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Introduction To Graph Theory 2Nd Edition Overview
This text offers a comprehensive and coherent introduction to the fundamental topics of graph theory. It includes basic algorithms and emphasizes the understanding and writing of proofs about graphs. Thought-provoking examples and exercises develop a thor
Introduction To Graph Theory 2Nd Edition Features
Others
Product Details
Language
English
Publication Date
January 1, 2006
Publisher
Penguin Books Ltd
Contributor(s)
Douglas B. West
Binding
Paperback
Page Count
470
ISBN 10
8177587412
ISBN 13
9788177587418
Editorial Reviews
From the Back Cover
This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science |
Mathematics
What is Mathematics?
Mathematics is the art of analysis, abstraction and application: we analyse observed phenomena and pick out the key concepts that explain them; we abstract these concepts so that we can study their logical relationships to each other; and we apply the understanding this gives us to predict and control our environment.
What will I study?
The concepts we study are of two broad types - arithmetical and geometric - but the most powerful mathematics exploits the interplay between the two. An example of this in the high school curriculum is the analysis of change which we call calculus, where a combination of "geometric" intuition (curve-sketching, tangents and slope) and "arithmetic" calculations (algebra, differentiation and integration) allow us to predict, for example, the path of a space-station orbiting the earth.
Mathematics is an indispensable tool in many areas of study. This includes traditional areas of application such as economics, engineering and physics, but also emerging areas such as biostatistics and robotics. At the University of Newcastle, our research strength is in functional analysis. Our work has applications in signal processing; for example it underpins the technique of digital TV transmission. |
The primary objective of this fundamental textbook is to expose and educate the engineering student, who has already taken the basic course in Statics, on the principles governing the behavior of structures – in any branch of engineering – and help him or her develop the ability to perform simple designs. The principles...
An Introduction to Numerical Methods using Mathcad is designed to be used in any introductory level numerical methods course. It provides excellent coverage of numerical methods while simultaneously demonstrating the general applicability of Mathcad to problem solving. This textbook also provides a reliable source of reference material to... |
CS 4236 Problem Sets
Your problem sets must be turned in as LaTeX documents. LaTeX is a powerful
and (relatively) straightforward way to typeset mathematical documents.
Basic LaTeX proficiency is a highly useful skill,
and using LaTeX in this course ensures that your problem sets will be
easily readable and look great
(which makes the TA happy, which is good for you).
Don't worry if you've never used LaTeX before (but do allocate a bit of
extra time for the first problem set); by the second or third
problem set you'll feel right at home.
You can click here
for a bare-bones introduction with a template file that you can modify
(there are also many good introductions
that you can find on the web).
All problem sets should be submitted to the TA in person at the start
of class. If you cannot submit a hard copy or are using late days,
you may email a .ps or .pdf file to the TA.
The time of your latest email will be taken as the time when
you turned in the problem set.
Note: If you are not using any late days on a problem set,
please bring a printout of your homework to class and give it to
the TA. |
The Pearson Guide to Mathematics for the ISEET/JEE retains the basic structure and coverage which made the earlier editions a popular success. Spread over 29 systematic and lucid chapters, this book covers the syllabus completely and will also prove a useful guide for the students appearing in ISEET/JEE.
Features
More than 5,000 problems with solutions
Short-cut methods covering each type of questions asked in the examinations.
Comprehensive practice exercises covering all topics are provided at the end of each chapter
Problems asked in previous years' examinations are provided after every chapter with explanations
A smart table that analyses the number of questions asked from various topics in the recent examinations |
What do you do when your child brings you an Algebra problem that he just can't solve? The book has the answer key, but how did they get to that point. "Ugh," you exclaim as you realize that it is well over 20 years since you even did Algebra. Now what?
Algebra 1 Solved!, published by Bagatrix, may be just the medicine that the doctor
ordered. This is not a curriculum but an amazing software tool that will help
your student successfully get through his curriculum when trouble points hit.
The software was designed as a homework helper. Its major point that is marketed is that your child can enter in her Algebra problems and see actual step by step solutions. Each of the topics that are covered in Algebra 1 curricula is contained within the software by topic. No need to just start at the beginning. The user interface allows the student to select the topic that they are struggling with and go directly to it. Your son or daughter can even have the computer generate example problems associated with the topic being reviewd. There is also a built in glossary that better explains the definition and concept of the topics selected.
Upon beginning the application, the user creates a notebook that will hold his work or opens a notebook that work was already begun in. Because the user is creating the notebook, each notebook can be labeled to correspond to the number of the lesson in the student's math curriculum, the date that the work is being done, or one notebook can be created for the full year's worth of problems. It is completely up to the student. The notebook categorizes work into four folders: problems, graphs, tests, and documents.
Upon needing help solving a problem, the student would click on the problem button on the toolbar or on the problem folder. A toolbox of algebraic symbols appears making it easy to enter those problems with proper nomenclature. Once the problem is entered, the student clicks on the answer button and then sees how the problem is solved step by step. The computer may prompt the student to specify which variable to solve for. If enough information was entered within the equations provided to solve for the variables, the graphing function of the program becomes enabled. Buttons on the toolbars are only enabled as they apply within the context of the student's work. If the user goes to Tools-Options, he can also set whether to see step by step solutions, explanations, or just the answer.
The application is very valuable in its graphing capabilities. The student may enter more than ten equations into the user interface to have plotted on the graph paper in the center of the screen. Color coding of each equation makes interpreting the graph very user friendly.
In addition to the software's usefulness as a problem set assistant, it also auto-generates tests on any of the algebraic topics contained in the database. Within the test generator, the user can specify the number of problems and level of difficulty. This can then be printed as a paper copy or be answered on screen using a multiple choice selection. If the multiple choice, on-screen test format is chosen the computer will grade the student's work when he is finished.
