per gallon, how much money would you need to save to cover the cost of the move? Would you have believed that when you learned to solve algebraic expressions it would help you find the answer to this unknown variable, too?
There is concern throughout the country that many American students lack the knowledge and skills necessary to succeed in algebra. Those students may not only have greater difficulty solving some of the "real world" problems listed above, but they also may need remedial course work in college and may have a lesser chance of becoming the next generation of American scientists, inventors, and engineers. And with research showing that students who complete Algebra II in high school are more than twice as likely than students with less mathematical preparation to earn a 4-year college degree, we must ensure that students are ready to tackle the more advanced mathematics courses in high school and beyond.
To compete in the 21st century global economy, proficiency in mathematics is crucial. To help ensure our nation's future competitiveness and economic viability, President George W. Bush created the National Mathematics Advisory Panel in April 2006. The Panel was charged with making recommendations on the best use of scientifically based research to advance the teaching and learning of mathematics. During the past two years, the Panel held meetings around the country, reviewed more than 16,000 research studies, received public testimony from 110 individuals, and considered written commentary from numerous organizations and individuals. In addition, the Math Panel conducted, in partnership with the National Opinion Research Center (NORC), a national survey of Algebra I teachers to determine what practices will best prepare American students to succeed in algebra. On March 13, 2008, the 24 expert panelists, including educators, cognitive psychologists, and leading mathematicians, released a report with actionable steps, containing 45 findings and recommendations on numerous topics. Some of these topics included instructional practices, materials, professional development for teachers, learning processes, assessments and research policies, and mechanisms. The report calls for students to attain a strong foundation in basic mathematical skills and for Americans to redefine how they view mathematics, shifting from a belief that particular people cannot learn mathematics to a belief that hard work and effort can pay dividends in achievement.
Some of the report's key findings include: 1.) there should be a systematic progression in mathematics curricula from pre-kindergarten through eighth grade with an emphasis on student mastery of each step; 2.) it is critical to understand and be able to work with fractions (including decimals, percents, and negative fractions), for such proficiency is foundational for algebra; 3.) it is crucial for students to demonstrate quick recall of computational facts if they are to be successful in mathematics; 4.) a student's effort in the learning process is an important factor to ensuring achievement; and 5.) teachers must have a strong understanding of mathematics both prior to and beyond the level they instruct, if students are to succeed.
The K J Clark Middle School of Mathematics, Science & Technology in Chickasaw, Ala., is a magnet school that provides a curriculum rich with many of these recommendations, and the school is producing impressive results for its students. Clark offers a rigorous and relevant mathematics curriculum with a multitude of hands-on activities to get students excited about learning. As the National Math Panel report recommends, the school's approach is systematic and emphasizes conceptual understanding, computational fluency, and problem-solving skills.
Under the leadership of Principal Dianne McWain, a 2007 U.S. Department of Education Terrell H. Bell award recipient, fourth through eighth grade students throughout the Mobile County are being prepared to succeed in mathematics and science in high school and beyond. McWain notes, "We accelerated learning a few years ago. Now our students are so much better prepared. We integrate mathematics into the curriculum everyday and in every class."
The mathematics program allows students to see what is important, according to Math Department Chair Julie Boren. For example, in one algebra class, the students work in groups as they tackle a question involving which one of three candidates won the school's student council election, and by how many votes. "They know we are not going to skip the word problems just because they are difficult. We meet challenges head-on," she said.
The school prepares students for algebra by providing a "core plus" curriculum. The "core plus" takes place in grades four through six, during which time the mathematics instructors teach the grade level county curriculum but add skills from the next grade level as well. By accelerating instruction, all seventh grade students are prepared for the foundations of algebra and all eighth grade students are taught Algebra I for high school credit. Clark also offers geometry for more advanced eighth graders. "We add skills in the sixth and seventh grade that students may need to ensure they take and pass Algebra I in eighth grade," said Boren.
Clark also offers an after-school tutoring program, an in-house tutoring program that removes students from their scheduled classes to obtain extra help, and one-on-one sessions during class with the teacher to ensure that all students, even those who are struggling initially, succeed in the rigorous math program. "It is critical that our students be competitive - it opens doors for them so they can take calculus and upper level math in high school," Boren asserts.
Student enrollment at Clark is determined by a lottery in which there are no academic requirements for admission other than passing the grade the student is in at the time of application. Students come to Clark from parochial or private schools and as many as 60 public elementary schools across the county. The students also arrive with very different backgrounds and levels of academic ability. Teachers work collaboratively to bridge the gap between students' initial levels of knowledge and experience and Clark's standards of proficiency required for promotion.
The U.S. Department of Education named Clark a No Child Left Behind (NCLB) Blue Ribbon School in 2007 in part because it is a high achieving school regardless of its student demographic. Although 58 percent of Clark's student population consists of those from disadvantaged backgrounds, all students have improved their performance on state assessments. Beginning in 2003, Clark began disaggregating information on student performance, in alignment with NCLB's accountability measures and focus on data to drive instruction. By looking at the data on student performance, Clark was able to identify subgroups of students that were not performing as well as the school average and implemented strategies detailed in its Title I School Improvement Plan to close the achievement gap. The data showed that the subgroups that needed more attention were their black students and students eligible for free and reduced-priced lunch. Clark faculty members worked diligently to address the educational needs of those students, and data from the 2006 SAT-10 and Alabama Reading and Mathematics Test (ARMT) showed the progress students had made; on those tests there was little difference between the scores of students in the "black" and "free and reduced-priced lunch" subgroups and students in any other subgroup. In some instances, students in the "free/reduced lunch" subgroup outperformed students in the "paid lunch" group and black students outperformed non-black students.
High-performing schools often share similar characteristics. For example, teachers work collaboratively; there are numerous opportunities for professional development; and data drives instruction and further assessment. All of these characteristics are present at Clark, where teachers use a hands-on approach to address the learning needs of all students. Most importantly, the school's faculty has high expectations, an approach that is paying off for teachers and students.
Teacher Knowledge Is Critical
Consistent with the Math Panel's recommendation that teachers must know in detail the mathematical content they are responsible for teaching and its connections to other important mathematics, Clark aims to increase its teachers' knowledge of math to positively influence student achievement. The district provides in-service training for teachers, and Clark's Math Chair Boren encourages her teachers to be active in professional organizations. Recently some teachers took an online course on differentiating learning strategies and used the strategies to help students use their strengths to master concepts. Clark also sends some teachers to conferences sponsored by the National Council of Teachers of Mathematics (NCTM). Those teachers share what they learn with others at departmental meetings. Principal McWain explains that opportunities for professional development abound at Clark. "We are always on the cutting edge. We try to think outside the box. We incorporate this into the curriculum by giving students new techniques and strategies to succeed. The teachers work cooperatively together-including rewriting and enhancing the curriculum."
Clark aims to increase their students' knowledge with each grade level. A good example of early work with the foundations of algebra is apparent in fourth grade when students study fractions. The fourth grade goal is to expose students to equivalent fractions and basic operations with fractions of like denominators. Some of the activities in the classroom might include making fraction bars and grids, and the elementary teachers use different colors with the bars and grids to help students "see" the fractions.
In fifth grade classes, students use operations with like and unlike denominators. Teachers also expose students to canceling when multiplying fractions and putting fractions in lowest terms. Operations with mixed numbers also are introduced, and by the end of fifth grade, teachers expect students to be proficient with operations with fractions of like denominators and to be able to find equivalent fractions. The sixth graders are expected to master these skills, in addition to changing fractions to decimals and then changing decimals to percents. In the "core plus" curriculum, teachers begin the process of teaching students to work with positive and negative fractions and mixed numbers early. In the seventh grade, students aim to master these skills.
Typical classrooms use a hands-on approach to help students understand key concepts. All of the teachers use games with fractions and white boards in the classroom to encourage students to be proficient. Sixth grade math teacher Angela Rocker said that her students enjoy "Fraction Face-Off," in which a small group of students will be given a fraction problem and race to get the correct answer. The winner of the game will face a new group of challengers. Students use white boards to check for understanding. All of the students in the class are required to do a specific problem and hold up their answer on the boards. According to Boren, "This is a quick way to make sure that all students are focused and understand how to complete the problem. Our students enjoy using these boards!"
Parents also see the advantage of Clark's approach to math. As one parent remarked, "My daughter doesn't even realize she's learning math. They integrate it throughout all the subjects and it's important because we can use it at home in real situations, like sewing skirts for our theater group and determining the circumference of the waists without a pattern. They also have everything a parent needs for the tools to help their child and for the child to work and get whatever they want in life."
U.S. Secretary of Education Margaret Spellings announced a new pilot program under No Child Left Behind (NCLB) aimed at helping states differentiate between underperforming schools in need of dramatic interventions and those that are closer to meeting the goals of NCLB. As part of the new pilot program, states that meet the four eligibility criteria may propose a differentiated accountability model. These eligibility criteria are based on the "bright line" principles of NCLB. (March 18)
During testimony before the U.S. House Committee on Education and Labor hearing on "Ensuring the Availability of Federal Student Loans," Secretary Margaret Spellings launched a new brochure, Federal Aid First, a resource for students and families that encourages them to maximize more affordable Federal student aid options before pursuing other options. To access the brochure and additional information about federal student aid, please visit (March 14)
Education Secretary Spellings announced the release of the final report of the National Mathematics Advisory Panel, and the findings were passed unanimously at the panel's meeting at Longfellow Middle School in Falls Church, Va. The panel reviewed the best available scientific evidence to advance the teaching and learning of mathematics and stressed the importance of effort, algebra, and early math education. (March 13)
Secretary Spellings joined Intel Chairman Craig Barrett to honor Intel Science Talent Search (STS) finalists. STS is America's oldest and most prestigious high school science competition. The top prize this year went to Shivani Sud of Durham, N.C, who developed a model that analyzed the specific "molecular signatures" of tumors from patients with Stage II colon cancer. She used this information to identify patients at higher risk for tumor recurrence and propose potentially effective drugs for treatment. (March 13)
Following a visit to Van Duyn Elementary School in Syracuse, N.Y., where Secretary Spellings highlighted progress toward NCLB goals in New York and across the nation, she joined Representative Jim Walsh (R-NY) and school officials at an education roundtable to discuss the state's accountability plan, standards, and assessments. She also discussed the new tool recently released by the Department known as Mapping New York's Educational Progress 2008. (March 10)
Continuing the dialogue on NCLB and priorities for 2008, Secretary Spellings convened an education roundtable at the West Virginia State Capitol Building with Congresswoman Shelley Moore Capito (R-WV), First Lady of West Virginia Gayle Manchin, West Virginia State Superintendent Steve Paine, and state education leaders and policymakers. She also visited Saint Albans High School in Saint Albans, W.V., and delivered remarks recognizing the progress of the school's students under NCLB. (March 7)
Secretary Spellings continued her national tour to discuss No Child Left Behind (NCLB) in North Carolina, where she addressed the North Carolina State Board of Education in Raleigh and discussed how the federal government can support and facilitate further academic gains made by the state's students under the law. She also participated in a roundtable with educators and school administrators. (March 5)
Secretary Spellings delivered remarks at the Reading First State Directors Conference and declared that with the help of the Reading First program, there have been dramatic gains in student and school achievement. She called on Congress to restore funding for the program to $1 billion, as requested in the President's fiscal year 2009 budget. (March 6)
The March edition of Education News Parents Can Use featured the work of the National Mathematics Advisory Panel and included a discussion about the Panel's final report and how its findings will lead to more effective math instruction in classrooms nationwide. The show also spotlighted what the Department and other key partners are doing to promote math and science literacy through the American Competitiveness Initiative and showcased the work of high-performing schools around the country that are excelling in math education and effectively implementing the Panel's recommendations. To find out more about the program, visit the Education News Parents Can Use Web site. The archived webcast of the show may be viewed online at (March 18)
Applications for the Teaching Ambassador Fellowship positions at the Department are due April 7, 2008. These positions offer highly motivated and innovative public school teachers the opportunity to contribute their knowledge and experience to the national dialogue on education. For more information go to the Teacher Fellowship Web site.
From the Office of Innovation and Improvement
The Full Service Community Schools (FSCS) Program is recruiting peer reviewers for its upcoming grant competition. This program encourages coordination of educational, developmental, family, health, and other services through partnerships between public elementary and secondary schools and community-based organizations and public or private entities. Grants are intended to provide comprehensive educational, social, and health services for students, families, and communities. To obtain additional information or to submit resumes, contact the program at FSCS@ed.gov, using the subject "Reviewer Information."
American History
Students at Henry E. Lackey High School in southern Maryland have developed one of the most comprehensive oral history projects of black life in the region. Students interviewed several of the region's oldest black residents and are creating an hour-long DVD that will be aired during Charles County's 350th anniversary celebration this summer. The project is one of several recent efforts to expand students' knowledge about the black population in Maryland's oldest counties. (March 6)
Elizabeth R. Varon, distinguished lecturer with the Organization of American Historians (OAH), writes in the OAH Newsletter about her experience visiting teachers who participate in the OII-funded Teaching American History (TAH) Program in Rockford, Ill. She notes, "The first thing that struck me was the dedication of the 60 or so teachers who were willing to give up their Saturdays… for a day of intensive collaboration." The Rockford Public School system is in its last year of a fiscal year 2004 TAH grant. (February 2008)
Arts Education
March is Arts in the Schools Month, and to bring attention to the importance of the arts in K-12, the American Association of School Administrators is putting the arts at "center stage" in its March edition of The School Administrator. Among the journal edition's features available to online readers are perspectives on the role of the arts in fostering innovation and the acquisition of skills needed in a knowledge-based economy, stories of schools and districts keeping the arts strong as part of leaving no child behind, and suggestions for policy leaders about the complete curriculum. (March 2008)
The Art of Collaboration: Promising Practices for Integrating the Arts and School ReformPDF (1.53 MB) is a new research and policy brief from the Arts Education Partnership. The brief describes promising practices for building community partnerships that integrate the arts into urban education systems. The publication resulted from a roundtable discussion among the directors of eight demonstration sites that are participating in The Ford Foundation's Integrating the Arts and Education Reform Initiative. (March 24)
Findings from studies by neuroscientists and psychologists at seven universities are helping scientists understand how arts instruction might improve general thinking skills. Learning, Arts, and the Brain, a Dana Consortium report on arts and cognition, does not provide definitive answers to the "arts-makes-you-smarter" question, but it does dispute the theory that students are either right- or left-brained learners. It also offers hints on how arts learning might relate to learning in other academic disciplines. (March 2008)
Charter Schools
Synergy Charter Academy in South Los Angeles was named Charter School of the Year at this year's California Charter School Conference. Caprice Young, former president of the Los Angeles Unified School Board who is now chief executive of the California Charter Schools Association, said, "[Synergy Charter] should be credited with not only closing the achievement gap, but eliminating it." The school was the highest-performing school in South Los Angeles in 2006 and 2007, and was named a National Charter School of the Year last year by the Center for Education Reform. (March 3)
Students in South Carolina might be interested in a new virtual charter school that will open this fall. South Carolina Connections Academy will be the state's first virtual charter school, and will enroll 500 students in its online K-12 program. Connections Academy, a company that runs schools enrolling 10,000 students in 14 other states, will manage the new school. (March 3)
The Center for Education Reform (CER), a Washington-based education reform advocacy group, recently ranked each state based on the strength of its charter school laws and found significant differences among the states. For example, Minnesota had the strongest charter laws in the country, while Mississippi had the weakest. Each state received a letter grade, "A" through "F," based on criteria developed by CER. (Feb. 13)
As charter schools across the nation gear up for lotteries, the National Alliance for Public Charter Schools is offering a free PDF (168 KB) "Charter School Lottery Day Tool Kit." Lottery days can present opportunities to: draw media attention to the demand for quality charters; create awareness among families of school choice, and create an opportunity for charters to communicate their success. Charter school staff can use the tool kit to create their own lottery day event. Materials on preparation, messaging, recruitment, media outreach, timelines, and costs are included. (February 2008)
Closing the Achievement Gap
Each year since the 2005 National Education Summit and the founding of the American Diploma Project (ADP) Network, Achieve has issued an annual report based on a 50-state survey of efforts to close the "expectations gap" between high school requirements and the demands of colleges and employers. Closing the Expectations Gap 2008 reveals that while a majority of states have made closing the expectations gap a priority, some states have moved much more aggressively than others. (February 2008)
Education Reform
Publicschoolinsights.org is a new online resource aimed at building a sense of community among individuals who are working at the local level to strengthen their public schools. The site also features a variety of success stories from U.S. schools and districts that have adopted effective strategies for addressing key challenges in education. (March 2008)
Mathematics and Science
Nearly three out of five U.S. teens (59 percent) do not believe their high school is preparing them adequately for careers in technology or engineering, according to the 2008 Lemelson-MIT Invention Index, an annual survey that gauges Americans' attitudes toward invention and innovation. The good news is that 72 percent believe technological inventions or innovations can solve some of the world's most pressing problems, such as global warming and water pollution. Sixty-four percent of those surveyed are confident that they could invent the solutions. (Jan. 16)
Raising Student Achievement
Fifty-nine exemplary middle schools across the country have been
named "Schools to Watch" as part of a recognition program developed by the National Forum to Accelerate Middle-Grades Reform. Each school was selected by state leaders for its academic excellence, responsiveness to the needs and interests of young learners, and commitment to helping all students achieve to high levels. In addition, each school has made a commitment to assessment and accountability to bring about continuous improvement, teachers who work collaboratively, and strong leadership. (March 14)
A nonprofit organization has launched a national campaign called "Ready by 21" that will work to help youth become better prepared for college, work, and life. Run by the Forum for Youth Investment, the initiative is intended to help state and local leaders improve education and social services during the first two decades of children's lives. The initiative urges leaders to work together on interrelated problems such as drug use, teenage pregnancy, and school dropouts. (March 2008)
Legislation under consideration in Maryland and many other states is intended to ease the transition for students whose parents serve in the military. These students change schools an average of six to nine times between kindergarten and 12th grade. A proposed PDF (341 KB) multi-state compact supported by the Pentagon is intended to reduce the complications involved with these school transfers. (March 2008)
California students who fail to earn a high school diploma before they turn 20 years old cost the state $46.4 billion over the course of their lives. Each year, about 120,000 students in the state drop out. The high cost associated with these dropouts is related to greater rates of unemployment, crime, and dependence upon welfare and state-funded medical care, as well as lost tax-revenues, according to a report from the California Dropout Research Project. (February 2008)
Teacher Quality and Development
Attrition would be lessened if schools offered new teachers more support and guidance, according to an Alliance for Excellent Education PDF (93.9 KB) issue brief. The report found that teachers who graduated from very selective colleges, or who had high SAT scores, were more likely to leave the teaching profession before retirement or transfer to higher-performing schools. (February 2008)
Charter Schools A mayoral change in Indianapolis, the only city nationwide in which the mayor's office authorizes charter schools, has not changed support for that city's 17 charter schools. The new mayor, Greg Ballard, voiced strong support for the charter movement created by his predecessor, Bart Peterson, at a recent conference of charter school leaders. The charter schools, according to Mayor Ballard, are in no danger, and they offer an important choice for parents and a way to improve education in the city.