The document folder can be used to generate custom assignments, quizzes, tests, handouts, or for the student to make notes to himself. The quick insert tool is available so that proper math notation and symbols can be used in creating these documents.
This mom would give this product a thumbs up, especially if one of your concerns in homeschooling through high school is the fear in teaching higher level math. Bagatrix, Inc. continues this product line through Algebra 2, Trigonometry, and Calculus. The CD case that the software ships with states that it is compatible with Windows 2000/XP/2003. We have a Windows Vista, 64-bit system and did not run into any installation issues, except for the optional loading of a particular version of the .NET framework which is not compatible with our version of windows. This did not affect the functionality of the software at all. |
Chapter
1: The Language of Algebra (Page 31) Deduction
and Induction
Read and learn about topics such as the discipline of logic, the structure of argument, recognizing arguments, deductive inferences, inductive inferences, and truth and validity.
Chapter 3: Addition and Subtraction Equations
(Page 111) Arithmetic
Sequences Explicit definition of a sequence, finding the sum of a sequence,
and the recursive definition of a sequence are covered on this page. |
I'm getting really bored in my math class. It's simplify radical expression calculator, but we're covering higher grade syllabus. The topics are really complicated and that's why I usually sleep in the class. I like the subject and don't want to drop it, but I have a real problem understanding it. Can someone help simplify radical expression calculator class will be the best one.
Hello, just a year ago, I was stuck in a similar situation. I had even considered the option of dropping math and selecting some other subject. A colleague of mine told me to give one last chance and gave me a copy of Algebra Buster. I was at comfort with it within few minutes. My ranks have really improved within the last year.
inequalities, like denominators and adding matrices were a nightmare for me until I found Algebra Buster, which is truly the best math program that I have come across. I have used it through many math classes – Algebra 2, College Algebra and Remedial Algebra. Just typing in the algebra problem and clicking on Solve, Algebra Buster generates step-by-step solution to the problem, and my math homework would be ready. I highly recommend the program. |
Buy print & eBook together and save 40%
Description
Theory and application of a variety of mathematical techniques in economics are presented in this volume. Topics discussed include: martingale methods, stochastic processes, optimal stopping, the modeling of uncertainty using a Wiener process, Itô's Lemma as a tool of stochastic calculus, and basic facts about stochastic differential equations. The notion of stochastic ability and the methods of stochastic control are discussed, and their use in economic theory and finance is illustrated with numerous applications.
Quotes and reviews
@from:R. Kihlstrom @qu:This book will almost certainly become a basic reference for academic researchers in finance. It will also find wide use as a textbook for Ph.D. students in finance and economics. @source:Mathematical Reviews |
Conference Proceedings Detail Page
This presentation from the 2006 PTEC Conference outlines the PRISMS Curriculum developed at the University of Northern Iowa. Information is presented about the strategies, resources, and activities in this program designed for high school students with a year of algebra.
2006 PTEC National Conference
Part of the PTEC series
Fayetteville, Arkansas:
March 24-25, 2006
Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications. |
McGraw-Hill Math Grade 2 by Editors McGraw-Hill
Now students can bring home the classroom expertise of McGraw-Hill to help them sharpen their math skills! McGraw-Hill's Math Grade 2 helps your elementary Know It!" features reinforce mastery of learned skills before introducing new material "Reality Check" features link skills to real-world applications "Find Out About It" features lead students to explore other media "World of Words" features promote language acquisition Discover more inside: A week-by-week summer study plan to be used as a "summer bridge" learning and reinforcement program Each lesson ends with self-assessment that includes items reviewing concepts taught in previous lessons Intervention features address special-needs students
Comment on McGraw-Hill Math Grade 2 by Editors McGraw-Hill
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Vibrant color photographs and simple sentences introduce students to a variety of graphs. Students will love learning about graphs while improving their reading skills. This series meets both math and reading standards.
Vibrant color photographs and simple sentences introduce students to a variety of graphs. Students will love learning about graphs while improving their reading skills. This series meets both math and reading standards.
This comprehensive new edition has been developed specifically for the Australian Curriculum. Covering all the content and requirements of the Year 9 curriculum this accessible text has also been written to cater for a wide range of ability levels |
The mission of the Mathematics discipline is to
advance knowledge of mathematics: by teaching
mathematics and its processes, by research in
mathematics and mathematical pedagogy, and by
dissemination of this knowledge to students and
the community we serve.
Historically, the study of mathematics has been
central to a liberal arts education. The
mathematics curriculum serves as an integral part
of students' active pursuit of a liberal arts
education.
The mathematics program serves
students who major or minor in mathematics,
seek secondary mathematics teaching licensure,
major or minor in programs that require a
mathematical background, or wish to fulfill
components of a general education.
The mathematics curriculum is designed to help
students develop competence in mathematical
techniques and methods; to sharpen the
students' mathematical intuition and abstract
reasoning as well as their reasoning from
numerical data; to encourage and stimulate
the type of independent thinking required for
research beyond the confines of the textbook; and
to provide students
with the basic knowledge and skills to make
mathematical contributions to modern society.
The program seeks to enable students to see and
communicate how the development of
mathematics has been part of the development of
several civilizations and is intimately interwoven
with the cultural and scientific development of
these societies. The curriculum prepares students
to enter graduate school, pursue careers in applied
mathematics, or teach mathematics.
The Mathematics Discipline has seven full-time
tenured or tenure-track faculty with a wide range
of background and expertise. All mathematics faculty have years
of teaching experience and at UMM, they teach
all Math courses from the freshmen level to the senior level.
In particular, faculty members with expertise in pure mathematics
are able to offer advanced courses in
Abstract Algebra ,
Combinatorics,
Differential Geometry,
Number Theory,
Real & Complex Analysis, and
Topology; while
faculty members with expertise in applied mathematics
are able to offer advanced courses in
Partial Differential Equations,
Mathematical Modeling,
Optimization and Operations Research,
Applications of Graph Theory, and
Applied Numerical Analysis.
In addition to being able to offer a plethora of advanced mathematics
courses, with their diverse expertise, UMM's mathematics faculty
are able to successfully involve their students
in undergraduate research projects specifically in
almost all of the aforementioned areas in mathematics.
Here are a few typical questions asked about UMM's Mathematics
Program: |
Textbook: Concepts of Mathematical Modeling by Walter J. Meyer (Dover Edition, ISBN
0486435156) Search multiple booksellers here
Amazon offers to students a free one-year subscription to "Amazon Prime", which allows you to receive books sold directly from Amazon within two business days for free! Sign up here. Make sure your order says "Eligible for Amazon Prime / Free Super Saver Shipping". Our book is here Software: Mathematica (learn about Mathematica access on MyQC)
This class covers: Various sections of the book, along with Mathematica tutorials.
Homework:
Homework is due weekly and is the key component to your learning of
the material, so DO IT!!! Each homework will be posted on the course web page the previous week.
Written Homeworks:
The written homeworks contribute towards your homework grade.
They will consist (normally) of five questions. I expect all answers to be fully justified, unless otherwise
noted. Each of the problems will be graded on a scale from 0-4, as follows:
4
**Perfect**
3
A well-written solution with slight errors.
2
A good partial solution.
1
A very partial solution or a good start.
0
No work, a weak start, or an unsupported answer.
I require you to follow some relatively strict guidelines.
It is especially important that your homework be legible and clearly presented, or I may not grade it.
It is important to learn how to express yourself in the
language of mathematics. In the homework, you should show your work and explain how
you did the problem. This is the difference between an Answer
and a Solution. It should be obvious to the person reading the homework how you
went about doing the problem. This will often involve writing out explanations for your
work in words. Imagine that you need an example to help refresh your memory for another
class in six months!
Late Written Homework:
I understand that outside factors may affect your ability to turn in
your homework on time. During the semester you will be allowed five total grace days. If a homework is due on
Wednesday and you turn it in on Friday, this counts as two of your five grace days. Once you have zero grace
days, I will not accept late homework. If you are not planning to be in class, let me know and get it to
me beforehand. This is your responsibility. I can accept clearly scanned homework by email.
Final Project:
In addition to the homeworks, you will be working in a group of around three students, where you will use the
techniques from class to model a real-life situation of your choosing. Click here for more information.
Study Groups:
It is useful to form study groups to work on homework.
Be sure to include an acknowledgment to your groupmates on your homework.
At the beginning the problems will seem easy enough to plug and chug on your own,
but as the quarter progresses the questions become quite complex indeed.
Study groups good. Copying solutions bad. When a group works on a problem, everyone can participate.
But when you write up the answers to the problems, write it up in your own way.
I will take off points from all parties if multiple solutions are the same.
Study groups have several advantages:
You can practice and learn how to solve more problems in less time (doing as many problems as possible is the key to success),
The best way to really learn something is to explain it to someone else (misunderstandings that you never knew you had will appear under someone else's questioning),
No two people solve the same problem the same way; in a group, you may discover new and more efficient ways to solve the same problem,
seeing that others also struggle with this material helps to put your own level of understanding in a better perspective and will hopefully reduce some of your
anxiety,
in making the homework assignments, I assume that you will be working in groups.
Exams:
There will be two exams during the semester.
They will be a class period in length and no calculators or study aides are allowed (or are necessary).
There will be no make-up exam except in the case of a documented emergency.
In the event of an unavoidable conflict with the midterm (an athletic meet, wedding, funeral, etc...),
you must notify me at least one week before the date of the exam so that we can arrange for you
to take the exam BEFORE the actual exam date.
I am happy to help you with your homework and other class-related questions during my office hours. I have official
office hours as posted on my schedule. In addition, you are welcome to make an
appointment or stop by my office in Kiely 409 at any time.
Cheating/Plagiarism: DON'T DO IT! It makes me very mad and very frustrated when students cheat. Cheating is the quickest way to lose the respect that I have for each student at the beginning of the semester. Both receiving and supplying the answers on an exam is
cheating. Copying homework solutions is considered cheating. Copying text from sources for your project is cheating. I take cheating very seriously. If you cheat, you will
receive a zero for the homework/exam and I will report you to the academic integrity committee in the Office of Student
Affairs. If you cheat twice, you will receive a zero for the class.
**Please do realize that working together on
homework as described above is not cheating.** |
Stoneham, MA Math these and other topics:
- math for finance including interest and annuities
- systems of linear equations and matrices
- linear programming
- Markov chains
- difference equations
- logic and sets
- probability and elementary statistics
Matrix methods and Linear Progra |
ALGEBRA I-P, ALGEBRA I-P/Freshman Focus
(VHS/WCW) (1 yr) 9th – 12th grade Prerequisite: Placement to be determined by a grade earned in a pre-algebra curriculum, state assessment results (STAR), district assessments, and teacher recommendation. Some students will be placed in one period of Algebra I-P while other students will be recommended for one period of Algebra I-P and one period of Algebra I-Support.
A rigorous two-semester course in first-year algebra. Topics include: operations in algebra, polynomials, special products and factors, formulas, linear equations, graphs, fractional equations, powers, roots, radicals, quadratic equations, simultaneous equations, proportions, and verbal problems. Emphasis is placed on preciseness and consistency in language and on the development of mathematical structure. Algebra I-P/Freshman Focus is designed to meet all of the above and is designed for the English learner students.
CONCEPTUAL GEOMETRY
students with a grade of "C" or "D" in Algebra I-P with an
Algebra I-Support class and/or Math Department approval. Students with a D- or below are highly recommended to repeat Algebra I.