[More—Indianapolis Star] (Feb. 22)
The proposition that teacher quality is a more important variable than class size and other factors will be put to the test next school year, when the Equity Project, a new charter middle school in New York City, is slated to open. Its creator and first principal, Zeke Vanderhoek, plans to pay the school's expected teachers $125,000 annually, plus potential bonuses based on school-wide achievement. Because that is nearly twice as much as the average teacher in the city earns, the experiment will no doubt garner more than just local attention. For their high salaries, Equity Project teachers will work a longer day and year and will accept some duties that fall to administrators in other schools.
[More—The New York Times] (March 7) (free registration required)
Mathematics and Science Two members of the USA Today's 2007 All-USA Teacher Team find ways to inspire their high school students in economics and mathematics. An economics teacher at the California Academy of Math and Science, where many students are the children of Asian or Hispanic immigrants, taps into students' creativity. The teacher uses techniques such as student playwriting to illustrate economic principles to semester-long assignments in which students develop a proposed start-up company. In College Park, Ga., at Benjamin Banneker High School, 63 percent of students are eligible for free- or reduced-priced meals, and many students already have children of their own or wear ankle bracelets that allow law enforcement officials to monitor their movements. It is at this school that one teacher has inspired his students to learn advanced mathematics and use education as a tool to improve their lives. The school's pass rate on the state graduation exam has jumped from 85 percent to 95 percent between 2005 and 2006.
[More—USA Today] (Feb. 25) and [USA Today] (March 3)
In search of answers to the question of why students in Scandinavia scored high on the latest Program for International Student Assessment (PISA), a U.S. delegation led by the Consortium for School Networking (CoSN) toured Finland, Sweden, and Denmark, where educators cited "autonomy, project-based learning, and nationwide broadband Internet access as keys to their success."
[More—ESchool News] (March 3)
Achievement in mathematics and science, rather than more general barometers of education attainments, are critical to the international economic performance of the U.S., according to a new study by professors at Stanford and the University of Munich. Reported in the spring issue of Education Next, the research supports the conclusion that "if the U.S performed on par with the world's leaders in science and math, it would add about two-thirds of a percentage point to the gross domestic product."
[More— Wall Street Journal] (March 3)
Interest in an international robotics competition among Minneapolis schools and the community's technology sector has flourished over the past two years, from two student teams competing in 2006 to 54 teams this year. For Inspiration and Recognition of Science and Technology (FIRST) is a catalyst for both public and private investments in science and technology programs in high schools, not only in Minneapolis, but across the state of Minnesota. Driving the investment among such private-sector contributors as Medtronic, Boston Scientific, and the 3M Foundation is a desire to encourage future engineers. The Minnesota Department of Education has increased its funding for science, technology, engineering, and mathematics (STEM) initiatives statewide as well, providing more than $4 million to school districts between 2006 and 2008.
[More—Minneapolis Star-Tribune] (March 4)
Raising Student Achievement An analysis of recently released College Board data on Advanced Placement tests by Education Week found that while more students are taking the exams, the "percentage of exams that received [the passing score of at least] a three…has slipped from about 60 percent to 57 percent." College Board spokesperson Jennifer Topiel, while noting that test scores often decline with increases in the number of test takers, observed, "Students should not be placed into AP classes without better preparation." The analysis also revealed a widening gap over the past four years between black and white students earning at least a three on the exams.
[More—Education Week] (Feb. 14) (paid subscription required)
First-year results of a federally supported study of two reading interventions for struggling adolescent readers indicate increases in proficiency, but not enough to get students to grade level in a single year. Research firm MDRC conducted the study of the Reading Apprenticeship Academic Literacy and Xtreme Reading programs, with support from the U.S. Department of Education's Institute of Education Science. It is the first of three reports under the Enhanced Reading Opportunities Study. Researchers plan to follow the 9th grade students involved in the two interventions through 11th grade.
[More—Education Week] (Feb. 14) (paid subscription required)
A majority of American parents believe that their children have the "right amount" of homework, according to the findings of a poll commissioned by MetLife. Parents, teachers, and students were surveyed concerning time spent on homework as well as the perceived value of it. Clear majorities of both students (77 percent) and teachers (80 percent) said homework is important or very important. In addition, three quarters of the more than 2,000 K-12 students surveyed reported that they had adequate time to complete their assignments.
[More—Education Week] (Feb. 15) (paid subscription required)
More than 10,000 preschool-aged youngsters in Dallas are expected to benefit from a city-sponsored early reading preparation program that is modeled on Ready to Read. With support from an $8 million grant from the Wallace Foundation, the Dallas Public Library will manage the "Every Child Ready to Read @ Dallas" program, which will focus on parents, teachers, day-care providers, and others in the city who work with young children. In announcing the new program, Dallas Mayor Tom Leppert said, "Everything revolves around reading," and indicated the city's annual costs for the new program will be less than $600,000, with the Wallace Foundation grant helping for the next three years.
[More—The Dallas Morning News] (Feb. 22)
Researchers from the Centers for Disease Control and Prevention (CDC) believe that physical education may be linked to academic achievement. This belief is based on a national study of students' reading and mathematics test scores and the students' degree of involvement in physical education between kindergarten and fifth grade. According to the CDC researchers, the connection was most notable for girls receiving the highest levels of physical education (more than 70 minutes per week), who scored consistently higher on the tests than those who received less than 35 minutes a week in physical education. The study is available online in the Journal of American Public Health.
[More—USA Today] (March 5)
School Improvement Standards for school leaders, originally drafted in the mid-1990s and used or adapted by more than 40 states, have been revisited and revised by a panel of experts convened by the National Policy Board for Educational Administration and managed by the Council of Chief State School Officers. The revised Interstate School Leaders Licensure Consortium (ISLLC) standards, which guide the preparation, licensure and evaluation of principals and superintendents, were approved last December. The two-year revision process was supported by the Wallace Foundation, which made the investment, according to its director of education programs, because "there's a lot more known now from the research in terms of understanding what leaders do to impact teaching and learning…"
[More—Education Week] (Feb. 27) (paid subscription required)
A $5 million grant from the Michael & Susan Dell Foundation will enable Dallas educators to have instant access to students' academic records from preschool through high school graduation. The plans for an eventual mega-database of student academic information and other related data will begin with a planned "data warehouse" pilot phase next school year. The new system will provide a "one-stop shop" for local educators and help the Dallas Independent School District with its goal of spotting weaknesses in academic performance under its Dallas Achieves reform plan.
[More—The Dallas Morning News] (Feb. 27)
Houston will have its first public Montessori middle school thanks to the perseverance of the parents of Wilson Elementary, an elementary school currently based on the instructional approach pioneered by Maria Montessori more than a century ago. Parents raised more than $345,000 over five years to expand the current school to grades seven and eight. The 25 seats in the school's inaugural seventh grade will be open to students from several public and private Montessori elementary schools in the area.
[More—The Houston Chronicle] (Feb. 27)
Pay-for-performance initiatives continue to attract the attention of local and national press. The National Center on Performance Incentives released its study of the Texas Educator Excellence Grant program, the largest merit-pay plan in the nation. Texas education department officials were reportedly pleased with the first year's results and the study's findings. An examination of The Teacher Advancement Program (TAP), launched six years ago by the Milken Foundation and with 180 participating schools nationwide produced uneven results, with TAP elementary schools doing better than comparison schools in test-score gains, but those at the middle and high school levels lagging behind their non-TAP counterparts.
[More— The Dallas Morning News] (Feb. 29) [Education Week] (March 3) (paid subscription required)
For more than two decades, Project STAR, a study of class size in Tennessee, has informed thinking about the policy issue of class-size reduction. Now, a Northwestern University professor's review of the study's data is questioning whether there is evidence that reducing class size reduces achievement gaps between groups of students. According to the study's author, the longitudinal data provides weak or no evidence that lower-performing students benefited more than others from small classes.
[More—The Washington Post] (March 10) (free registration required) and [Education Week] (Feb. 21) (paid subscription required)
Teacher Quality and Development Can a single set of standards for accrediting teacher-education institutions be developed? This is the question that a new task force of the American Association of Colleges of Teacher Education (AACTE) will seek to answer this spring. Task force members include representatives of the two national accrediting entities – the longstanding National Council for Accreditation of Teacher Education (NCATE) and the relatively new Teacher Education Accreditation Council (TEAC). While the two entities take very different approaches to granting their seals of approval, AACTE's board of directors is hopeful that the task force can agree on a single set of standards.
[More—Education Week] (Feb. 21) (paid subscription required)
The burgeoning field of online learning has launched its first voluntary national standards that will help policymakers and practitioners judge the credibility and worthiness of virtual teaching and online course work. Released last month by the North American Council for Online Learning, the standards address such topics as teacher prerequisites and licensure, technology skills, and subject matter proficiency, as well as instructional issues like online interaction, intellectual property rights, and learning assessments and program evaluations.
[More—Education Week (Feb. 29) (paid subscription required) | 677.169 | 1 |
Be sure to read
the Mathematics Department Policies. There
is some very important
information there (such as our policies on exams, what to do if you
cannot come to class, etc.)
Make sure you
include your name, contact information, etc. on the syllabus above.
You can implement your own homework policies, statements on
classroom behaviors, dropping a score, grading standards, etc. Be sure to review the
entire document before you print and distribute it to your class.
Please send your syllabus
to saburo.matsumoto@canyons.edu
prior to the beginning of the semester. Also, use this address to
send your exams. Any questions/concerns should be addressed there as
well.
Unlike some
other coordinated courses, there is no common final in this course. You
write (and grade) your own final examination.
Below are some
specific guidelines. Please contact me in advance if you deviate
significantly from these.
Here are
the department guidelines regarding tests:
No take-home
exams
No Scantron (machine-gradable) exams
No notes for exams
No make-up exams are recommended. (You can either drop the lowest
test score or replace it with the final exam's score).
You
should also outline the method you use to assign grades. Students should
have a clear understanding of how their grade is calculated. It is
suggested you use the following scale. Let x be the student's overall
percentage.
Grade
if
A
x is at least 90%
B
x is in [80%, 90%)
C
x is in [70%, 80%)
D
x is in [60%, 70%)
F
x is in [0%, 60%)
The
syllabus must
contain student learning outcomes (SLOs). You can find them in the
sample syllabus above. The SLOs will be used as a measure of what our
students are learning in each class. We have started to assess SLOs in
all classes.
If you
need any books or supplementary materials, contact me. If you are not
planning to teach this course again next semester, please return your
books and materials to me before the break. | 677.169 | 1 |
8th Grade Algebra I - Mrs. Loch
Welcome to my website which is designed to inform you of the procedures, events, and learning activities for the 2012-2013 school year.
My name is Mrs. Loch and I am the Math teacher for the 8th grade Red Team.
This year 8th grade students will gain knowledge in the areas of number sense, geometry, expressions and equations, functions, statistics and probability. This course introduces students to the fundamentals of algebraic concepts. Students will begin to explore patterns, relations, and functions. They will learn to represent and analyze mathematical situations using algebraic symbols and graphing in preparation for high school. The course will emphasize problem-solving strategies and incorporate applications to real world situations while aiding students in becoming 21st century learners.
This year we will be utilizing the "Flipped Classroom" concept. Students will watch instructional videos at home at their own pace. Class time will be spent communicating with peers and the teacher in discussions about the video, completing practice problems related to the topic, and doing interactive activities to illustrate the concept. For more information regarding the "Flipped Classroom," see "What is the Flipped Classroom?" in the document section to the right.
For valuable information regarding algebra class, assignments, or to see what we have coming up in class, please view the content below or the links listed in the "classroom pages" section to the right. | 677.169 | 1 |
Excellent resource for the class! I like your style and I'm interested in your products and store! I'm your new follower! You can visit my store and leave a comment if you wish! hugs and Happy Easter! Hernan
This lesson is the introduction to a unit on Functions for Algebra 2 Honors students. The lesson is taught at the beginning of the school year when students may not be quite prepared for the rigor of Algebra 2 Honors. It is just a general review of the basic vocabulary that will be needed throughout the unit. While we may think the lesson is touching only at the surface, students continue to struggle throughout the school year with domain, range, and function notation.
It is interesting to discuss the ideas of continous domains and discrete domains for Example #3 and the idea that function notation indicates the coordinate. Both of these ideas are introduced to students in this textbook here and the understanding continues to grow through the next two courses. I would be glad to send you another lesson for your dissatisfaction. Contact me at jean.adams@ocps.net
no, you can teach the lesson by just placing the Foldable under a document camera. I use a wireless slate and the smart notebook software. This way I can use the lesson repeatedly and write on the smart lesson fresh each class. I believe there are other ways that smart software can display. possibly with an iPad and splashtop software. you might ask a tech person in your school.
May 21, 2013
Julie Larsen re: ALG 2 UNIT: Sequences and Series FOLDABLES ONLY
The quality of the notes is great. My big question is...how do I tell which is page 1, 2, 3, etc. It seems essential in order to copy the pages correctly to make the foldable. I can figure some out based on the example numbers, however, is the Arithmetic Sequences with the vocab page 1, 2, etc. What page number is the Arithmetic sequences with the formulas?
The foldable was created in order. If your printer copies on two sides, you can choose to flip them on the short side and they copy double sided in the correct order. The vocabulary is always the first or front page and the side with the blank sheet on the third page of the document will be the last sheet or page 8 on the foldable. My students glue this blank page into their composition books to save them in order of their textbook lessons. In this particular lesson, the formulas appear on the 5th page of the foldable. If you need more assistance, you can email me at jean@j-adams.com
You might think this is a crazy question, but I am trying to figure out something. On problem B, which has 2Z + B = ____, if you only have say 6 brown or Z M&M's, how are you showing the 2 times Z with the M&M's? My husband and myself are both math teachers and we are trying to use this lesson as a dynamic lesson in an 8th grade math classroom. We love the idea. Thank you! my email is acawood@roaneschools.com or avols845@hotmail.com
Amy, If I understand your question correctly, I think you mean since Z=Brown M&M's and B=Blue M&M's if you have 6 brown the question in the B prompt has two equations 2Z + B = ___ and Z-B = ____.
Students would write 2Z + B = 6 and Z-B=6.
Now, say that the students bag had only 3 blue M&M's, and had 6 brown M&M's. Their system would now read2Z+B=9 and Z-B=3. When students use substitution method or elimination method, they will get Z=6 and B=3 for the answer if their algebra is correct. Hope this helps.
Yes, each lesson has a full answer key. Whether you purchase the single lesson or the set of handouts only or Smartboard Lessons only, each has the answer key provided.
April 7, 2013
mhilvert
I recently bought the Families of Functions Foldable book and am having a hard time figuring out how to put it together correctly. Do you have any suggestions? Everytime I put it together the 'summary of transformations' page is between #5/6 and #7/8?
Thanks
I have uploaded a more detailed assembly directions for you which shows the layout for printing. You can see this free document at Foldable Assembly Directions.