This is a survey of the most important concepts in college prep Geometry. This .course will provide an informal introduction to those topics covered in more depth in Geometry-P while concurrently reviewing the essential topics that will be covered in Algebra I-P
The scope and sequence of this course is designed to bridge the gap between Algebra and Geometry, allowing time for students to master and extend concepts necessary for their success in Geometry and further study in Mathematics.
In addition, students will be reviewing topics covered on the CAHSEE exam.
GEOMETRY-P
This course is designed for students to develop the ability to discern, conjecture, reason, invent, and construct mathematically in real-life applications. Two-dimensional geometry, coordinate geometry, brief units in solid geometry, deductive reasoning, and area probability will be introduced. This course differentiates clearly between giving examples that support a conjecture and giving a proof on a conjecture. This course will provide for the consistent use of algebra and a full range of problem-solving skills in the development of geometric concepts. In addition, students will communicate their knowledge of basic skills, understanding of concepts, and appropriate applications.
ALGEBRA II-P
This course is an in-depth study of the topics listed in Algebra I-P, and an introduction to the theory of functions, probability, sequences, series, complex numbers, matrices, properties of conic sections, and exponential, logarithmic, and trigonometric functions. Critical thinking and problem solving skills will be emphasized.
The course begins with a short review of functions and their properties. Circular functions, their inverses applications.
TRIGONOMETRY/ANALYSIS-HP
The course begins with a short review of functions and their properties. Circular functions, their inverses, its applications. Students who successfully complete this course will be properly prepared to take a college level calculus course.
This course is primarily designed to prepare students for the AP test in statistics. Because many college majors require the use of statistics and/or a strong understanding of statistical data, this course's secondary purpose is to provide students with the tools necessary for success at the college level. The last purpose is to expose students to the uses of statistics in every day life and how different professions employ statistics in their work.
AP CALCULUS AB
AP Calculus AB is designed to be the high school equivalent of the "calculus for math and/or science majors" at the college or university level. Students will take the AP Exam or an equivalent exam as part of their final course grade.
MATH EXIT EXAM BASICS
(VHS/WCW) (1 sem - may be repeated with instructor's permission) 11th – 12th grade Prerequisite: Counselor recommendation or failure to pass the Mathematics part of the
CAHSEE
This course is designed to specifically address the mathematics skills necessary to pass the California High School Exit Exam (CAHSEE), a graduation requirement. Seniors as well as retained juniors who have not passed the CAHSEE will be enrolled in this course unless a written waiver from a parent/guardian is received by the school. Students in the spring semester of their junior year are also eligible to enroll in this course.
BUSINESS MATH
(VHS/WCW) (1 yr) 10th – 12th grade Prerequisite: None
Business Math fulfills one year of the graduation requirements in mathematics. This course reviews and fosters improvement of basic computational skills (addition, subtraction, multiplication, and division) involving whole numbers, decimals, percentages, and fractions. Students apply these skills to practical business problems. Calculators and/or computers are used for some problem solving activities. This course is recommended for students preparing to major in business in college as well as for vocational preparation.
(This course is also listed under Business Department) |
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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 [email protected], 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) |
GeoGebra is a dynamic mathematics software that
joins geometry, algebra, and calculus. Two views
are characteristic of GeoGebra: an expression in
the algebra window corresponds to an object in the
geometry window and vice versa |
Wikipedia in English (2)
Algebra, the foundation for all higher mathematics, is taught here both for beginners and for those who wish to review algebra for further work in math, science and engineering. This superior study guidethe first edition sold more than 600,000 copies!includes the most current terminology, emphasis and technology. It treats many subjects more thoroughly than most texts, making it adaptable for any course and an excellent reference and bridge to further study. Also available as a Schaum's Electronic Tutor.
ALGEBRA. "Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately, for you, there's "Schaum's Outlines". More than 40 million students have trusted "Schaum's" to help them succeed in the classroom and on exams. "Schaum's" "Schaum's Outline" gives you: practice problems with full explanations that reinforce knowledge; coverage of the most up-to-date developments in your course field; and, in-depth review of practices and applications. Fully compatible with your classroom text, "Schaum's" highlights all the important facts you need to know. Use "Schaum's" to shorten your study time - and get your best test scores! "Schaum's Outlines" means problem solved.… (more) |
@article {MATHEDUC.02335168,
author = {Antoniazzi, Stefano},
title = {An experience of "discrete" calculus. (Un'esperienza di calcolo 'discreto'.)},
year = {2000},
journal = {L'Insegnamento della Matematica e delle Scienze Integrate},
volume = {23B},
number = {3},
issn = {1123-7570},
pages = {259-269},
publisher = {Centro Ricerche Didattiche Ugo Morin, Paderno del Grappa TV},
abstract = {In this paper we report about a didactical experience in the field of algebra realized in a first class of secondary school. The topic concerns the use of the ``Ruffini's method'' as a technique for assessing a polynomial (not only for doing the divisions) and the ``discovery'' of its computation efficiency/complexity. During the experience the students have obtained three different ways for expressing the sum of the natural numbers from 1 to n. (orig.)},
msc2010 = {H23xx},
identifier = {2000e.03533},
} |
Course Descriptions
Following certain course descriptions are the designations: F (Fall), Sp (Spring), Su (Summer) . These
designations indicate the semester(s) in which the course is normally offered and are intended as an aid to students planning their programs of study.
202 Mathematical Concepts for
Preschool through Primary Teachers-4 hours. This course includes extensions of the fundamental concepts studied in Math 103 with emphasis on the procedures as they relate to the early elementary student. Topics include processes in advanced counting, the four basic operations, elementary fractions, decimals, probability, statistics, angles and other geometric concepts beyond shapes. The use of manipulatives and technology will support the teaching and learning for this course. Enrollment is open to students in the early elementary program only. Prerequisite:
Math 103 (grade of C or better). This course satisfies the A2 category of the University Core Curriculum.