If you still have trouble, please let me know. Thanks.
My colleague and I bought this unit but we are having a hard time with the foldables. I've created this type of booklet before. I tried to create yours several times but the pages are all out of order. The question I have is about the copies. Is there a certain way these need to be copied?
Yes, the copies should be double sided. If you have a printer that prints on both sides of the paper, you can choose to flip the paper on the short side to create the proper order. If you print the four pages single-sided and us a copy machine, orient the pages so that page 1 and page 3 are up and pages 2 and 4 are down. I will send you a snapshot personally, if you will send me your email address. I'm sorry you are having difficulty. pre-calculus and calculus threeThat's a good question. I use Smart Notebook 11 software to write my lessons for display. They are shared with my students through a projector but I use an wireless slate in order to teach the lessons "Live" to my students. The smart file that I sell is a blank document. You need to have the ability to work the problems on some wireless writing tablet. There are many that are compatible with Smart Technology products. I don't believe just a projector will work for this product. You can purchase the foldables only for this unit and write on that document under your document camera to display through the projector. If this is confusing, ask an "IT" person at your school. Unless you have a wireless tablet it would waste your money.
Thanks,
Jean Adams
Hi Chris,
Thanks for the vote on my clean writing style. Yes, I do sell the whole Quadratics Unit as a set. You can purchase the Foldables only at or Smart Notes only, as well.
My students buy a small composition book at the beginning of the school year. The last page of each Foldable is blank so they apply glue and glue them into their book each day. I have some students who work their homework after each lesson in the composition book. They use two books each year in that case. Then, I have some students who store their lessons in a Gallon-Sized Zip-Lock Bag. I really see "ownership" in what they do by the way they protect each document and never want me to skip any example.
Hi Amy,
Yes they will. I've got three more to finish. Hopefully, today. There are nine in all. I got behind with Thanksgiving and Christmas. Sorry. I know you are waiting. I'm working on them now.
Thanks for your loyalty.
Jean
Yes, it should include 5 documents, a cover page, the foldable as a PDF file, the Final notes as a PDF File, the SmartBoard Lesson, and direction for making the foldable. I'll repost the files for you. Sorry for the inconvenience.
Thanks for letting me know.
Jean Adams
Is it intended that the section of student notes on Extrema on an Interval is missing some information and examples that are in the filled in teacher version? The other units I have purchased matched up exactly to one another...
I'll check into that for you. Thanks for the watchful eye.
Jean
Yes Amy, Actually my students had a difficult time with this idea last year. They forgot to check the endpoints, so we went back to the notes, revisited the procedure, thought about a few "What if" situations, and I just left that in the presentation to give a little extra while we talked and taught the lesson. So it is intentional.
November 26, 2012
mkesselman re: Blank Unit Circle Small
You have an extra degree symbol at both 90 degrees and at 270 degrees.
Two questions: The file '4 Real Zeros of Polynomial Functions Cover.pdf' is generating an error message from Adobe that the file is damaged and cannot be repaired.
What program is needed to open the file with the 'notebook' extension? Is this a SmartBoard file?
Yes, the *.PDF file was corrupt. I have uploaded a version that should work now. Please let me know if it doesn't.
The notebook extension is a SmartNotebook 11 document. You can open with a Smart Notebook 11 software, and I believe it is compatible with Prometheus products also. I personally use my presentation files only with the Smart Airliner Wireless slate.
No, I don't. I have a Smart Airliner Wireless Slate. It costs about $200 and allows me to walk around my room. I actually had an older model of SmartBoard and gave it up when the Wireless slate came out about 3 years ago. I love it. I'm no longer tied to the front of the classroom. Even my students can write on the slate from their seats. The software SMART NOTEBOOK 11 is a separate item, I write the lessons with that software and use the slate to teach the lesson.
Jean,
I cannot get the Using Linear Models flipchart to open, the PDF's will open, and I have no problem opeining any other flipcharts. Is there any way you can email me the flipchart, my email is Gingerduckett@yahoo.com.
Thanks.
Amy,
I have the whole year available, but I'm currently uploading one unit at a time. There are seven total units. My future plans are to offer the entire year as a bundle, but that is in the future. I'm glad that you like my lessons and appreciate your positive feedback. I will definitely offer the entire year at a reduced price, just not sure what that will be at the present time.
Jean
Hi Layla,
When we have open house, I use a quick lesson on making a foldable with my parents then I have them take notes on the foldable about our class, their students needs, and where to go for help. They leave with a product in hand on how to contact me, my website info, where to find tutoring, and what calculator needs their student will have.
Jean
November 4, 2012
vwasmuth re: CALCULUS DIFFERENTIATION UNIT: Lesson 7 Related Rates
I have downloaded "related rates" but as I tried to extract it , a black window appeared with an error message . I updated my adobe reader. It looked for adobe air, so I updated it, but it could not continue due to an apparent error.
Hunter, I have a test with most of those items that I can share with you. It covers the entire chapter from the Larson PreCalculus text if that would interest you. Email me: jean@j-adams.com
February 4, 2012
TEACHING EXPERIENCE
Jean has taught grades 8 through 12 for over 18 years in the Central Florida area. In addition she shares her strategies with colleagues through local and national math conferences.
MY TEACHING STYLE
Jean is known for her energetic, hands-on strategies that engage students to learn cooperatively. There is always something new happening in her classroom.
HONORS/AWARDS/SHINING TEACHER MOMENT
1998-Teacher of the Year at Thomas Jefferson Junior High, Merritt Island, FL.; 2001-Teacher of the Year at George Jenkins High School, Lakeland, FL.; 2001-AIChE Mathematics Teacher of the Year,Polk County, FL.; National Board Certified Teacher, Adolescent Young Adult Mathematics,2001.2009-2010 Math Teacher of the Year, Orange County Public Schools
Jean Adams teaches AP Calculus AB, Pre-Calculus, Trigonometry,and Analytic Geometry in the Metro-Orlando area. She is the owner an eduational website with instructional lessons and teacher resources for Algebra and higher ( Jean is an active teacher-trainer when opportunities arise. | 677.169 | 1 |
Calculus (non-AP*)
This comprehensive text introduces calculus to a wide variety of students with three initial chapters of precalculus, followed by an accessible component of first-semester calculus.
Two primary objectives guided the writing of this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus, and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and saves the teacher time.
Calculus I with Precalculus features an in-depth, systematic study of each basic class of functions—algebraic, exponential and logarithmic, and trigonometric—along with nearly 10,000 carefully graded exercises that progress from skill-development to more rigorous problems involving applications and proofs.
Titles marked with asterisk (*) indicate product is restricted from sale to individuals and may only be purchased by a registered institution. Go here if you are not already logged in or need to register. | 677.169 | 1 |
Basic Algebra, Like Terms, Add and Subtract Expressions Part 1
This class is intended for the novice student who wants to learn algebra beginning with the basis. This video will teach you how to learn three basic components of beginning algebra.This class will teach: Definitions, Collecting Like Terms, and Adding and Subtracting Algebraic Expressions. | 677.169 | 1 |
Presenting worked examples and solutions leading to practice questions, this helps students to learn maths. It features sample past exam papers for exam preparation, and includes regular review sections. It includes a CD ROM which contains what students need to motivate and prepare themselves.
Synopsis:
Edexcel and A Level Modular Mathematics C4 features: *Student-friendly worked examples and solutions, leading up to a wealth of practice questions. *Sample exam papers for thorough exam preparation. *Regular review sections consolidate learning. *Opportunities for stretch and challenge presented throughout the course. *'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. *Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. *Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary | 677.169 | 1 |
Globalshiksha has come up with LearnNext Jharkhand Board Class 8 CDs for Maths and Science. Included lessons with syllabuses are in audio and visual format, solved examples, practice workout, experiments, tests and many more related to Jharkhand Board Class 8 Maths and Science. It also include a various set of visual tools and activities on each Lesson with Examples, Experiments, Summary and workout. You can understand all the concepts well, clear all doubts with ease through this Educational CD and get score in the exams.
This multimedia comes with a useful Exam Preparation like Lesson tests usually 20-30 minutes in duration, which will help you to evaluate the understanding of each lesson and Model tests usually 150-180 minutes in duration, which cover the whole subject on the lines of final exam pattern. This package can help you to sharpen your preparation for final exams, identify your strengths and weaknesses and know answers to all tests with a thorough explanation, overcome exam fear and get well scores in final exams. | 677.169 | 1 |
In this Unit we deal with trigonometric identities. These identities are particularly useful in doing the algebra of trigonometry. In this application of the identities complex expressions are simplified and converted into different equivalent forms. This algebraic nature of trigonometry is taught at secondary school level, not only as a stepping stone towards further tertiary studies, which may require some form of trigonometry knowledge, but also as a tool to develop learners' logical reasoning.
Often learners don't know how to start to prove an identity without any hint, even if they know every trigonometric formula. In this unit we will explore some general ideas to prove an identity, and in doing so provide an opportunity for you to pass this on to your learners, in order to improve their mathematics problem solving skills.
The usual approach to identities is the memorisation of the basic identities with little or no reference to the graphical meaning of the identities. The learners are then expected to be able to substitute and manipulate to prove given more complex identities. In this module we will try to give some graphical interpretation of the use of identities. | 677.169 | 1 |
Description
Using and Understanding Mathematics: A Quantitative Reasoning Approach, Fifth Edition increases students' mathematical literacy so that they better understand the mathematics used in their daily lives, and can use math effectively to make better decisions every day. Contents are organized with that in mind, with engaging coverage in sections like Taking Control of Your Finances, Dividing the Political Pie, and a full chapter about Mathematics and the Arts.
This Fifth Edition offers new hands-on Activities for use with students in class, new ways for students to check their understanding through Quick Quizzes, and a new question type in MyMathLab that applies math to excerpts from recent news articles. In addition, the authors increase their coverage of consumer math, and provide a stronger emphasis on technology through new Using Technology features and exercises. The new Insider's Guideprovides instructors with tips and ideas for effective use of the text in teaching the course.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
Preface
Prologue: Literacy for the Modern World
Part 1 Logic and Problem Solving
Chapter 1 Thinking Critically
1A Recognizing Fallacies
1B Propositions and Truth Values
1C Sets and Venn Diagrams
1D Analyzing Arguments
1E Critical Thinking in Everyday Life
Chapter 2 Approaches to Problem Solving
2A The Problem-Solving Power of Units
2B Standardized Units: More Problem-Solving Power
2C Problem-Solving Guidelines and Hints
Part 2 Quantitative Information in Everyday Life
Chapter 3 Numbers in the Real World
3A Uses and Abuses of Percentages
3B Putting Numbers in Perspective
3C Dealing with Uncertainty
3D Index Numbers: The CPI and Beyond
3E How Numbers Deceive: Polygraphs, Mammograms, and More
Chapter 4 Managing Money
4A Taking Control of Your Finances
4B The Power of Compounding
4C Savings Plans and Investments
4D Loan Payments, Credit Cards, and Mortgages
4E Income Taxes
4F Understanding the Federal Budget
Part 3 Probability and Statistics
Chapter 5 Statistical Reasoning
5A Fundamentals of Statistics
5B Should You Believe a Statistical Study?
5C Statistical Tables and Graphs
5D Graphics in the Media
5E Correlation and Causality
Chapter 6 Putting Statistics to Work
6A Characterizing Data
6B Measures of Variation
6C The Normal Distribution
6D Statistical Inference
Chapter 7 Probability: Living with the Odds
7A Fundamentals of Probability
7B Combining Probabilities
7C The Law of Large Numbers
7D Assessing Risk
7E Counting and Probability
Part 4 Modeling
Chapter 8 Exponential Astonishment
8A Growth: Linear versus Exponential
8B Doubling Time and Half-Life
8C Real Population Growth
8D Logarithmic Scales: Earthquakes, Sounds, and Acids
Chapter 9 Modeling Our World
9A Functions: The Building Blocks of Mathematical Models
9B Linear Modeling
9C Exponential Modeling
Chapter 10 Modeling with Geometry
10A Fundamentals of Geometry
10B Problem Solving with Geometry
10C Fractal Geometry
Part 5 Further Applications
Chapter 11 Mathematics and the Arts
11A Mathematics and Music
11B Perspective and Symmetry
11C Proportion and the Golden Ratio
Chapter 12 Mathematics and Politics
12A Voting: Does the Majority Always Rule?
12B Theory of Voting
12C Apportionment: The House of Representatives and Beyond
12D Dividing the Political Pie
Credits
Answers | 677.169 | 1 |
Description: Five class periods. Not open for credit to students who have passed MATH 1010(110), or any Q course. Strongly recommended as preparation for Q courses for students whose high school algebra needs reinforcement.
The course emphasizes two components necessary for success in 1000-level courses which employ mathematics. The first component consists of basic algebraic notions and their manipulations. The second component consists of the practice of solving multi-step problems from other disciplines, called mathematical modeling. The topics include: lines, systems of equations, polynomials, rational expressions, exponential and logarithmic functions. Students will engage in group projects in mathematical modeling. Offered: Fall Spring Credits: 3
These are the most recent data in the math department database for Math 1011Q in Storrs Campus.
There could be more recent data on our class schedules page, where you can also check for sections at other campuses. | 677.169 | 1 |
Mathematics
The Mathematics curriculum is structured to best address the broad needs of students. All courses are designed for students who learn best in an applied approach. The department advances five major goals for students:
Learn to value mathematics as a tool to explore relationships between mathematics and the many disciplines it serves.
Gain confidence in using mathematical power to make sense of new problem situations and the world we live in.
Develop ability in solving problem situations independently and in a cooperative group setting.
Given opportunities to read, write and discuss ideas, use the signs, symbols and terms of mathematics.
Gather evidence, make conjectures, develop and support rationale using mathematical reasoning.
The Mathematics department also applies the six guiding Principles of the Massachusetts Curriculum Frameworks:
Guiding Principle 1: Learning
Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of understanding.
Guiding Principle 2: Teaching
An effective mathematics program is based on a carefully designed set of content standards that are clear and specific, focused, and articulated over time as a coherent sequence.
Guiding Principle 3: Technology
Technology is an essential tool that should be used strategically in mathematics education.
Guiding Principle 4: Equity
All students should have a high quality mathematics program that prepares them for college and a career.
Guiding Principle 5: Literacy Across the Content Areas
An effective mathematics program builds upon and develops students' literacy skills and knowledge.
Guiding Principle 6: Assessment
Assessment of student learning in mathematics should take many forms to inform instruction and learning.
Students are required to successfully complete the objectives of six credits of mathematics coursework but may elect up to eight credits. Aspects of mathematics that emphasize real-life situations are integrated regularly throughout all the mathematics courses. All courses are college preparatory and fully address the goals and objectives of the Massachusetts Curriculum Frameworks.
The Honors mathematics pathway moves from Algebra II to Geometry to Advanced Algebra and Pre Calculus with senior year expectation of Calculus. Additional electives are available dependent upon student career plans. The majority of students follows a college preparatory pathway beginning with Algebra I but may elect Honors-level courses.
The need for technological proficiency is recognized at all levels and in all courses. Students are encouraged and trained to use calculators to speed arithmetic calculations, for advanced analysis, and to explore relationships and concepts, visualize solutions and promote hypothetical modeling of real-life situations. Additional methods utilizing computer software for exploration and analysis are also employed in all courses. | 677.169 | 1 |
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics courses, on the other hand, emphasize a particular guiding principle for all mathematical inquiry, namely the "algorithmic viewpoint." Discrete mathematics emphasizes mathematical induction and proofs, while finite mathematics avoids proofs and emphasizes applications and intuitive understanding. Because of this, finite mathematics is a terminal math course for many students, whereas discrete mathematics is an introductory course for its constituency. In spite of differences, courses in discrete and finite mathematics have similar prerequisites and cover a number of the same topics. The main difference between the two is the clientele served. Discrete mathematics courses serve mainly computer science students, and finite mathematics courses serve students from commerce and social science backgrounds. Therefore, and unfortunately, finite mathematics courses tend to be less rigorous. Given that mathematical expectations are rising for students in business and social sciences, a common course merging discrete and finite mathematics should be developed. A chart showing the overlap in the content of finite and discrete mathematics textbooks is attached. (AYC)
Abstractor:
N/A
Reference Count:
N/A
Note:
Paper presented at the Annual Meeting of the American Mathematical Association for Two-Year Colleges (Baltimore, MD, October 25-29, 1989). | 677.169 | 1 |
During this webinar Maplesoft will present a number of examples of mathematics in film. See relevant, exciting examples that you can use to engage your students. Have you ever wondered if the bus could really have jumped the gap in "Speed?" We've got the answer! Anyone with an interest in mathematics, especially high school and early college math educators, will be both entertained and informed by attending this webinar. At the end of the webinar you'll be given an opportunity to download an application containing all of the Hollywood examples that we demonstrate.
This webinar, presented by Dr. Robert Lopez, Maple Fellow and Emeritus Professor from the Rose-Hulman Institute of Technology, will provide you with tips and techniques that will help you get started with Maple 17.
With an intuitive multidomain modeling environment and powerful multibody modeling technology, Maplesoft's suite of modeling and simulation tools are uniquely suited to developing mechatronic systems, including such diverse applications as robotics, guidance systems, active stabilizers, vibration attenuators, and "X-by-wire" systems found in road vehicles and aircraft. In this webinar, learn how to quickly create multi-link robots by simply defining DH parameters in MapleSim. After a model is created, learn to extract the kinematic and dynamic equations symbolically in Maple. Examples will be presented where inverse kinematic problems will be solved both symbolically and using optimization techniques. | 677.169 | 1 |
Secondary Curricula
Carnegie Learning Geometry incorporates the van Hiele model of Geometric thought; a theory that describes how students learn geometry. Our curriculum will enable students to develop a deep understanding of Geometry. The course assumes number fluency and basic algebra skills such as equation solving. Carnegie Learning Geometry is aligned to NCTM and Achieve standards. It is designed to be taken after an algebra course and can be implemented with students at a variety of ability and grade levels.
Please use the tabs below to learn more about the features and contents of this curricula and its various implementation options. Use the content browser on the left to view videos and image galleries of the new enhancements.
Tools of Geometry
Parallel & Perpendicular Lines
Area & Perimeter
Triangles
Similarity
Congruence
Right Triangle Trigonometry
Quadrilaterals
Geometry in the Coordinate Plane
Simple Transformations
Circles
Volume & Surface Area
Three Dimensional Figures & Extensions
Vectors
Features of our Textbooks
Research-based
Designed for a collaborative, student-centered classroom
The classroom environment promotes discourse, collaborative work and depth of understanding
Students engage in problem solving, communication and reasoning while making connections using multiple representations
Students take ownership of their learning, making notes using their texts like a workbook
Recommended for 40% (or two class periods/week) of the total instructional time in a course, the software is most often accessed via a web delivery model using the Carnegie Learning Online website. It can be delivered via a standalone installation, network/LAN, or remote-hosted local client-server model.
Our Geometry content can be delivered in a blended course format, with a combination of collaborative, student-centered textbook lessons and adaptive Cognitive Tutor software lessons. Can be used as core instruction.
Carnegie Learning Geometry content can be delivered via textbooks that support a collaborative classroom. Our classroom activities address both mathematical content and process standards. Students develop skills to work cooperatively to solve problems and improve their reasoning and communication skills.
Our Geometry content is available in our Adaptive Math Software Solutions, which are packages that feature our research-based Cognitive Tutor Software product line. Available in both the Carnegie Learning Adaptive High School Solution and the Carnegie Learning Adaptive Secondary Math Solution.
Webinars
...this is hands-down the best academic program I've ever used. The students are developing some hard-core problem solving abilities, way beyond my wildest dreams. The students feel successful, and recognize that the program forces them to look at concepts in a way that they've never encountered before. | 677.169 | 1 |
How about giving some more details of what precisely is your difficulty with excel polynomial roots? This would assist in finding out ways to look for a solution. Finding a teacher these days fast enough and that too at a price that you can afford can be a frustrating task. On the other hand, these days there are programs that are offered to help you with your math problems. All you have to do is to choose the most suitable one. With just a click the right answer pops up. Not only this, it helps you to arriving at the answer. This way you also get to learn to get at the right answer.
You all must be pulling my leg! How could this not be common knowledge or published here? Where can I obtain additional information for testing Algebra Buster? Forgive someone for appearing to be a bit doubtful, but do you know if someone can acquire a test version to apply this program?
Algebra Buster is a very simple product and is surely worth a try. You will also find many exciting stuff there. I use it as reference software for my math problems and can say that it has made learning math much more enjoyable. | 677.169 | 1 |
Honestly, I doubt you'd find math major level learning sites for Number Theory. But if you like you could take a look at Elementary Number theory by Jones and Jones. Its a SUMS springer book, so it has solutions at the back for every problem. Maybe after something like that you could read Tom Apostols Introduction to Analytic Number Theory.
Your description of "basic knowledge of number theory" is a little bit vague. It would be easier to recommend books/sites if we know more about your background.
This probably isn't what you're after but here's a link to some "cute" stuff in Number Theory | 677.169 | 1 |
Why Study Maths?
A Mathematics qualification beyond GCSE is always highly regarded by university admissions tutors and by employers. In fact there are some courses at university which require you to have Mathematics at AS or A2.
We offer a wide variety of Mathematics courses:
AS and A2 Further Mathematics
AS and A2 Mathematics
AS use of Mathematics
GCSE Mathematics and Level 1/Level 2 Adult Numeracy
AS and A2 Statistics
AS Mathematics supports many other subjects but especially Physics and Computing.
You choose which applied modules to study as part of AS/A2 Mathematics. i.e. Statistics, Mechanics or Decision Mathematics.
The "problem solving" aspect of Mathematics is very satisfying especially when you turn to the back of the textbook and find you've got the right answer!
Your tutors are well qualified and committed to ensuring that you do well. There are regular workshops staffed by teachers where extra help is available.
Which Maths should I choose? Statistics links with Economics, Business Studies, Biology, Geography, Journalism, Psychology, Medicine, Pharmacy, Law and Education.
Use of Maths is useful if you need Maths to support other
subjects such as Physics, Chemistry, Electronics and Computing.
Further Maths is useful for careers in Maths,
Engineering and Computer Science.
AS and A2 Statistics is useful if you want to develop the skills needed to work with data, but don't want to do lots of traditional maths like algebra. AS and A2 Statistics links well with subjects like Biology, Business, Sociology and Pyschology.
The UK Senior Maths Challenge
This is open to any of our AS and A2 level Maths students. It is designed to stimulate mental agility and mathematical reasoning and the paper consists of 25 puzzles with multiple choice answers. Gold, silver and bronze certificates are awarded to many participants, with the most successful being invited to the British Mathematical Olympiad. | 677.169 | 1 |
Mathematics 1152
Calculus II
Credit hours: 5 GEC categories: Quant reason math and logical analysis Prerequisites:
Course Objectives: To provide students with a solid foundation in calculus (integration, sequences and series, Taylor series, vector and parametric curves, and polar curves). Problem solving will be emphasized throughout the course to promote a deeper understanding of the theory of calculus and its applications. | 677.169 | 1 |
Algebra 1
Description
An outstanding text that presents mathematics as a study of absolutes with a logical approach from one concept to another. Concepts are developed and mastered through an abundance of worked examples and student exercises. Many application problems relate algebra to the physical world | 677.169 | 1 |
Pre-Algebra Solved! 20.10.0009
Bridge the gap between basic math and algebra with Pre-Algebra Solved!®, the smart way to ace your homework and get better grades. Simply enter in your homework problems and Pre-Algebra Solved!
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Bridge the gap between basic math and algebra with Pre-Algebra Solved!®, the smart way to ace your homework and get better grades. Simply enter in your homework problems and Pre-Algebra Solved!® does the rest, providing the solution with step-by-step explanations. With additional powerful features including infinite example problems, practice tests, progress tracking, and a math document designer, Pre-Algebra Solved!® is the only pre-algebra solution you need. As an added bonus, Pre-Algebra Solved!® includes a FREE tutoring session with a live pre-algebra tutor at Tutor.com - the world's #1 online tutoring company
Speedstudy Pre Algebra improve grades and test scores. Multimedia learning system makes even the toughest math concepts come alive. Great for new learners or students studying for college entrance exams Build pre-algebra skills fast!
Algebra Vision is a piece of algebra educational software. About half of students learning algebra have difficulty making the conceptual leap from arithmetic. Algebra Vision helps students by presenting algebra in a more tangible light.
The Personal Algebra Tutor is a comprehensive algebra problem solver for solving algebra problems from basic math through college algebra and preCalculus. The user can enter his/her own problems to get step-by-step solutions. | 677.169 | 1 |
Calculator - We suggest that you
purchase a graphing calculator for this course.You may use a TI-83, TI-83 Plus, TI-84, TI-84
Plus, or TI-Nspire(non-CAS).You
may not use the TI-89, TI-92, or
TI-Voyage.We will have 4 function calculators available
for you to use in class when needed.
Pencils, Paper, Rulers, and Graph
Paper - graded work must be done in pencil.Work in pen will not be graded.
Topics Covered:In this course, students will: analyze
polynomial functions of higher degree; explore logarithmic functions as
inverses of exponential functions; solve a variety of equations and
inequalities numerically, algebraically, and graphically; use matrices and
linear programming to represent and solve problems; use matrices to represent
and solve problems involving vertex-edge graphs; investigate the relationships
between lines and circles; recognize, analyze, and graph the equations of conic
sections; investigate planes and spheres; solve problems by interpreting a
normal distribution as a probability distribution; and design and conduct
experimental and observational studies.
Homework: Homework will be assigned every day and checked
the next day, either for completeness or accuracy.ANSWERS BY MAGIC (no work shown or steps
skipped) WILL NOT RECEIVE CREDIT. You
also WILL NOT RECEIVE CREDIT if your work does not represent the material on
the assignment.
Quizzes, Tests: There will be at least one quiz and one test in each unit. Preparation for these assessments includes
doing your homework assignments and practicing problems from the unit and
previous units.
Final Exam: This is a comprehensive test for this semester
only.It will contain problems similar
to those found on your quizzes and tests.A good recommendation would be to keep all graded papers in your
notebook so you have a good review for the exam.
Make-up work: MAKE-UP WORK IS YOUR RESPONSIBILITY!!!!
Any missed handouts can be found
in the "I was absent!" bin in the front of the room. Any additional missed
assignments or notes can be obtained from a classmate. For an excused absence,
you will have the same amount of time as you missed to complete makeup work. If
a test or quiz is missed, you will need to arrange a time to take the test or
quiz. An unexcused absence will result in a 10% reduction for any work graded
that day.
Tag, Field Trips, TDE, etc.:The student is responsible forwork
missed.Since these are prearranged, you
must have your assignment on the normal due date.
Tardies: Students late to class are required to sign in.The following disciplinary consequences will
result:
Ø1
to 2 tardies – teacher warning
Ø3rd
tardy – teacher detention
ØMore
than 3 tardies – office referral
Recovery:According
to Fulton County's policy, opportunities designed to allow students to recover
from a low or failing cumulative grade (below 74) will be allowed when all work
to date has been completed and the student has shown a legitimate effort to
meet all course requirements (completion of ALL homework, good attendance,
seeking extra help from the teacher, etc.). You should contact the teacher
concerning recovery opportunities and a time for recovery work will be
established.All recovery work will be
directly related to course objectives and must be completed ten school days
prior to the end of the semester.
Honor Code: Please read the Honor Code of RHS in your agenda
book.Academic dishonesty will not be
tolerated in this class.
Extra Help:I
encourage you to come in for extra help! I am available Monday-Thursday from
8:00-8:25am unless I have another scheduled meeting. If necessary, we can set up
another time to meet.
NOTE:If you need help in
this class, please come for extra help! Keeping up with the material is very
important.Don't wait until it is too late to ask for help!
Average:Your grade
will be averaged by the following:
Homework, Daily Classwork = 15%
Quizzes/Tasks = 20%
Chapter Tests/ Projects = 50%
Semester Exam = 15%
Student Expectations:The student is expected to adhere to the following rules:
**We reserve the
right to change these policies as the year progresses, if they do not work out
as expected.
PARENTS:
Please sign and fill out the information below and return this page with your
student. If you prefer, you may send me an email letting me know you received
and understand this syllabus. Thanks!
WISH LIST: If
you are able, the following supplies are needed: AAA batteries, hand sanitizer,
tissues, and colored paper | 677.169 | 1 |
Scientific Computing
Scientific computing studies the world around us. Known and unknown quantities are related through certain rules, e.g. physical laws, formulating mathematical problems. These problems are solved by numerical methods implemented as algorithms and run on computers. The numerical methods are analyzed and their performance (e.g. accuracy, efficiency) studied. Problems, such as choosing the optimal shape for an airplane (to achieve, for example, minimal fuel consumption), finding the fair price for derivative products of the market, or regulating the amount of radiation in medical scans, can be modelled by mathematical expressions, and solved by numerical techniques.
Students wishing to study scientific computing should have a strong background in mathematics, in particular calculus of several variables, linear algebra and statistics, be fluent in programming, and have a good understanding of data structures and algorithm design. | 677.169 | 1 |
Description
Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included.
The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse-Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions.
The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.
From the reviews:
"This is a book which many mathematicians could enjoy browsing, and one which a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparently disparate parts of mathematics."
--Canadian Mathematical Society
"As a source for information on the 'reach' of number theory into other areas of mathematics, it is an excellent work."Number Theory: An Introduction to Mathematics (.PDFNumber Theory: An Introduction to Mathematics (.PDFNumber Theory: An Introduction to Mathematics (.PDF | 677.169 | 1 |
Elementary Linear Algebra
9780131871410
ISBN:
0131871412
Edition: 2 Pub Date: 2007 Publisher: Prentice Hall
Summary: "Elementary Linear Algebra, 2/e" -- Lawrence Spence, Arnold Insel, and Stephen Friedberg Embracing the recommendations of the "Linear Algebra Curriculum Study Group, the authors have written a text that" students will find both accessible and enlightening. Written for a matrix-oriented course, students from a variety of disciplines can expect a greater understanding of the concepts of linear algebra. Starting with ma...trices, vectors, and systems of linear equations, the authors move towards more advanced material, including linear independence, subspaces, and bases. The authors also encourage the use of technology, either computer software (MATLAB) or super-calculators, freeing students from tedious computations so they are better able to focus on the conceptual understanding of linear algebra. Lastly, students will find a variety of applications to engage their interest, demonstrated via economics, traffic flow, anthropology, Google searches, computer graphics, or music to name a few. By leveraging technology and incorporating engaging examples and numerous practice problems and exercises, this text best serves the needs of students attempting to master linear algebra.[read more0131871412 ALMOST BRAND NEW. NEVER USED. We are a tested and proven company with over 700, 000 satisfied customers since 1997. Choose expedited shipping (if available) for mu [more]
0131871412 ALMOST BRAND NEW. NEVER USED | 677.169 | 1 |
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing... more...
A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed... more...
The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and... more...
Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization... more...
Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce... more...
A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts. more...
Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which... more... | 677.169 | 1 |
This is a supplement to reinforce understanding of mathematical physics concepts. Contains problems that bring physics to life by relating it to daily experiences. The chapters are divided into two or more topic sections, each with its own Solved Examples and Practice Exercises. | 677.169 | 1 |
Maths
Why Should I Study This Subject?
There are many reasons why people choose to study A Level Mathematics. It might be a requirement for what you want to study at university. Since maths is one of the most traditional subjects a good grade in maths can boost an application for almost every course! Studies have also shown that people with Maths A Level also tend to earn more on average than people without it. Though this itself may or may not be a good enough reason to study maths, the skills it allows you to develop include problem solving, logic and analysing situations. Add in the improvements to your basic numeracy skills and that bit of creativity needed to solve maths problems and you've got yourself a set of skills which would make you more desirable for almost any job! Finally, you might also really like maths - this is as good a reason as any to continue studying it. If you study something you enjoy you are likely to do better at it. With maths there is the excitement of new discoveries you will make. You will see more of the beauty of it and realise just how much everything in the universe is connected to mathematics.
The bottom line is, maths is an amazing subject to have at A Level and provided you have a solid understanding of the GCSE concepts before you start, alongside some perseverance and effort, you should be able to do well.
What Will I Study?
Year 1: Core 1, Core 2 & either Mechanics 1 or Statistics 1 or Decision 1
Year 2: Core 3, Core 4 & either Mechanics 1 or Statistics 1 or Decision 1 or Mechanics 2 or Statistics 2
How Will it be Assessed?
Each of the modules is assessed by an exam only.
Exam Board
Edexcel, for further details:
What Can I do Next?
Many university courses such as physics, psychology, economics, computing, engineering and business studies prefer students to have A Level maths if possible. Having A level maths is a great signal to any employer that you can think logically, work hard and have a great level of numerical skill.
What Grades Will I Need?
8 GCSE grades A*- C. Students are required to have at least an A grade at GCSE to study maths at A Level. | 677.169 | 1 |
Course Overview
About Self-Directed Courses
In a self-directed course, you can start and stop whenever you like, progressing entirely at your own pace and going back as many times as you want to review the material.
Explore more than half a dozen of the most important math tools that journalists encounter — and have fun doing it.
This course covers everything from reducing fractions and other math essentials to topics specifically for journalists, such as calculating costs of living and estimating crowd sizes. The goal is to make routine math routine.
Along the way, you'll find a range of resources to give you additional learning support. Quizzes, activities, interactive activities and games — complete with high-score boards — offer fun ways to learn the math basics that every journalist needs to know.