203 Mathematics for Elementary Teachers II-This
course is the second in a two-course sequence designed to enhance the
conceptual understanding and processes of the reasoning, algebraic
reasoning, geometry, measurement, data analysis, and probability. The
use of manipulatives and technology will support learning and teaching
of the topics studied. Enrollment is only open to students seeking a
degree in elementary education or a related degree. This course
satisfies the A2 category of the University Core Curriculum. Prereq: C
or better in Math 103.
213 Algebraic Concepts for
Teachers-3
hours. This course is designed to develop conceptual understandings for
topics in algebra and number theory found in the middle-grades math
curriculum. This course will include the study of sequences, the binomial
theorem, fundamental theorem of arithmetic, modular arithmetic, systems of
linear equations, matrix arithmetic and algebra, and coding with matrices;
the use of manipulatives and technology will support the teaching and
learning of these topics. Prerequisite: MATH 115
(grade of C or better) or MATH 118
(grade of C or better).
215 Survey of Calculus-3 hours. An
introduction to calculus and its applications in business, economics,
and the social sciences. Not applicable to the Mathematics major or
minor. This course satisfies the A2 category of the University Core Curriculum. Prerequisite: MATH 111
(grade of C or better). NOTE: A TI-83 or TI-83 Plus graphing calculator is required for this course. F, Sp, Su Sample MATH 215 Syllabus
230 Calculus I-4 hours. The theory of limits, differentiation, successive differentiation, the definite integral, indefinite integral, and applications of both the derivative and integral. This course satisfies the A2category of the University Core Curriculum. Prerequisite: MATH 115 (grade of C or better), MATH 118 (grade of C or better), satisfactory placement score or consent of instructor. NOTE: A TI-83 or TI-83 Plus graphing calculator is recommended for this course. F, Sp, Su Sample MATH 230 Syllabus
238 Data Analysis and Probability for Teachers-3
hours. This course is designed to develop conceptual understanding for topics in
data analysis and probability. The study of selecting and using appropriate
statistical methods to analyze data, the developing and evaluating of inferences
and predictions that are based on data, and the applying basic concepts of
probability will be covered in this class. The use of manipulatives and
technology will support learning and teaching of the topics studied.
291 Mathematics for Secondary
Teachers- 3 hours. This course was designed to enhance the
conceptual and procedural understandings of the mathematics that is
taught at the secondary level--number theory, algebra, geometry,
functions, probability and statistics. Concepts and problems will be
viewed from an advanced perspective where the students will investigate
alternate definitions and approaches to mathematical ideas; consider
proofs, extensions and generalizations of familiar theorems; investigate
multiple approaches to problem solving, and study connections between
topics from different courses. Understanding and communication of
mathematical concepts and processes will be emphasized; the use of
technology and manipulatives will be used when appropriate. This course
will not serve as an upper-level mathematics elective for the major or
minor in mathematics. Prerequisite: Math 253, grade C or better. |
Automatic Learning Guide for Mathematical Word Problem
Mathematical word problems often pose a challenge to most students. This phenomenon is because solving a word problem requires skills in reading and comprehending the text of the problem, identifying the question that needs to be answered, sorting the important information from the distracting information, selecting the mathematical operations to be used and finally creating and solving a numerical equation. Therefore, we proposed MATHMASTER, the system that was designed to help a student practice to understand mathematical word problems and translate the problem into appropriate equation(s). MATHMASTER guides students through step-by-step instructions at their own pace and at a level adapted to help each student toward the solution.
At the time of present study, Wanintorn Supap is a Ph.D. candidate of the Institute for Innovative Learning, Mahidol University, Thailand. Supap received B.Sc. in science (Mathematics) and Diploma in Teaching Profession from Mahidol University in Thailand. She has received a scholarship from the Project for Promotion of Science and Mathematics Talented Teacher of the Institute for the Promotion of Teaching Science and Technology, Thailand.
Kanlaya Naruedomkul is an associate professor of Mathematics Department at Mahidol University, Bangkok, Thailand. Her research interests in center on artificial intelligence applications, including automated natural language processing, computational linguistics, and machine translation. Naruedomkul received a PhD in computer science from the University of Regina.
Nick Cercone is a professor of computer science and engineering at York University, Toronto, Ontario, Canada. His research interests include natural language processing, knowledge-based systems, knowledge discovery in databases, data mining, and design and human interfaces. Cercone received a PhD in computing science from the University of Alberta. He is a member of the ACM and Fellow of the IEEE. |
Railroad Statistics was in honors and AP English classes. In college, I have continued to study English and have a total of 9 credits that are from English classes. I am, essentially a mathematics major and have been taking math classes for a total of six semesters in college and my basic as well as advanced math skills are very strong.
...The topics covered in a discrete math course vary depending on where the course is taken. Since discrete numbers are those that can be counted, topics in discrete math revolve around these numbers. Typically topics include voting theory, combinatorics, matrices, fair division, probability (including Venn diagrams), and graph theory. |
Sequences and Series
Sequences and Series teaches students how to define, notate and interpret different types of series and sequences, such as arithmetic and geometric, and how to use mathematical induction in proofs and on their homework. |
Elementary Algebra W/PAC-Now
9780495389606
ISBN:
0495389609
Edition: 4 Pub Date: 2008 Publisher: Cengage Learning
Summary: This text blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, and communication skills. With an emphasis on the 'language of algebra', the author's foster students' ability to translate English into mathematical expressions and equations Major moisture staining to textblock Book is ACCEPTABLE with noted wear to cover and pages. Binding intact. May contain highlighting, inscriptions or notationsWell-worn copy. Major moisture staining to textblock Book is ACCEPTABLE with noted wear to cover and pages. Binding intact. May contain highlighting, inscriptions or notation |
Mathematics
Math has often been called the queen of the sciences, and for good reason. From the scientific study of subatomic particles to the exploration of our vast universe, mathematics is the language that must be spoken. Did you know that in the theory of black holes, mathematical division by zero signifies the existence of these astounding features of our universe?