What Will I Learn:
Upon completing this course, you will be able to:
List the terms, syntax and rules for performing calculations necessary for math proficiency
Work with fractions
Perform arithmetic more accurately and efficiently
Find help – both on and off the Web
Calculate a percentage and recognize the subtle differences between percent change, percent of total and percentage points vs. percent
Calculate means, medians and modes, and know when it's best to use each as a measure of "average"
Compare numbers more meaningfully by creating ratios, ranks and rates
Understand the basic approaches to and pitfalls of calculating cost of living, weighted averages and crowd estimates
Who should take this course:
Anyone who wants to get better at the routine math every journalist needs when writing or editing a story, covering an event or creating infographics. If you don't know how to calculate a crowd estimate or don't know the difference between percentage points and percents, this course is for you. | 677.169 | 1 |
Course
4 Unit 7 - Functions and Symbolic Reasoning 1st Edition
In Course 4, the
mathematical strands in the Contemporary Mathematics in Context
program become increasingly blended within units. The content of this
unit is from both the algebra and functions strand and the geometry and
trigonometry strand. (See the descriptions of Course
4 Units.)
Unit Overview
Functions and
Symbolic Reasoning extends student ability to manipulate symbolic
representations of exponential, common and natural logarithmic, and trigonometric
functions and to solve exponential, logarithmic, and trigonometric equations.
Trigonometric identities are developed and proved or disproved. Geometric
representations of complex numbers are used to reason about and to find
roots of complex numbers.
Unit Objectives
To use properties of exponents to transform exponential expressions
into equivalent exponential expressions
To solve exponential equations
To use relationships between logarithms and exponentials to
write logarithmic equations in forms without logarithms
To know and be able to use the definitions of the six trigonometric
functions of angles in standard position
To know and be able to use the fundamental trigonometric identities
To prove a statement of equality is an identity
To solve trigonometric equations
To represent complex numbers geometrically
To interpret multiplication of complex numbers geometrically
To use DeMoivre's Theorem to find all the roots of a complex
number
Sample Overview
There are two different
samples from Functions and Symbolic Reasoning. The first sample
consists of Investigations 1 and 2 from Lesson 2, "Reasoning with Trigonometric
Functions." These investigations introduce the cosecant, secant, and
cotangent functions and begin work with trigonometric identities.
The second sample
is the "Looking Back" lesson for this unit. This lesson is intended to
provide students with tasks that will encourage them to look back at the
unit as a whole. Students review, synthesize, and apply the knowledge
gained during the study of the unit.
Instructional
Design
Throughout the curriculum,
interesting problem contexts serve as the foundation for instruction.
As lessons unfold around these problem situations, classroom instruction
tends to follow a common pattern as elaborated under Instructional
Design.
Contact
Adobe with any technical questions
about their software or its installation.
How the Algebra
and Functions Strand Continues
Algebraic representations
of surfaces and conic sections are introduced in Unit 8, Space
Geometry.
A unit from the algebra and functions strand that develops understanding
and skill in the use of standard spreadsheet operations while reviewing
and extending many of the basic algebra topics from Courses 1-3 is recommended
for students intending to pursue college programs in social, management,
and some of the health sciences or humanities. | 677.169 | 1 |
Course starts out easy and then suddenly gets difficult. The math isn't too tough but there are a LOT of formulas to memorize. We didn't need the book at all for the class as we used StatsPortal (a service you need to purchase) but that has an ebook on it. | 677.169 | 1 |
Students will develop reasoning and problem solving skills as they study topics such as congruence and similarity, and apply properties of lines, triangles, quadrilaterals, and circles. Students will also develop problem solving skills by using length, perimeter, area circumference, surface area, and volume to solve real-world problems.
ALGEBRA 1
RGL: 9
PRE: Completion of Algebra A & B with a grade of C- or better
In this course the student will learn some of the basic operations needed to transform and solve equations involving one or more unknown quantities. The study of geometry is included with a focus on the concepts of area and volume.
ALGEBRA II
RGL: 9
PRE: Completion of Algebra 1 with a grade of a C- or better
A study of more advanced algebraic concepts with an introduction to the fundamental trigonometric ratios. Geometric figures and their properties are introduced as are deductive reasoning and proof.
ALGEBRAA
PRE: successful completion of 8th grade math
RGL: 9-12
Algebra ½ is the first class of a two year Algebra 1 program. Students will explore the following topics: algebraic equations, expressions, and functions, rational numbers, linear equations, proportions, graphing relations, analyzing linear equations, and inequalities. A scientific calculator is recommended.
ALGEBRA B
RGL:
PRE: Completion of Algebra A
This is the second part of the two year Algebra 1 program. Students will begin with a review of concepts from the previous class. New explorations include: statistics, probability, systems of linear equations, graphic solutions, multiplication, division, and factoring of polynomial expressions, Pythagorean Thermos, and operations with rational expressions and equations.
PRE CALCULUS-INDEPENDENT STUDY (Honors Class)
RGL: 12
PRE: consent with Instructor
Students who wish to pursue degrees in the sciences or engineering may want to consider completing Algebra II and Geometry in their junior year so they would be able to take calculus in their senior year. Taking calculus will provide students with an advantage on the ACT and SAT tests and on college mathematics placement exams. | 677.169 | 1 |
From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience. contents
Preface
Diagnostic Pretest
0. Prealgebra Review
0.1 Simplifying Fractions
0.2 Adding and Subtracting Fractions
0.3 Multiplying and Dividing Fractions
0.4 Using Decimals
How Am I Doing? Sections 0.1–0.4
0.5 Percents, Rounding, and Estimating
0.6 Using the Mathematics Blueprint for Problem Solving
Use Math to Save Money
Chapter 0 Organizer
Chapter 0 Review Problems
How Am I Doing? Chapter 0 Test
Math Coach
1. Real Numbers and Variables
1.1 Adding Real Numbers
1.2 Subtracting Real Numbers
1.3 Multiplying and Dividing Real Numbers
1.4 Exponents
1.5 The Order of Operations
How Am I Doing? Sections 1.1–1.5
1.6 Using the Distributive Property to Simplify Algebraic Expressions
1.7 Combining Like Terms
1.8 Using Substitution to Evaluate Algebraic Expressions and Formulas
1.9 Grouping Symbols
Use Math to Save Money
Chapter 1 Organizer
Chapter 1 Review Problems
How Am I Doing? Chapter 1 Test
Math Coach
2. Equations, Inequalities, and Applications
2.1 The Addition Principle of Equality
2.2 The Multiplication Principle of Equality
2.3 Using the Addition and Multiplication Principles Together
2.4 Solving Equations with Fractions
How Am I Doing? Sections 2.1–2.4
2.5 Translating English Phrases into Algebraic Expressions
2.6 Using Equations to Solve Word Problems
2.7 Solving Word Problems: The Value of Money and Percents
2.8 Solving Inequalities in One Variable
Use Math to Save Money
Chapter 2 Organizer
Chapter 2 Review Problems
How Am I Doing? Chapter 2 Test
Math Coach
3. Graphing and Functions
3.1 The Rectangular Coordinate System
3.2 Graphing Linear Equations
3.3 The Slope of a Line
How Am I Doing? Sections 3.1–3.3
3.4 Writing the Equation of a Line
3.5 Graphing Linear Inequalities
3.6 Functions
Use Math to Save Money
Chapter 3 Organizer
Chapter 3 Review Problems
How Am I Doing? Chapter 3 Test
Math Coach
Cumulative Test for Chapters 0–3
4. Systems of Linear Equations and Inequalities
4.1 Systems of Linear Equations in Two Variables
4.2 Systems of Linear Equations in Three Variables
How Am I Doing? Sections 4.1-4.2
4.3 Applications of Systems of Linear Equations
4.4 Systems of Linear Inequalities
Use Math to Save Money
Chapter 4 Organizer
Chapter 4 Review Problems
How Am I Doing? Chapter 4 Test
Math Coach
5. Exponents and Polynomials
5.1 The Rules of Exponents
5.2 Negative Exponents and Scientific Notation
5.3 Fundamental Polynomial Operations
How Am I Doing? Sections 5.1–5.3
5.4 Multiplying Polynomials
5.5 Multiplication: Special Cases
5.6 Dividing Polynomials
Use Math to Save Money
Chapter 5 Organizer
Chapter 5 Review Problems
How Am I Doing? Chapter 5 Test
Math Coach
6. Factoring
6.1 Removing a Common Factor
6.2 Factoring by Grouping
6.3 Factoring Trinomials of the Form x2 + bx + c
6.4 Factoring Trinomials of the Form ax2 + bx + c
How Am I Doing? Sections 6.1–6.4
6.5 Special Cases of Factoring
6.6 A Brief Review of Factoring
6.7 Solving Quadratic Equations by Factoring
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Chapter 6 Organizer
Chapter 6 Review Problems
How Am I Doing? Chapter 6 Test
Math Coach
Cumulative Test for Chapters 0–6
7. Rational Expressions and Equations
7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions
How Am I Doing? Sections 7.1–7.3
7.4 Simplifying Complex Rational Expressions
7.5 Solving Equations Involving Rational Expressions
7.6 Ratio, Proportion, and Other Applied Problems
Use Math to Save Money
Chapter 7 Organizer
Chapter 7 Review Problems
How Am I Doing? Chapter 7 Test
Math Coach
8. Rational Exponents and Radicals
8.1 Rational Exponents
8.2 Radical Expressions and Functions
8.3 Simplifying, Adding, and Subtracting Radicals
8.4 Multiplying and Dividing Radicals
How Am I Doing? Sections 8.1—8.4
8.5 Radical Equations
8.6 Complex Numbers
8.7 Variation
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Chapter 8 Organizer
Chapter 8 Review Problems
How Am I Doing? Chapter 8 Test
Math Coach
9. Quadratic Equations and Inequalities
9.1 Quadratic Equations
9.2 The Quadratic Formula and Solutions to Quadratic Equations
9.3 Equations That Can Be Transformed into Quadratic Form
How Am I Doing? Sections 9.1—9.3
9.4 Formulas and Applications
9.5 Quadratic Functions
9.6 Compound and Quadratic Inequalities in One Variable
9.7 Absolute Value Equations and Inequalities
Use Math to Save Money
Chapter 9 Organizer
Chapter 9 Review Problems
How Am I Doing? Chapter 9 Test
Math Coach
Cumulative Test for Chapters 0-9
10. The Conic Sections
10.1 The Distance Formula and the Circle
10.2 The Parabola
10.3 The Ellipse
How Am I Doing? Sections 10.1—10.3
10.4 The Hyperbola
10.5 Nonlinear Systems of Equations
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Chapter 10 Organizer
Chapter 10 Review Problems
How Am I Doing? Chapter 10 Test
Math Coach
11. Additional Properties of Functions
11.1 Function Notation
11.2 General Graphing Procedures for Functions
How Am I Doing? Sections 11.1—11.2
11.3 Algebraic Operations on Functions
11.4 Inverse of a Function
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Chapter 11 Organizer
Chapter 11 Review Problems
How Am I Doing? Chapter 11 Test
Math Coach
12. Logarithmic and Exponential Functions
12.1 The Exponential Function
12.2 The Logarithmic Function
12.3 Properties of Logarithms
How Am I Doing? Sections 12.1—12.3
12.4 Common Logarithms, Natural Logarithms, and Change of Base of Logarithms
12.5 Exponential and Logarithmic Equations
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Chapter 12 Organizer
Chapter 12 Review Problems
How Am I Doing? Chapter 12 Test
Math Coach
Practice Final Examination
Appendix A: Foundations for Intermediate Algebra: A Transition from Beginning to Intermediate
Appendix B: Practice with Operations of Whole Numbers
Appendix C: Tables
Appendix D: Determinants and Cramer's Rule
Appendix E: Solving Systems of Linear Equations Using Matrices
Appendix F: Sets
Solutions to Practice Problems
Answers to Selected Exercises
Glossary
Applications Index (Available in MyMathLab)
Index
Photo Credits
New to this edition
New and Updated Features
The end-of-chapter material has been further enhanced to provide more alsoUse Math to Save Money features practical, realistic examples in every chapter of how students can use math to cut costs and spend less. The topics discussed in Use Math to Save Money have been updated based on a student survey of more than 1,000 developmental math college students.
Steps to Success (formerly called "Develop Your Study Skills") has been updated and expanded to provide students with more guided techniques for improving their study skills and succeeding in math.
New Instructor and Student Resources
Worksheets with the Math Coach tie the complete learning package together, providing extra vocabulary and practice exercises for every section of the text. Every chapter also includes the Math Coach Problems from the book and videos so students can follow along, and have plenty of space to show their work.
The Lectures Series on DVDfeaturing Math Coach and Chapter Test Prep Videos has been completely revised to provide students with extra help for each section of the textbook. The videos include:
A new interface allows easy navigation to objectives and key examples and exercises.
The new Math Coach Videos give students an office hour with the authors! In these videos, the authors expand upon the end-of-chapter Math Coach materials that are in the text and coach students on how to avoid commonly made mistakes.
Chapter Test Prep Videos provide step-by-step video solutions to every problem in each "How Am I Doing?" Chapter Test in the textbook.
Chapter Test Prep Videos and Math Coach Videos are available in MyMathLab and on YouTube™.
New to MyMathLabPre-made (and pre-assigned in the Ready to Go course) "How Am I Doing?" mid-chapter review homework that lets students pause at critical junctures to make sure they are "getting it."
Pre-made chapter review quizzes that are pre-assigned in the Ready to Go course and generate personalized homework assignments based on students' quiz results.
A Pre-made (and pre-assigned in the Ready to Go Course) pre- and post- test for every chapter.
A new Stepped-OutConcept Check Questions exercise style that guides students through solutions, helping them understand not only the steps involved, but the reasoning behind them.
Pre-made (and pre-assigned in the Ready to Go course) Math Coach Homework for every chapter that uses the stepped-out concept check approach to coach students before the test to the areas where mistakes are most commonly made and show them how to avoid these pitfalls.
Use Math to Save Money Animations are assignable and offer an interactive way for students to use the math they are learning to cut costs and spend less.
All videos from the Lecture Series on DVD with Math Coach and Chapter Test Prep Videos.
Content Updates
Section 0.6: Using the Mathematics Blueprint for Problem Solving has been added to Chapter 0.
The presentation of topics in Chapter 2 has been refined, including the addition of Section 2.7: Solving Word Problems: The Value of Money and Percents
Updates to Chapter 3 include the introduction of a new Graphing Organizer. This organizer summarizes the graphing methods presented in the chapter and notes the advantages and disadvantages of each. The objective of finding the slopes of parallel and perpendicular lines has been relocated to Section 3.4.
Features & benefits
Students will find many opportunities to check and reinforce their understanding of concepts throughout each chapter:
Student Practice problems are paired with every example in the text. The full solutions to each practice problem are located in the back of the text, allowing students to check their work as they go.
The "How Am I Doing?" mid-chapter review exercises let students pause at a critical juncture to make sure they are "getting it."
End-of-Section Exercises progress from basic to challenging, and each exercise set includes Verbal and Writing Skills, and Mixed Practice exercises.
A Quick Quiz at the end of each exercise set contains three problems that cover the essential content of that section. This simple assessment tool measures whether students know when they are ready for new material, and when they need further review.
A Concept Check question at the end of each Quick Quiz asks students to explain how and why a method works in their own words, forcing students to analyze problems and reflect on the mathematical concepts.
Classroom Quizzes in the Annotated Instructor's Edition parallel every Quick Quiz, which allows instructors to quickly assess the understanding of the class at any point in the chapter.
The End-of-Chapter Material provides severalThe Chapter Test Prep and Math Coach Videos are available in MyMathLab and on YouTube.
Use Math to Save Money features practical, realistic examples in every chapter of how students can use math to cut costs and spend less. Topics have been updated based on a student survey of more than 1,000 developmental math colleges.
Author biography
John Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and served as the Mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.
Jeffrey Slater has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year award in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Massachusetts with his wife Shelley and his yellow lab Gracie.
Jamie Blair has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the Center, and as a result of this effort has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007 Jamie was appointed to the Team of Basic Skills Specialist by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California.
Jennifer Crawford received her BS in mathematics from the University of Minnesota – Duluth in 1995 and her MS in mathematics from the University of Minnesota – Twin Cities in 1998. She taught a wide range of courses at North Shore Community College in Danvers, Massachusetts for five years. She currently teaches at Normandale Community College in Bloomington, Minnesota where her focus is working with developmental math students. She lives in Minneapolis, Minnesota with her husband, two young children, and black lab. | 677.169 | 1 |
Algebra I is a comprehensive course that provides an in-depth exploration of key algebraic concepts. Through a "Discovery-Confirmation-Practice" based exploration of algebraic concepts, students are challenged to work toward a mastery of computational skills, to deepen their conceptual understanding of key ideas and solution strategies, and to extend their knowledge in a variety of problem-solving applications. Course topics include an Introductory Algebra review; measurement; an introduction to functions; problem solving with functions; graphing; linear equations and systems of linear equations; polynomials and factoring; and data analysis and probability.
Within each Algebra I lesson, students are supplied with a post-study "Checkup" activity, providing them the opportunity to hone their computational skills in a low-stakes, 10-question problem set before moving on to a formal assessment. Additionally, many Algebra I lessons include interactive-tool-based exercises and/or math explorations to further connect lesson concepts to a variety of real-world contexts.
To further assist students for whom language presents a barrier to learning, this course includes audio resources in both Spanish and English | 677.169 | 1 |
Hartshorne's Geometry: Euclid and Beyond (Springer Undergraduate Texts in Mathematics). I think it's a very instructive book and seems to be suitable for your purposes. He presents various geometrical constructions, Hilbert's Axioms (incidence, betweenness, congruence etc. ), geometry over fields, rigid motions, and so forth. | 677.169 | 1 |
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Mathematics, along with English, is a core content area that transcends disciplines. Math is used in biology, chemistry, engineering, statistics, and many other subject areas. It is also an area in which students tend to struggle. Educators on all levels and in many disciplines have come together in the math transitions meetings to discuss how to better align lessons, learning expectations, and scores between the K-12 and post-secondary levels. These events are coordinated by the Wyoming School-University Partnership and funded by support from the Qwest Foundation.
Mathematics Transitions Events
2013 Mathematics Lost in Transition Institute
April 4-5 Gillette, Wyoming
Number of participants: 35 7 K-12 educators 17 Community college educators 9 University of Wyoming educators 2 other | 677.169 | 1 |
Introduction of the GMAT, the CAT methodology, GMAT strategic preparation plan, and use of the GMATWorkshop mistake log, GMAT Math I – GMATWorkshop Data sufficiency best practice; timing/pacing best practice and guessing strategies for time-pressure situations. Number properties; divisibility rules. GMATWorkshop Data sufficiency best practice.
Session 2:
Roots and powers, percentage and fractions, etc. All building-block concepts such as odds and evens, prime number, fractions, factorials and functions discussed with most representative examples.
Session 3:
Concepts and examples about Ratio, proportion and variation, statistics, mixture and alligations, speed, time and distance, races, etc.
Session 4:
An overview of critical concepts including necessary conditions, sufficient conditions and others. Different types of arguments and major/minor types of CR questions are discussed, such as typical methods to strengthen, weaken an argument, or find out the assumptions. Common logical fallacies and CR strategies are explained so that you can apply them in the Critical reasoning section and the analytical writing part. | 677.169 | 1 |
Make algebra more approachable for struggling students with these practice problems, definitions, clear examples, tips, and references! Instructions designed to simplify difficult concepts cover number systems, exponential expressions, square roots and radical expressions, graphing, as well as linear and quadratic functions. An assessment section with answer keys allows students to see how much they have learned. | 677.169 | 1 |
Complex Analysis,2 Edition
The idea of this book is to give an extensive description of the classical complex analysis, here ''classical'' means roughly that sheaf theoretical and cohomological methods are omitted.
The first four chapters cover the essential core of complex analysis presenting their fundamental results. After this standard material, the authors step forward to elliptic functions and to elliptic modular functions including a taste of all most beautiful results of this field. The book is rounded by applications to analytic number theory including distinguished pearls of this fascinating subject as for instance the Prime Number Theorem. Great importance is attached to completeness, all needed notions are developed, only minimal prerequisites (elementary facts of calculus and algebra) are required.
More than 400 exercises including hints for solutions and many figures make this an attractive, indispensable book for students who would like to have a sound introduction to classical complex | 677.169 | 1 |
Mathematical Asset Management presents an accessible and practical introduction to financial derivatives and portfolio selection while also acting as a basis for further study in mathematical finance.
Assuming a fundamental background in calculus, real analysis, and linear algebra, the book uses mathematical tools only as needed and provides comprehensive, yet concise, coverage of various topics, such as:
Interest rates and the connection between present value and arbitrage
Financial instruments beyond bonds that serve as building blocks for portfolios
Trading strategies and risk performance measures
Stochastic properties of stock prices
The difference between expected return and expected growth and the geometric Brownian motion
Diversification through the creation of optimal portfolios under various constraints
The use of the Capital Asset Pricing Model to accurately estimate the difference between the return of the market and the short rate
To further demonstrate the reality of the discussed concepts, the author analyzes five active stocks over a four-year period and highlights the different methods and portfolios that exist in today's economic world. Exercises are also provided throughout the text, along with the solutions, allowing readers to measure their understanding of presented techniques as well as see how the methods work in real life.
Mathematical Asset Management is an excellent book for courses in mathematical finance, actuarial mathematics, financial derivatives, and financial engineering at the upper-undergraduate and graduate levels. It is also a valuable reference for practitioners in banking, insurance, and asset management industries. | 677.169 | 1 |
The purpose of this book is to help students in calculus1 get a good practice for the midterms and final exams during their school year in calculus1. All the finals and midterms are real exams (with little changes) from several Universities around America ( USA, Canada, Puerto Rico, Mexico).
We believe to get a good grade in the midterms and final, the student should after reviewing his/her homework and notes pick some real midterms and final and do them.
We tried this idea with several students and it works very well.
We wish you all success in your studies.
Muslim Mathematical Society and Salah Abdel Hamid
Preview coming soon.
Mumas "Muslim Mathematical Society" is a group graduate Muslim students who are master in different field in mathematic and decide to get together and write a collection of practice books for the students in different area in math.
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Essential Math With Application - 8th edition
Summary: The latest book from Cengage Learning on Essential Mathematics As in previous editions, the focus in ESSENTIAL MATHEMATICS with APPLICATIONS remains on the Aufmann Interactive Method (AIM). Users are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of ''active participant'' is crucial to success. Presenting students with worked examples, and then providing ...show morethem with the opportunity to immediately work similar problems, helps them build their confidence and eventually master the concepts53.71 +$3.99 s/h
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To understand and connect concepts of the calculus with real
world problems and other scientific disciplines.
To value mathematics and develop an ability to communicate mathematics,
both in writing and orally.
To develop mathematical reasoning, and an ability to solve problems.
To attain computational facility in integral calculus, and sequences
and series.
WITHDRAWAL:
The last day for undergraduates to withdraw from a full-session couse is
Friday, March 8.
GRADING:
Grades for 230 will be assigned on the basis of 650 points,
as follows:
3 one-hour exams worth 100 points each
Quizzes and/or homework, 150 points total
Final exam, 200 points
ADVICE:
Perhaps the single most important factor in your success
in this course is your study habits .
Think of learning math as "working out" in the gym.
Study at least 3 times per week; do not wait until the day before the exam.
Learn mathematics like you would learn a language.
Work on the concepts until they make sense.
Don't just memorize facts and then forget them a few weeks later.
You will need to know this stuff for Calc III and other courses.
Master each homework problem - beyond just getting a correct answer.
Be on the lookout for mistakes in algebra and trig.
Always come to class!
While you're there, listen, think, and ask questions. | 677.169 | 1 |
Dyslexia, Dyscalculia and Mathematics will be an essential resource for teachers, classroom assistants, and SENCOs who help dyslexic and dyscalculic children with their understanding of mathematics. Written in an accessible style with helpful illustrations, this practical book reveals helpful ways in which to tackle both simple and complex concepts... more...
This book (along with vol. 2) covers most of the traditional methods for polynomial root-finding such as Newton's, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent's method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation... more...
Mathematicians is a remarkable collection of ninety-two photographic portraits, featuring some of the most amazing mathematicians of our time. Acclaimed photographer Mariana Cook captures the exuberant and colorful personalities of these brilliant thinkers and the superb images are accompanied by brief autobiographical texts written by each mathematician.... more...
The Clemsons' clear and readable book takes the reader from debates about how children learn and what children know and can do when they start school; through to a discussion of how mathematics can be managed, assessed and evaluated in the school and classroom. Linking these two parts of the book is a section on the subject of mathematics itself, from... more... | 677.169 | 1 |
(cur | prev) 19:15, 29 December 2011Barta(Talk | contribs)(3,042 bytes)(Created page with "Many institutions have liberal arts courses in mathematics. Creating a mathematics course that satisfies the math requirement and at the same time shows students how mathematics ...") | 677.169 | 1 |
Helping Students Pre-AlgebraFacilitate students transition from arithmetic to algebra! Includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, and answer keys. Supports NCTM standards. | 677.169 | 1 |
Saxon Algebra I textbook is designed to differ from a
traditional textbook in three areas: (1) the text is organized into
lessons to avoid the uneven or abrupt flow of material that can result
when topics are organized into chapters, (2) Saxon uses an extensive
conversational presentation of the material rather than charts and
diagrams, and (3) only a small number of the exercises in each lesson are
on the new material, the majority are practice and drill of previously
presented concepts and skills.
Strategy: Graphing
calculator Subjects: 294 pre-university Dutch
students, 16-17 years old. Results: Students in the
treatment group made significantly more use of graphical solutions than
the students in the control group. Males used the graphing calculator
significantly more than females. The graphing calculator had a positive
effect on the weaker math students.
Description: This study utilized two experimental
conditions and one control condition in a senior high mathematics
classroom. Three classrooms used the graphing calculator throughout the
year with all topics in their textbook. Five classrooms used the graphing
calculator for only one topic for a two-month long implementation and four
classrooms (control group) covered the topics in the textbook without
using the graphing calculator Skills and concepts learned and applied
using the University of Chicago School Mathematics Project (UCSMP)
Advanced Algebra textbook Subjects: 306
students in heterogeneous classes studying second-year algebra in four
high schools. The high schools selected were in a White middle-class
suburb of Atlanta, a rural area that is becoming a suburb of Chicago, a
small semi-rural community in Mississippi, and an affluent suburb of
Philadelphia. Of the students, 19% were in Grade 10, 76% in Grade 11, and
5% in Grade 12. Additionally, 84% were Caucasian, 3% African American, 1%
Hispanic, while the remainder were classified as other or
unknown. Results: Students using the UCSMP curriculum
significantly outperformed students in the comparison curriculum
(p=0.0014) on all items of the post-test. However, analysis of
the items all students in the study had the opportunity to learn did not
indicate a significant difference (p=0.108). Performance on the
eight skill items in this last analysis was comparable for the two
curricula.
Description: UCSMP is a curriculum that uses
reading and problem solving, realistic applications, technology (graphing
calculators and/or computers), a multidimensional approach understanding,
and an instructional format featuring continual review combined with a
modified mastery-learning strategy. It emphasizes
understanding of concepts through multiple representations, realistic
contexts, and the use of technology. There is less emphasis on skills than
in a traditional curriculum. The instructional method often uses
small-group explorations and extended projects, both involving writing
about mathematics Webb.
The impact of the
Interactive Mathematics Program on student learning teachSubjects: Eighty volunteer students with
lower-middle to middle SES status enrolled in a college algebra
course.
Results: Treatment subjects achieved gains in
the concepts of modeling, translating, and interpreting as they relate to
functions. There was no significant difference in groups in regard to the
concept of reification.
Description: CIA teaches college algebra using
computer technology and with a focus on real-world
situations.
Results:
No attempt was made to verify the comparability of the
treatment and control groups prior to performing the experiment,
therefore, although students in the treatment group outscored the control
group, it is not possible to meaningfully attribute these gains to the
intervention.
Description: This strategy employs an algebra
text written to provide continuous review of four or five problem sets for
each fundamental part of a skill. Each problem set has only four or five
problems on the new facet of the skill and approximately twenty review
problems of prior facts or skills. This method provides the student a
longer period of time in which to learn a skill or develop a
concept • Number
& Operations
Math Topic(s): Computation and
concepts/application skills.
9th to 12th grade.
(Also in
Diverse Learners)
Study: Austin.
An experimental study
of the effects of three instructional methods in basic probability and
statistics.
Strategy:
The use of manipulatives and pictorial
modes. Subjects: Freshman and sophomore students
(n=71) at Purdue University who did not major in science or
mathematics. Results: Computational achievement did
not differ among the three different methods. Using pictorial figures
improved students' achievement, but there was no significant difference as
a result of using manipulatives.
Description: Students were divided into three
different treatment groups; manipulative-pictorial (MP); pictorial (P);
and symbolic (S). The MP group manipulated such things as coins, dice,
random-number tables, and marble-selection devices and used graphs,
diagrams, and figures for the pictorial portion of the experiment. The P
group looked at the data from the experiments and the same pictorial
elements of the MP group. The S group used no pictorial aids; only
mathematical symbols and words were used confront
Math Topic(s): Computation and
concepts/application skills.
9th to
12th grade.
(Also in
Diverse Learners)
Study:
R. Wertheimer.
Title: The Geometry Proof Tutor: An "Intelligent"
Computer-Based Tutor in the Classroom.
Strategy: Individualized instruction with the
Geometry Proof Tutor (GPTutor) Subjects:
Geometry students from a public high school: 10 students from one gifted
class, 18 students from one scholars class, and 9 students from each of
three regular classes. Racially mixed and with a wide range of
socioeconomic statuses. Results: All
experimental groups outperformed the control group on the
posttest:
Description:
The Geometry Proof Tutor is a computer-based tutoring software
for proof construction that provides individualized instruction. It is
composed of the following three components: 1. Expert: embodies the
knowledge (i.e. theorems, axioms, and definitions) necessary for
successfully solving problems. 2. Tutor: contains information
that is used to tutor students with messages about students' errors and
strategies to attack problems; and 3. Interface:
presents students with problems and handles students' input tutorsStrategy: Conceptually Oriented Instruction Subjects:
Two ninth grade general math classes from a Midwest suburban high
school with a population of 700 students. Subject students ranged from
14-17 years old. The average age was 15 years old. First semester: the
"conceptually oriented" class had 28 students and the "computational"
class had 19 students. Second semester: the "conceptually oriented"
class had 23 students and the "computational" class had 21
students. Results: Students in the conceptually oriented class
outperformed students in the drill and practice class on a test of
computation. Effect Size = +0.96.
Description: Conceptually oriented instruction
focuses on estimation, mental arithmetic, whole number concepts and
relationships, and arithmetic word problems. It examines set, region, and
linear models for fractions (as a part of a whole), and the connections
between fractions, decimals, and percents. The intervention uses
calculators, manipulatives, models, and illustrations. It employs
questioning strategies and encourages student communication | 677.169 | 1 |
An introduction to the various branches of mathematics within the historical framework of their origin. Such topics as sets, systems of numeration (ancient and modern), logic (Aristotelian and symbolic), geometry (Euclidean plane and solid, non-Euclidean, analytic), arithmetic (simple and modular), probability, statistics and computers are explored from the standpoint of their development and impact on modern living. Does not fulfill the mathematics requirement for elementary education majors. Does not satisfy the general education requirement for mathematics.
Prerequisite: Satisfactory math placement test score or a grade of P4 in DVM 0050 [DVM 005] or DVM 0070 [formerly DVM 007].
Book:
As determined by the Mathematics Department.
Outcomes:
Upon successful completion of the course, each student should be able to:
1. Compare and/or contrast the mathematics of the ancient civilizations of Egypt, Mesopotamia, Greece, India and Persia with that of the present, especially with respect to the foundations of arithmetic, algebra, geometry, trigonometry, number theory, logic and calculus. 2. Discuss the relationship between mathematics and the natural biological sciences, the social sciences and the humanities. 3. Apply mathematics to daily existence, in skill areas such as probability, statistics, calculus and analytic geometry. 4. Use the hand-held calculator and the microcomputer to solve appropriate mathematical problems. | 677.169 | 1 |
Custom Classes for Mathematics in ActionScript 3
In this section we give links to Flash and Math tutorials and the MathDL Flash Forum articles that provide
custom AS3 classes and templates for building math applications. We also list AS2 articles whose AS3 version is coming soon.
All graphing applications listed below use our custom math formula parser, MathParser.
NEW! Sketching Derivatives Applet in AS3 Flash - The Code
We present a math applet for sketching derivatives with complete AS3 source code.
The applet uses a large collection of custom AS3 classes developed by the Flash and Math team
over the past few years. The newest of the classes are related to an interesting drawing
and smoothing techinique. The user draws by dragging and shaping a curve.
Function Grapher with Zooming and Panning
In this tutorial, we present a math function grapher which has a drag and drop panning
and mouse click zooming functionality. Panning has a cool easing
effect, too. All the source code including parsing and graphing
custom AS3 classes available for download.
Contour Map Plotter and 3D Function Grapher in Flash Combined
We use our custom AS3 classes in the package flashandmath.as3.*
to build an applet which combines a contour diagram plotter
and a 3D function grapher. The user's can input formulas for functions and variables ranges. The applet uses our custom classes: MathParser,
GraphingBoard, GraphingBoard3D, and many helper classes. We provide complete, well-commented source code and a pdf guide of custom classes.
Custom AS3 Math Classes, Implicit Plotter in Flash
The implicit equations grapher presented in this tutorial is another example of how
the custom AS3 math classes provided at flashandmath.com can be used to easily create
custom math applets. In this tutorial, we use our custom MathParser and GraphingBoard
classes that do all the work for you. The tutorial contains complete, well-commented source code.
The SimpleGraph class An alternate title for this tutorial could be, "How to make a functional grapher in 30 lines of code." With the custom SimpleGraph class available from flashandmath.com, creating a graph of an expression in one variable is a snap!
Visualizing Regions
for Double Integrals This article in the Sharing Area of the MathDL Flash Forum presents a mathlet for
students learning double integrals in rectangular and polar coordinates.
The mathlet draws regions of integration
corresponding to the limits entered by the user and provides many
practice problems.