If you want to work on a math problem right now that will either teach you something new or review a fundamental skill which you have most likely forgotten, click on any one of the math links to the right.
There are two websites that we recommend for those of you interested in math; they are the American Mathematical Society and the Mathematical Association of America. However, our absolute favorite is MIT Open Courseware, where you can actually sit in on math courses taught by MIT professors by viewing the videos they made of the lectures, right at home on your computer. We sampled the one on differential equations, and it was superb!
Our problem solvers and tutors are experts in all areas of math, including very advanced topics. And, if we don't have the specialist to handle your topic when you submit, we'll get one! It's that simple. No other tutoring service can say that. |
Mathematics in Non-math Courses
In introductory courses such as chemistry, economics,
political science, and psychology, you will often see discussions
of examples and topics that require an understanding of concepts
in mathematics such as decimals, percents, ratios, and proportions.
While the examples below are taken directly from different economics
textbooks, they demonstrate the kinds of skills that you will
be required to use in many non-math introductory courses.
Example
Rising divorce rates and births
out of wedlock have reduced married couples as a percentage of
total families from 70% in 1970 to 60% in 1990. Further, the
percentage of married-couple households in which the wife was
working increased by roughly 50% over the last two decades. These
trends mean...
The paragraph above is part of a discussion on the economic
impact of decline in married couple households. As we can see,
the use of percentage is central to this discussion, and without
a full understanding of percents this discussion would be difficult
to fully understand.
Example
The ratio of new deposits to
the increase in reserves is called the money-supply multiplier.
In the simple case analyzed here, the money-supply multiplier
is equal to:
Ratios and decimals can be found in discussion in text books.
They also often occur in conjunction with the use of percents.
The paragraph above came from a discussion on the money-supply
multiplier which uses ratios and proportions.
Decimals, percents, ratios, and proportions come up again and
again in both everyday and academic life. Whether they are used
in discussions as the ones shown above, or in tables, charts,
and graphs (This will be discussed in Book III of this series.),
understanding how to working with these concepts is important
to your success in your introductory courses.
In many introductory courses you will come across decimals,
percents, ratios, and proportions in discussions and be asked
to perform calculations using these. This book provides you with
the math skills you will need for these courses. |
Thompsons Calculus?re the starter, the playbook is in your hands, you...
...During the last century comprehension lesson/s usually comprised students answering teachers' questions, writing responses to questions on their own, or both. There is not a definitive set of strategies, but common ones include summarizing what you have read, monitoring your reading to make sure... design of parts and assemblies.
...My I... |
Tables, Charts, and Graphs
Integrate a real-world, problem-solving focus into math classes! Covers key middle school and high school topics in context of everyday life scenarios Teachs students to create, read, and interpret a variety of visual presentations
How to Use This Series
p. v
Foreword
p. vi
Tables
Reading Tables
Quilting
p. 1
Hat Sizes
p. 4
Reading a Nutrition Table
p. 6
Stock Quote Tables
p. 9
Tax Tables
p. 12
Lumber Inventory
p. 15
Box Scores
p. 18
Making Tables
Making a Nutrition Table
p. 21
Creating Tax Tables
p. 24
Postal Rates
p. 26
Loan Payments
p. 28
Charts
Reading Charts
Genealogy (Reading Family Trees)
p. 30
Reading Work Schedules
p. 33
The Marker Game (Grid Charts)
p. 36
Reading PERT Charts
p. 39
Making Charts
The Electoral College (Making Colored Graphics Charts)
p. 42
Making Work Schedules
p. 45
Creating PERT Charts
p. 48
Logic Puzzles (The Grid Solution Method)
p. 50
Graphs
Reading Graphs
Class President Election (Pie Charts and Bar Graphs)
p. 52
Rating Car Traits (Augmented Bar Graphs)
p. 54
Reading Stock Graphs (Augmented Vertical-Line Graphs)
p. 56
Grading on a Curve (Stem-and-Leaf Plots)
p. 59
Making Graphs
Baseball Attendance (Scatter Plots)
p. 61
Average Rental Prices (Box-and-Whisker Plots)
p. 64
Is It Steroids? (Broken-Line Graphs)
p. 66
Charting Stock Performance (Augmented Vertical-Line Graphs)
p. 68
Table of Contents provided by Ingram. All Rights Reserved.
List price:
$21.00
Edition:
2nd
Publisher:
Walch Education
Binding:
Perfect
Pages:
70
Size:
8.50" wide x 10 |
Get Math Answers
Maths is considered to be a very difficult subject by most of the students. Mathematics is full of concepts. Each concept has loads of exercises and problems. These problems should be understood properly and should be solved systematically to get right answer and hence to get expertise in a particular topic . Sometimes, students get stuck in the question and do not get the clue how to solve it. Sometimes, even after getting the clue, they are not able to reach at right answer.
In this difficult situation, someone is required to help students. Tutor Vista provides online help in order to get answers of math problems. Step-by-step answers of math problems are available at our sites. All that is needed to be done is to go to the right section about which help is required. Our online tutors are available to help you out with step-by-step answers within least possible time. Our detailed solutions to the questions make math learning easy which makes you equipped with better and deeper understanding of math.
Math Answers Step by Step
From Framing of Formulas to Expansions, Indices, Linear Equations to Factorization and Quadratic Equations you get all Math answers online using our well structured and well thought out Math tutoring program. Students get not just the answer but answers step by step. Below is provided a demo example of getting math answers step by step from us: |
Calculus: Single Variable (5th Edition)
Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique.
Ebook details ISBN : 0470089156 | December 3, 2008 | 739 pages | PDF | 22MB
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i just recently discovered you from the top 100 ebook list on the TPB list, was pleasantly surprised to see that from the way you are going you are a future popular legend here....pls i have some requests-the baroness comics and ebooks are very raunchy , do you have any?. pls upload any Nick carter-killmaster novels too.thanks in advance
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Single Variable Calculus
9780495012337
ISBN:
0495012335
Edition: 6 Pub Date: 2007 Publisher: Thomson Learning
Summary: Study smarter and work toward the grade you want with this helpful guide. You'll find a short list of key concepts; a short list of skills to master; a brief introduction to the ideas of each section; an elaboration of the concepts and skills, including extra worked-out examples; and links in the margin to earlier and later material in the text and Study Guide |
1111780706
9781111780708
College Algebra: This text bridges the gap between traditional and reform approaches to algebra encouraging students students' majors. «Show less
College Algebra: This text bridges the gap between traditional and reform approaches to algebra encouraging students to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling,... Show more»
Prologue: Algebra and Alcohol
Data, Functions, and Models
Making Sense of Data
Analyzing One-Variable Data
Analyzing Two-Variable Data
Visualizing Relationships in Data
Relations: Input and Output
Graphing Two-Variable Data in a Coordinate Plane
Reading a Graph
Equations: Describing Relationships in Data
Making a Linear Model from Data
Getting Information from a Linear Model
Functions: Describing Change
Definition of Function
Which Two-Variable Data Reprsent Functions?
Which Equations Represent Functions?
Which Graphs Represent Functions?
Four Ways to Represent a Function
Function Notation: The Concept of Function as a Rule
Function Notation
Evaluating Functions---Net Change
The Domain of a Function
Piecewise Defined Functions
Working with Functions: Graphs and Graphing Calculators
Graphing a Function from a Verbal Description
Graphs of Basic Functions
Graphing with a Graphing Calculator
Graphing Piecewise Defined Functions
Working with Functions: Getting Information from the Graphs
Reading the Graph of a Function
Domain and Range from a Graph
Increasing and Decreasing Functions
Local Maximum and Minimum Values
Working with Functions:Modeling Real-World Relationships
Modeling with Functions
Getting Information from the Graph of a Model
Making and Using Formulas
What is a Formula?
Finding Formulas
Variable with Subscripts
Reading and Using Formulas
Review
Test
Bias in Presenting Data
Collecting and Analyzing Data
Every Graph Tells a Story
Linear Functions and Models
Working with Functions: Average Rate of Change
Average Rate of Change of a Function
Average Speed of a Moving Object
Functions Defined by Algebraic Expressions
Linear Functions: Constant Rate of Change
Linear Functions
Linear Functions and Rate of Change
Linear Functions and Slope
Using Slope and Rate of Change
Equations of Lines: Making Linear Models
Slope-Intercept Form
Point-Slope Form
Horizontal and Vertical Lines
When is the Graphp of an Equation a Line?
Varying the Coefficients: Direct Proportionality
Varying the Constant Coefficient: Parallel Lines
Varying the Coefficient of x: Perpendicular Lines
Modeling Direct Proportionality
Linear Regression: Fitting Lines to Data
The Line That Best Fits the Data
Using the Line of Best Fit for Prediction
How Good is the Fit? The Correlation Coefficient
Linear Equations: Getting Information from a Model
Linear Equations: Where Lines Meet
Where Lines Meet
Modeling Suppply and Demand
Review
Test
When Rates of Change Change
Linear Patterns
Bridge Science
Correlation and Causation
Fair Division of Assets
Exponential Functions and Models
Exponential Growth and Decay
An Example of Exponential Growth
Modeling Exponential Growth: The Growth Factor
Modeling Exponential Growth: The Growth Rate
Modeling Exponential Decay
Exponential Model: Comparing Rates
Changing the Time Period
Growth of an Investment: Compound Interest
Comparing Linear and Exponential Growth
Average Rate of Change and Percentage Rate of Change
Comparing Linear and Exponential Growth
Logistic Growth: Growth with Limited Resources
Graphs of Exponential Functions
Graphs of Exponential Functions
The Effect of Varying a or C
Finding an Exponential Function from a Graph
Fitting Exponential Curves to Data
Finding Exponential Models for Data
Is an Exponential Model Appropriate?
Modeling Logistic Growth
Review
Test
Extreme Numbers: Scientific Notation
So You Want to Be a Millionaire?
Exponential Patterns
Modeling Radioactivity with Coins and Dice
Logarithmic Functions and Exponential Models
Logarithmic Functions
Logarithms Base 10
Logarithms Base a
Basic Properties of Logarithms
Logarithmic Functions and their Graphs
Laws of Logarithms
Laws of Logarithms
Expanding and Combining Logarithmic Expressions
Change of Base Formula
Logarithmic Scales
Logarithmic Scales
The pH Scale
The Decibel Scale
The Richter Scale
The Natural Exponential and Logarithmic Functions
What is the Number?
The Natural Exponential and Logarithmic Functions
Continuously Compounded Interest
Instantaneous Rates of Growth or Decay
Expressing Exponential Models in Terms of e
Exponential Equations:Getting Information from a Model
Solving Exponential and Logarithmic Equations
Getting Information from Exponential Models: Population and Investment
Getting Information from Exponential Models: Newton's Law of Cooling
Finding the Age of Ancient Objects: Radiocarbon Dating
Working with Functions: Composition and Inverse
Functions of Functions
Reversing the Rule of a Function
Which Functions Have Inverses?