We welcome your comments, suggestions, and contributions. Click the Contact Us link below
and email one of us. | 677.169 | 1 |
In the words of the author: Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful. My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country has made it all worthwhile! I'm proud to have played even a small role in raising peoples' respect and enthusiasm for mathematics. I have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024). In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, and of course, a large bank of skill problems. The curve-fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course. | 677.169 | 1 |
and is self-contained. It is suitable both as a text and as a reference.
* A wide ranging all encompasing overview of mathematical programming from its origins to recent developments * A result of over thirty years of teaching experience in this feild * A self-contained guide suitable both as a text and as a reference less | 677.169 | 1 |
Goal
Introduction to advanced topics in optimization theory and algorithms. The course "Mathematical Optimization" gives the background knowledge to attend various special state-of-the-art lectures at IFOR like "Geometric Integer Programming".
Target Audience
Students with a mathematical interest in optimization. This course assumes the basic knowledge of linear programming, which is taught in courses such as "Introduction to Optimization | 677.169 | 1 |
Search Loci: Convergence:In J. R. Newman
(ed.), The World of
Mathematics, New
York: Simon and
Schuster, 1956.
The Unique Effects of Including History in College Algebra
The Modules (2)
Introduction to Polynomials: Looks at the efforts put forth in finding zeros of polynomials and includes a brief introduction to the lives of Niels Henrik Abel and Evariste Galois. This historical module excerpt illustrates the difficulties Abel and Galois had in breaking into the mathematical circles of their time. "Niels Henrik Abel, at the age of sixteen, proved that a general formula for solving a quintic (fifth degree) polynomial did not exist…. However, since he was largely self taught, leading mathematicians in Paris, such as Cauchy, largely ignored him… Evariste Galois had equally important discoveries. At sixteen, Galois had the desire to enter the most prestigious engineering school of the day, the École Polytechnique… [W]hen Galois submitted a paper to the school as part of the admission process, Cauchy lost the paper. He attended another school for the purpose of training to become a teacher. However, he kept his mathematical studies up and submitted a second paper to the École Polytechnique. This paper also appears to have been lost." (Hagerty and Smith, 2006).
Polynomials: Looks at theoretical methods to help find zeros of polynomials. The module looks at Horner's method and how information traveled in eras prior to modern-day technology. It includes a discussion of the difficulty of crediting the correct civilization with the development of a topic as it is believed that Horner did not develop the method credited to him; in fact, the Ancient Chinese knew of this method (Eves, 1992).
Technology: Looks at methods to use technology to find zeros of polynomials, and discusses the rapid changes in technology. The goal is to have the students take a look at when the Internet was developed and realize that instant messages were not always possible. The students need to realize that their parents enjoyed "Pong" and "Pacman" and their grandparents had the radio. Thus, the students need to revaluate the question "My parents didn't need math, why do I?" | 677.169 | 1 |
The elementary school curriculum in recent years has begun
to include a significant amount of geometry, including reasoning about
important and fundamental ideas.This course is designed to provide students intending to become
elementary school teachers with the beginnings of a strong background to teach
this geometry.
While the geometry topics will be basic, the course will go
into them deeply.There is much to
think about in considering basic geometry ideas. Since the course will
emphasize understanding, reasoning, and communication, class discussion and
writing will be key components of the course.
Because this course is for future elementary teachers, few
of whom are math majors, the course will be designed to be friendly and
accessible to students who have not been in a math course recently.The subject matter lends itself to
visual and hands-on approaches, and these will be utilized fully.
As suggested above, there will regular writing, projects and
some assigned readings beyond the textbook.Because of the importance of reasoning and communication,
in-class work will be essential. In particular, attendance at all of every (or
almost every) class is required. If you will miss all or part of class on a
regular basis, you should not take this course.
Since this is a Credit/No Credit course on topics in
elementary mathematics, one might assume that this would be an easy course,
especially if one has a strong math background.On the contrary, to get Credit in the course, a student must
achieve a satisfactory level in all components of the course, including writing
and classroom participation.So
the course will demand a significant and consistent amount of work from
everyone, whatever her/his math background.On the positive side, consistent serious work should suffice
for a Credit grade, even if a student brings a weaker math background.
There will be some tests and also a final exam at the
regularly scheduled time, but it will not be the conventional sort of exam.
Note that this is a content course, not a methods course.
While we will aim to model good teaching techniques, we will be addressing
mainly questions of mathematical content, not methods for teaching elementary
school students. If you enter the Teacher Education Program in the UW College
of Education, you will take a methods course on teaching elementary mathematics. | 677.169 | 1 |
You, too, can understand geometry---- just ask Dr. Math ? ! Are things starting to get tougher in geometry class? Don't panic. Dr. Math--the popular online math resource--is here to help you figure out even the trickiest of your geometry problems. Students just like you have been turning to Dr. Math for years asking questions about math problems,... more...
Learn geometry at your own pace What are congruent circles? How do you find the hypotenuse of a triangle? What is the sum of the angles in a decagon? How can you apply geometric equations to your daily life? With the unbeatable study companion Geometry: A Self-Teaching Guide, you'll discover the answers to these questions and many more. This thorough... more...
There's no such thing as too much practice. This reproducible program builds skills incrementally. By inviting students to "show what they know" in a variety of new formats, these stimulating lessons will enable struggling students to actually enjoy the learing process. As in all of the binder programs, the dual emphasis is on (1) mastery of the basics... more...
Meyer's Geometry and Its Applications, Second Edition , combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text... more...
Part of the ''Demystified'' series, this title teaches complex subjects in an easy-to-absorb manner and is designed for users without formal training, unlimited time, or genius IQs. It helps users understand circle and triangle models; inverses of circular functions; graphs of functions; coordinate conversions; angles and distances; and more. more...
Tough Test Questions? Missed Lectures? Not Enough Time? Lucky for you there is Schaum's.... more...
Deformable objects are ubiquitous in the world, on various levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. This book provides an overview of the state of science in analysis and synthesis of non-rigid shapes. more...
Like other areas of mathematics, geometry is a continually growing and evolving field. Computers, technology, and the sciences drive many new discoveries in mathematics. For geometry, the areas of quantum computers, computer graphics, nanotechnology, crystallography, and theoretical physics have been particularly relevant in the past few years. There... more...
The family in this book is moving to a new neighborhood. They have a lot of work to do! They need to unload the moving truck, unpack boxes, and put everything away. The kids make new friends and discover all the fun they can have with the empty boxes. While building forts from the empty packing boxes, the kids discover many new shapes and their dimensions.... | 677.169 | 1 |
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It's all about computers: when they do the calculating, people can work on harder questions, try more concepts, and play with a multitude of new ideas. Conrad Wolfram discusses a new project to build a completely new math curriculum with computer-based computation at its heart - alongside a campaign to refocus math education away from historical hand-calculating techniques and toward relevant and conceptually interesting topics.
Presented at the Learning Without Frontiers Conference, January 25th 2012, London
So are you saying that applied maths should be taught at schools? Well, applied maths is basically engineering, computer science, actuarial studies, etc. which are specialized fields and more suitable to be studied at university. If you teach applied maths to student, they won't have the skills to do the problems. I believe that maths at school should be pure maths with an emphasis on rigor, problem solving and understanding so students can make use of the maths in university.
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Um,.. Albert Einstein, Stephen Hawking, both people that were only able to ASK QUESTIONS in mathematics due to their deep understanding in maths. Thus deep understanding was only caused by learning maths. How else is someone meant to learn maths. We must be able to tackle completely theoretical problems before we are good enough to tackle real life problems
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One thing which does not necessarily include computation or at least complex computation is mathematical proof. Something like a proof module might go well with these proposals, especially to teach the understanding of mathematical concepts. | 677.169 | 1 |
Welcome to our Classjump website for Intermediate Algebra! This website is a tool to help connect our classroom to home. Throughout the year, use this website to find class notes, homework assignments, important due dates and information regarding access to the online version of the textbook. These tools will be especially useful if you are absent or know that you will be gone in advance!
We only have about 55 minutes together each day, so it is extremely important that you come to class prepared and ready to engage in learning each and every day. This website will help to keep you prepared, so please check it regularly (like your Facebook!). Intermediate Algebra is a co-taught class in order to provide the best learning opportunities for students. I will be co-teaching Intermediate Algebra with Jesse Ziebarth, so please feel free to contact either of us with any questions or concerns. I look forward to an exciting and wonderful year!
Math lab serves as a support class for students enrolled in one of my sections of Intermediate Algebra w/ Statistics.
Each day, we will start off by checking and working through homework problems from the previous day. Students are expected to come to lab each day with every problem from their assignment ATTEMPTED. Students will work in their assigned groups in order to practice collaboration and teach each other before we come together as a whole class.
We will then extend the lesson from the previous day either through extra practice or some sort of activity, usually involving groupwork.
Time permitting, we will spend the end of the period previewing the lesson students will have in Intermediate Algebra later that day so they can get a jump start on learning that material.
Students will not be receiving extra homework in lab. All work will be done in class.
For any other information, such as the online version of the textbook and contact information, please look under the Intermediate Algebra with Statistics ClassJump page. | 677.169 | 1 |
Book Description: Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition. | 677.169 | 1 |
Fundamental Theorem of Calculus
In this lesson, Professor John Zhu gives an introduction to the fundamental theorem of calculus. He goes over the properties for the fundamental theorem of calculus as well as the definition of integral. He reviews four rules/ properties for calculus and performs a few example problems.
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Fundamental Theorem of Calculus
Simply evaluating integral at 2
bounds
Area under a curve
Accumulated value of
anti-derivative function
Fundamental Theorem of Calculus
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. | 677.169 | 1 |
MATH 2432
This is an archive of the Common Course Outlines prior to fall 2011. The current Common Course Outlines can be found at Credit Hours 4 Course Title Calculus II Prerequisite(s) MATH 2431 with a "C" or better Corequisite(s)None Specified Catalog Description
This course includes the study of techniques of integration, applications of the definite integral, an introduction to differential equations, polar graphs, and power series.
Expected Educational Results
As a result of completing this course, the student will be able to: 1. Evaluate integrals using techniques of integration. 2. Use integrals to solve application problems. 3. Solve separable differential equations and apply to elementary applications. 4. Investigate the convergence of series and apply series to approximate functions and definite integrals. 5. Apply polar representations including graphs, derivatives, and areas.
General Education Outcomes
I. This course addresses the general education outcome relating to communication by providing additional support as follows: A. Students improve their listening skills by taking part in general class discussions and in small group activities. B. Students improve their reading skills by reading and discussing the text and other materials. Reading mathematics requires skills somewhat different from those used in reading materials for other courses in that students are expected to read highly technical material. C. Unit tests, examinations, and other assignments provide opportunities for students to practice and improve mathematical writing skills. Mathematics has a specialized vocabulary that students are expected to use correctly. II. This course addresses the general education outcome of demonstrating effective individual and group problem-solving and critical-thinking skills as follows: A. Students must apply mathematical concepts to non-template problems and situations. B. In applications, students must analyze problems, often through the use of multiple representations, develop or select an appropriate mathematical model, utilize the model, and interpret results. III. This course addresses the general education outcome of using mathematical concepts to interpret, understand, and communicate quantitative data as follows:
A. Students must demonstrate proficiency in problem-solving skills by using the definite integral to solve application problems. B. Students must be able to solve applied problems that can be modeled by differential equations. C. Students must use power series techniques to approximate function values to a specified degree of accuracy. IV. This course addresses the general education outcome of locating, organizing, and analyzing information through appropriate computer applications (including hand-held graphing calculators). As a result of taking this course, the student should be able to use technology to: A. Approximate definite integrals using Simpson's rule or a built-in integration feature. B. Approximate points of intersection of curves for use in determining approximate limits of integration in application problems. C. Investigate series representations of functions, their graphs, and the convergence or divergence of series. D. Approximate values of functions and definite integrals using Taylor series. V. This course addresses the general education outcome of using scientific inquiry by using techniques of Calculus including integration or differentiation to apply scientific inquiry to problem solving.
Course Content
1. Techniques of Integration 2. Applications of the Definite Integral 3. Differential Equations 4. Series 5. Polar representations ENTRY LEVEL COMPETENCIES Upon entering this course the student should be able to do the following: 1. Investigate limits using algebraic, graphical, and numerical techniques. 2. Investigate derivatives using the definition, differentiation techniques, and graphs. The classes of functions studied include algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and implicit. 3. Apply the derivative as a rate of change, optimize functions, use Newton's Method, and sketch curves. 4. Define the definite integral and approximate definite integrals using Riemann sums. 5. State and apply the Fundamental Theorem of Calculus. 6. Graph and use parametric equations.
Assessment of Outcome Objectives
The Calculus Committee or a special assessment committee appointed by the Chair of the Math, Computer Science, and Engineering Executive Committee, will accumulate and analyze the results of the assessment and determine implications for curriculum changes. The committee will prepare a report for the Academic Group summarizing its finding. | 677.169 | 1 |
Technology in Education
Monday, April 5, 2010
Cabri 3D is one of dynamic geometry software. This software helps students with the visualization of 3D figures their properties. The purpose of this software is to help students to better understand three-dimensional space, since three-dimensional space is difficult to visualize. Cabri 3D allows students and teachers to construct and manipulate solid geometry objects in three dimensions. It provides a tool for teachers and students to explore properties of 3D geometric constructions
Even though it is Cabri 3D, two dimensions objects can still be created. The software is suitable with many two dimensions concepts such as length, sectors of circles, lateral area, surface area. Cabri 3D will help students to learn analyzing characteristics and properties of two- and three-dimensional geometric shapes and develop arguments of mathematics about geometrical relationships. Students also can learn to use visualization, spatial reasoning, and geometric modeling to solve problems
Cabri 3D is appropriate for secondary school students. Even though the software is not very user friendly, the students can be successful with the program if they learn through the manual. Teachers who want to use it in their classes have to be advanced in using it. Even though the software is not user friendly, it still offers a lot of great features that help student to get success in learning mathematics especially in geometry class.
Monday, March 15, 2010
I reviewed a Mathematics WebQuest. Its title is Vector WebQuest. There are some weaknesses and strengths of this WebQuest. The weaknesses are it is not complex, does not have analytical question and does not has sufficient explanation on the process. On the other hand, the strengths of the WebQuest are an interested introduction and a range of web sites been accessed.
The most weakness of the WebQuest is it is not complex. It has only three parts. They are introduction, task and process. The WebQuest does not have evaluation, conclusion, and teacher page. Based on the criteria of a WebQuest, these elements are very important. Without Evaluation and conclusion, a WebQuest will be less useful. Another weakness is there is no any analytical question. Analytical questions are very important, since one of the purposes of a Webquest is to support learner thinking at the level of analysis. On this WebQuest, The level of questions is comprehension. Overall, the questions are not able to encourage students to think at high level thinking. The last weakness is it does not have sufficient explanation that is provided to students in order to accomplish the task. The WebQuest does not have full potential of web such as sound and video.
One of strength of the WebQuest is its introduction provides information that engages students to explore further. It is started with interesting issues. This issue will grab students' attention. Another strength is its link to supported documents such as vector form. Moreover, it also provides various web sites such as .com, .edu and .gov. Some of the links take students directly to pages they need to go.
Even though the web quest has an interested introduction and various web sites been accessed, it is still inappropriate to be used by students because it does not fulfill the basic criteria of a WebQuest.
Friday, February 19, 2010
I am curious to learn and assess computer technology for learning mathematics and science. Even though there are many issues surround the using of computer technology in learning mathematics and science, computer technology offers new ways to learn. It helps students to learn based on problem solving. Another advantage is by using computer technology teachers can create inquiry-based mathematics and science classroom. Of course, besides those things, There are many other advantages of using computer technology in learning mathematics and science.
One of software that I am interested to learn is TinkerPlots. TinkerPlots is software for students in grades 4 through 8. The use of software is to build fluency with data representation and exploration. Animation, color, and dynamic manipulation support students in moving from simple representations to increasingly complex and analytic graphs. Another aim is to get students excited about what they can learn from data. TinkerPlots also helps teachers to create inquiry-based mathematics classrooms
TinkerPlots is friendly and intuitive interface that allows the user to play with the data plotted in an infinite variety of formats.
Tuesday, February 9, 2010
Speech Recognition. Windows 7 has a feature that allows people to use their voice to operate a computer and compose text. It is Speech Recognition. We can find this feature on Ease of Access. Before we get started using Speech Recognition, we will need to connect a microphone to our computer. There are some issues that we have to think about before using Speech Recognition: (1) Speech Recognition needs a good microphone. (2) Training the computer to identify the speaker sounds and pronunciation. (3) Speak clearly and pronounce words carefully, not too fast and or too slow. To open Speech Recognition: (1)Start the Speech Recognition by clicking the Start button , clicking All Programs, clicking Accessories, clicking Ease of Access, and then clicking Windows Speech Recognitions. (2)Click microphone button to start the listening mode
By using Speech Recognition we can do the following things: (1) We can use our voice to control our computer. (2) We can say commands that the computer will respond (3) We can dictate text to the computer.
Speech Recognition makes a classroom or lesson more Universally Designed. Speech recognition allows students to use their voice to operate a computer and compose text. This feature is useful to students with a wide range of disabilities including those with visual, mobility and language impairments. This feature will be very useful in a classroom which the numbers of students with disabilities integrated into it. Today, nearly every class and schoolwork are related to computer. For example statistics class, students will analyze graphical displays of data, including dot plots, stem plots, and histograms, to identify and describe patterns and departures from patterns. In this class they will use computer to create graphical displays. By using Speech recognition and Microsoft excel, students with mobility impairment are still able to participate well in the class. They can input data and command to create a graphic.
Speech Recognition helps students with mobility and visual impairment. Students with mobility impairments might be unable to use (or be without) arms or fingers to interact with their computers using a standard keyboard or mouse. Using their voice is a way to interact with their computer. By using speech recognition they can operate their computer and compose text. Another is visual impairment, blindness, for example. Students who are blind interact with their computers through keyboards, Braille devices, and audio/voice rather than a traditional monitor and mouse. If they don't have these special devices, they are still able to operate their computer by using Speech Recognition.
Conclusion A more accessible technology is good for everyone, including students with disabilities and students without disability. All students benefit from technology in which it is easier to function. Providing accessible technology in the classroom to students with disabilities enables all students to have the same opportunities in education. Speech Recognition gives an easy way to interact with computer not only for students with a disability but also those without a disability. It also helps us to make an inclusive classroom with equal access for all students.
Monday, January 25, 2010
Mathematics is my subject domain, during I taught mathematics I used some dynamic geometry software, such as Cabry, Geometer's Sketchpad, GeoGebra and Autograph. These are typically used in the classroom or the computer lab and they are very helpful in teaching the difficult concept.
It is little bit difficult to find an appropriate technology device in everyday life for teaching and learning the difficult concept of mathematics. Since mathematics concept is completely different from other concepts such as social science, English, etc.Based on my teaching experience in primary school, when I teach a difficult concept, I had to prove the concept and visualized it. these things can be done by using a software for teaching mathematics that requires a certain specification of a computer.
However, Nowadays, there is a technology in education known as mobile learning. Mobile Learning is a learning model adopted cellular technology development and mobile phones where this technology can be used as a learning medium. To use this technology, we can download the applications and install them on a mobile phone or use them online by using mobile phone.
Mobile learning technology can be used to teach mathematics. One of web sites that provides mobile learning applications for teaching and learning mathematics is So far, Mobile Learning is very helpful as a supplement material for teaching mathematics. It is easy for students to bring mobile phones wherever they go, this technology will help them to learn mathematics wherever and whenever. | 677.169 | 1 |
Math for Merchandising : A Step-by-Step Merchandising Math and Buying courses offered by Junior Colleges and Vocational Schools. This book provides a practical application of the skills necessary to a merchandising career. Beginning with the fundamentals of working with numbers, it moves into the skills needed to communicate words and thoughts into calculators or computers as a means of translating business needs into clear mathematical answers. | 677.169 | 1 |
Bob Miller's fail-safe methodology helps students grasp basic math and pre-algebra. All of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding in the fundamentals, principles, and techniques of basic math and pre-algebra, yet many students have difficulty grasping the necessary concepts. Utilizing... more...
Everything you need to know to ace the math sections of the NEW SAT!. He's back! And this time Bob Miller is helping you tackle the math sections of the new and scarier SAT! Backed by his bestselling ''Clueless'' approach and appeal, Bob Miller's second edition of SAT Math for the Clueless once again features his renowned tips, techniques, and insider... more...
Boiled-down essentials of the top-selling Schaum's Outline seriesFlummoxed by formulas? Queasy about equations? Perturbed by pi? Now you can stop cursing over calculus and start cackling over Math, the newest volume in Bill Robertson's accurate but amusing Stop Faking It! best sellers. As Robertson sees it, too many people view mathematics as a set of rules to be followed, procedures to memorize, and theoremsBlending theoretical constructs and practical considerations, the book presents papers from the latest conference of the ICTMA, beginning with the basics (Why are models necessary? Where can we find them?) and moving through intricate concepts of how students perceive math, how instructors teach-and how both can become better learners. Dispatches as... more...
Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Geometry, students will enjoy the same clear, concise approach and extensive exercises to key fields they've come to expect from the series--but now within mathematics. Practice Makes Perfect: | 677.169 | 1 |
Solving Compound Inequalities Test Recovery 16 compound inequality problems. At the top of the worksheet is 2 worked out examples that are excellent guides for students to follow.
I actually use it as a way for them to raise up their test grade. For each 2 problems they get correct, I will raise their grade 1%. After each test they have the opportunity to raise their test grade by doing extra problems. I only allow them to have one of the worksheets at a time and when they complete it I grade it and go over it with them if there is still some misunderstandings. I have found that it works great because the students that truly care about understanding the material will do these worksheets. This is helpful because a lot of the time when I try and go over a test in class, students lose focus and are uninterested. This way I don't spend time in class going over the test and I don't get frustrated with them not taking advantage of the reviews.
Word Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
69 | 677.169 | 1 |
Mathematics / Pangarau
It is generally acknowledged that everyone needs to learn and use mathematics. Most areas of employment require at least some ability in understanding and using numbers. It is also used in many areas of daily life; anyone who wants to manage a household budget, organise a holiday, decorate a room or build a fence will need mathematics.
An understanding of mathematics helps people to develop and use logical approaches to procedures and arguments. A grasp of geometrical ideas helps people to appreciate symmetry and patterns and helps them to make sensible designs.
Mathematics involves skills of calculation and estimation and the ability to reason logically. It develops the creativity and problem solving involved in technological and scientific innovation and discovery.
Skills learned and practiced in the mathematics curriculum can be applied across a wide range of occupations such as banking, accountancy, statistics, management, architecture, science, teaching, engineering, insurance, financial planning, economics, weather forecasting, trades and so on. | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Specification
Aims
to supply evidence that such problems are both intriguing and provocative, and require rigorous proof;
to explain the fundamental ideas of sets, numbers and functions;
to compare and contrast language and logic;
to introduce a detailed study of the integers, including prime numbers and modular arithmetic;
to show how mathematicians generalize ideas, so unique factorization of integers is shown to hold for permutations;
to introduce the ideas of algebraic structures and so show, by examples throughout the course, how the same structure can arise in many different situations.
Brief Description of the unit
This course introduces students to the concept of proof, by studying
sets, numbers and functions from a rigorous viewpoint. These topics
underlie most areas of modern mathematics, and recur regularly in years
2, 3, and 4. The logical content of the material is more sophisticated
than that of many A-level courses, and the aim of the lectures is to
enhance students' understanding and enjoyment by providing a sequence of
interesting short-term goals, and encouraging class participation.
Learning Outcomes
On completion of this unit successful students will be able to:
analyze statements using truth tables;
construct simple proofs including proofs by contradiction and proofs by induction;
prove statements about sets and functions;
prove standard results about countable sets;
apply Euclid 's Algorithm to find the greatest common divisor of pairs of integers and to solve linear Diophantine equations;
to solve simultaneous linear congruences;
multiply and factorize permutations;
prove the infinitude of prime numbers, prove Fermat's Little Theorem and use it to find modular inverses and to solve linear congruences;
construct multiplication tables for congruence classes, reduced congruence classes and sets of permutations. Have an informal understanding of isomorphisms between the groups seen in the course.
Future topics requiring this course unit
Almost all Mathematics course units, particularly those in pure mathematics.
Assessment
Arrangements
Midterm Test
The Midterm Test will be in-class and closed book, and will relate
to the first five weeks of the course ONLY. It will involve
answering questions similar to those on the relevant Problem Sheets;
students who have taken full advantage of their supervision classes
should therefore find the Test straightforward. It will be worth
15% of the final mark for the course. Answers will be marked
and returned in due course, as part of the learning process. | 677.169 | 1 |
Categories
Other Links
A review of basic arithmetic operations and algebraic operations. Topics covered include the arithmetic of fractions
and decimals, algebraic manipulations of polynomials, linear equations, and factoring. This course cannot be used to satisfy
General Education requirements or for credit toward a Mathematics major or minor. | 677.169 | 1 |
MAA Review
In a 1990 paper entitled "What Is Geometry?" Shiing-Shen Chern [3] identified six pivotal developments in the history of geometry:
Euclid's axiomatic treatment,
the introduction of coordinates (Fermat and Descartes),
the invention of the calculus (Newton and Leibniz),
the recognition of the fundamental role of transformation groups (Klein and Lie),
manifolds (Riemann), and
fiber bundles (E. Cartan and Whitney).
The geometry presently taught in American high schools includes significant parts of (1) and (2), and some students get an introduction to (3). Transformations (4) make a cameo appearance in many contemporary American high school geometry textbooks, and play a featured role in a few. (5) and (6) have not influenced the high school curriculum.
The Common Core State Standards for Mathematics, which have now been adopted as a guide for the K–12 mathematics curriculum in 44 states, put transformations in center stage. Students in Grade 8 are introduced to geometry by experimenting with rotations, reflections and translations and they are expected to understand congruence in terms of rigid motions. High-school students develop these ideas more rigorously, learning standard terminology and fundamental facts about rigid motions and dilations of the plane as a foundation for the study of Euclidean geometry. In giving such prominence to transformations, the authors of the Common Core took into account both pedagogical evidence as well as the structure of the mathematics underlying the curriculum. Nonetheless, in view of the traditional organization of the curriculum, this is one of the bolder proposals of the Common Core.
The challenge will be implementation. We will need K–12 textbooks that are very different from those most widely used. At least as important will be assuring that teachers are intellectually equipped. Good scholarship presented in a form accessible to teachers (or those planning to become teachers) and focused on the meaning and role of transformations in geometry is needed. One would hope to find this in textbooks for junior/senior-level college geometry courses, but unfortunately few books fill the bill. There is no standard undergraduate course in geometry, and the available textbooks have less in common than the books for courses such as abstract algebra or basic analysis that have acquired a canonical form. Geometry textbooks tend either to present some kind of axiomatic treatment and then to branch off into topics or else to be, through and through, a sampling of approaches and ideas. Transformations tend to be treated in college in the same way that they are treated in high school, namely, as an interesting branch of a great tree.
The purpose of the book of Barker and Howe is to develop the main ideas about geometric transformations of the Euclidean plane and their applications. It could play a valuable role in introducing college students, especially future teachers, to this topic. However, it does not jump immediately to its main topic. Chapter I, which takes up the first 120 pages of the 529 pages of this text, is devoted to a careful development of Euclidean plane geometry based on an axiom system similar to SMSG, which features the Ruler and Protractor Postulates. This opening chapter sets the mathematical tone. It is careful, rigorous, thorough and explicit in its attention to detail. I expect that this would not only be a good book from which learn some geometry, but also a fine introduction to the habits of logical thinking and precise exposition that a math major needs to acquire.
Transformations make their first appearance in Chapter II, which culminates on pages 157–161 by classifying the isometries of the plane according to the number of their fixed points, demonstrating that every isometry is a composite of at most three reflections, and proving that, for any pair of congruent triangles, there is an isometry that takes one to the other. Readers who are familiar with these theorems might wonder if 160 pages of preparation are needed. The main ideas in the proofs are intuitively clear, and can be conveyed vividly by well-designed paper-folding activities. But what a student will take away from an informal presentation is very different from what he or she might acquire by following the course that the book lays out. Paper-folding, whatever legitimate pedagogical purposes it may serve, does not equip learners with a useful language for reasoning about transformations. This book will provide plenty of opportunity to learn good mathematical language and practice its use.
Chapter III begins with a discussion of compositions of reflections and the kinds of plane isometries that may be produced, leading up to the classification of isometries as reflections, rotations, translations or glide reflections on page 188. Numerous fine color illustrations make the twenty pages of preparation for this theorem a delightful visual experience. This is followed by a discussion of orientation based on the proposition that the parity of an isometry is well-defined. The chapter then introduces the idea of a group of transformations and in a sequence of exercises beginning on page 203 invites readers to investigate the structure of many examples. The remainder of the chapter deals with factorization in the plane isometry group.
Chapter IV concerns similarities. This chapter is especially important for future teachers because of the prominence of similarities in high-school mathematics. The treatment here parallels the treatment of isometries in the previous chapters, building up to the structure and classification theorems.
Chapter V studies the conjugacy relation in transformation groups and the decomposition of groups into conjugacy classes. This chapter ends with an interesting but sketchy discussion of the idea of developing geometry from the group of symmetries alone by means of the correspondences between lines and reflections and between points and 180-degree rotations. As a matter of fact, this is an idea that was developed extensively in the early 20th century by German-speaking mathematicians Gerhard Hessenberg, Johannes Hjelmslev and Gerhard Thomsen; see [4]. The standard reference is Friedrich Bachmann's book [1]. Unfortunately, the works of Hessenberg, Hjelmslev and Thomsen have not been translated into English, nor has Bachmann's book. However, a good synopsis in English is contained in chapter 5 of [2].
Chapter VI describes applications of transformations to Euclidean plane geometry. Running from page 287 to 346, it includes numerous interesting results. Transformations appear sometimes as essential tools, sometimes as useful aids, sometimes as a way to interpret a construction and sometimes merely as a point of view. Section 2 describes some theorems on the concurrence of special lines in triangles.
The first theorem on the circumcenter (the point of concurrence of the perpendicular bisectors of the sides of triangle ABC) helps to illustrate my remark about the varying role of transformations. The proof is essentially as follows: Let w be the perpendicular bisector of segment AB and let u be the perpendicular bisector of segment BC. Let P be the point of intersection of w and u. Then P is equidistant from A and B because it's on w and also P is equidistant from B and C because it's on u. Therefore, P is equidistant from A and C, so P lies on the perpendicular bisector of segment AC. Transformations illuminate the argument — w and u are axes of reflections and it is these reflections that show the congruence of segments AP, BP and CP — but certainly it is not necessary to know this to follow the proof.
The incenter, centroid and orthocenter are treated in a similar fashion, using arguments in which the role of transformations is clear, illuminating but not essential. Section 3 uses dilation about the centroid by a factor of –2 to unify a discussion of the Euler line and the nine point circle. Here, the transformation does some real work. Section 5 of this chapter concerns the orthocenter (the point of concurrence of the altitudes). The discussion hinges on the analysis of the composition of the reflections whose axes are the sides of a triangle. Here, transformations are not only hard at work, but are leading the development.
Chapters VI (pages 347–375) concerns the symmetries of bounded figures in the plane, leading up to a discussion of dihedral groups. Chapter VII (pages 376–458) is a careful treatment of frieze and wallpaper groups. The last chapter concerns area, volume and scaling.
I had hoped to use this book in a one-semester course in geometry that I teach periodically, but up till now the scheduling has not worked out. The course is populated primarily by math majors who are seeking certification as secondary teachers. Most of these people take a proof-based course in real analysis as well as other junior/senior courses, including probability, abstract algebra, number theory and other advanced topics. The typical student in this group will likely struggle at first with the level of exposition in Continuous Symmetry, particularly if he or she has not previously taken the analysis course, but surely will be capable of handling it. Because the text is detailed and methodical, patience and persistence is needed. However, it clear and explicit enough that it will never leave students helpless or befuddled, provided they are serious and spend the time to read carefully.
I plan to use the text next time I teach the class. I expect to have to pick and choose carefully, especially in the first chapter. I find the level of rigor of Euclid to be a very workable goal in this class. It does not pay off to be overly concerned with facts, such as the Crossbar Theorem, that are evident from the topological properties of diagrams. I think the geometry of the number line is an essential topic, and a good opening for the course. This is consistent with the layout of the book.
My goal will be to spend only enough time in chapter I to prepare for chapters II, III and IV. These, I want to treat carefully because of the tasks these future high-school teachers will face in the classrooms where they will eventually teach. I shall need to include some material on area and volume, and Chapter IX can support this. Some discussion of coordinates, particularly linear change of coordinates, will be desirable. For this, I shall need to supplement the book. R. Hartshorne has made some observations about conventions related to the Ruler Postulate in a review of this book that appeared recently in the American Mathematical Monthly. Anyone who plans to use the book should be aware of his remarks.
Although I have mentioned them only once, the abundant, high-quality illustrations throughout the text are one of the most attractive features.
The book does not always choose the quickest or most elegant route to a result. For example, Proposition IX.2.14 on the area of a parallelogram could have been proved more elegantly by repeating Euclid's proof of Proposition 35 of Book 1 of the Elements. Nevertheless, I learned a lot by reading the book, mainly because the material is arranged in a manner that invites and inspires one to reflect about the connections among the ideas being discussed. It is thought-provoking throughout. If a textbook is meant to be a tool for learning, then the extent to which it makes one think in the manner of a mathematician is by far the most important feature — much more important than any quibbles about the slickness of a proof. I am very much looking forward to the opportunity to use this book in my classes.
Comments
A full review of Continuous Symmetry was written by Robin Hartshorne for the American Mathematical Monthly, Volume 118, Number 6, June 2011, pp. 565–568. Subscribers can see this review online by going to | 677.169 | 1 |
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