Exponential and Logarithmic Functions as Inverse Functions
Review
Test
Super Origami
Orders of Magnitude
Semi-Log Graphs
The Even-Tempered Clavier
Quadratic Functions and Models
Working with Functions: Shifting and Stretching
Shifting Graphs Up and Down
Shifting Graphs Left and Right
Stretching and Shrinking Graphs Vertically
Reflecting Graphs
Quadratic Functions and Their Graphs
The Squaring Function
Quadratic Functions in General Form
Quadratic Functions in Standard Form
Graphing Using the Standard Form
Maxima and Minima: Getting Information from a Model
Finding Maximum and Minimum Values
Modeling with Quadratic Functions
Quadratic Equations: Getting Information from a Model
Solving Quadratic Equations: Factoring
Solving Quadratic Equations: The Quadratic Formula
The Discriminant
Modeling with Quadratic Functions
Fitting Quadratic Curves to Data
Modeling Data with Quadratic Functions
Review
Test
Transformation Stories
Toricelli's Law
Quadratic Patterns
Power, Polynomial, and Rational Functions
Working with Functions: Algebraic Operations
Adding and Subtracting Functions
Multiplying and Dividing Functions
Power Functions: Positive Powers
Power Functions with Positive Integer Powers
Direct Proportionality
Fractional Positive Powers
Modeling with Power Functions
Polynomial Functions: Combining Power Functions
Polynomial Functions
Graphing Polynomial Functions by Factoring
End Behavior and the Leading Term
Modeling with Polynomial Functions
Fitting Power and Polynomial Curves to Data
Fitting Power Curves to Data
A Linear, Power, or Exponential Model?
Fitting Polynomial Curves to Data
Power Functions: Negative Powers
The Reciprocal Function
Inverse Proportionality
Inverse Square Laws
Rational Functions
Graphing Quotients of Linear Functions
Graphing Rational Functions
Review
Test
Only in the Movies?
Proportionality: Shape and Size
Managing Traffic
Alcohol and the Surge Function
Systems of Equations and Data in Categories
567
Systems of Linear Equations in Two Variables
Systems of Equations and Their Solutions
The Substitution Method
The Elimination Method
Graphical Interpretation: The Number of Solution
Applications: How Much Gold is in the Crown?
Systems of Linear Equations in Several Variables
Solving a Linear System
Inconsistent and Dependent Systems
Modeling with Linear Systems
Using Matrices to Solve Systems of Linear Equations
Matrices
The Augmented Matrix of a Linear System
Elementary Row Operations
Row-Echelon Form
Reduced Row-Echelon Form
Inconsistent and Dependent Systems
Matrices and Data in Categories
Organizing Categorical Data in a Matrix
Adding Matrices
Scalar Multiplication of Matrices
Multiplying a Matrix Times a Column Matrix
Matrix Operations: Getting Information from Data
Addition, Subtraction, and Scalar Multiplication
Matrix Multiplication
Getting Information from Categorical Data
Matrix Equations: Solving a Linear System
619
The Inverse of a Matrix
Matrix Equations
Modeling with Matrix Equations
Review
Test
Collecting Categorical Data
Will the Species Survive?
637
Algebra Toolkit A: Working with Numbers
Numbers and Their Properties
The Number Line and Intervals
Integer Exponents
Radicals and Rational Exponents
Algebra Toolkit B: Working with Expressions
Combining Algebraic Expressions
Factoring Algebraic Expressions
Rational Expressions
Algebra Toolkit C: Working with Equations
Solving Basic Equations
Solving Quadratic Equations
Solving Inequalities
Algebra Toolkit D: Working with Graphs
67
The Coordinate Plane
Graphs of Two-Variable Equations
Using a Graphing Calculator
Solving Equations and Inequalities Graphically
85
Answers
Index
11 |
Pathways is a Los Angeles area mathematics outreach program based in the Department of Mathematics at Harvey Mudd College. All of our volunteers are professional mathematicians who are eager to share their love of mathematics with elementary, junior high, and high school students.
Details
Our 40-50 minute presentations are designed to expose students to parts of mathematics that are often unseen outside of college, but that are nonetheless accessible and often incredibly eye-opening. There is absolutely no cost for a visit from Pathways, and no group is too big or too small. We are also happy to work with individual teachers to tailor our presentations to meet the needs of different groups.
Interested?
If you are interested in having Pathways visit your class or math club, or if you have any questions about Pathways, please send an email to [email protected]. You may also want to check out our Pathways Presentations page where you can find detailed information (e.g., titles, abstracts, and suggested grade levels) about several of the talks listed to the right. We hope to hear from you soon!
SCHOOLS VISITED
Sage Hill School
The Webb Schools
Claremont High School
Chaparral Elementary School
Rancho Cucamonga High School
Los Altos High School
Harvard-Westlake School
Diamond Bar High School
Bonita High School
Mark Twain Middle School
Ramona Junior High School
Westwood Charter Elementary School
Vistamar School
Foothill Country Day School
Schurr High School
Winward School
Holy Name of Mary Elementary School
Stanton Elementary School
MESA at El Camino College
Magnolia Elementary School
Century Academy for Excellence
Stanton Elementary School
Cortez Mathematics and Science Magnet School
Walnut High School
Alverno High School
Locke High School
Paloma Elementary School
Immaculate Conception Elementary School
FUNDING
Pathways is funded by a grant from the Harvey Mudd College Office of Institutional Diversity. |
More categories you may be interested in:
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GCSE Maths is required by Higher Education establishments and many employers. If you struggled with Maths at school, this course will develop your number skills and help you to gain that vital qualification.
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Did you just miss the UMS score required to give you that all-important Grade C in Maths? Don't despair - this intensive revision course will help you to pass with flying colours in the November re-sits.
By the end of your course, you will be able to work with complex functions and understand how to calculate forces in mechanics. You will cover topics such as geometry, calculus, trigonometry and algebra and gain the ability to manipulate fi...
A LEVEL MATHEMATICS WITH STATISTICS
Level: AS and A2 (Full)
This A level course builds on work covered in GCSE Maths at Higher Level, so you need to be familiar with all the mathematics at this level, and your skills should beAn essential subject for all students, IGCSE Mathematics is a fully examined course which encourages the development of mathematical knowledge as a key life skill, and as a basis for more advanced study. The syllabus aims to build students'... |
FX Emulator
The perfect teaching aid for the classroom! This PC software
replicates the FX-83GT Plus and FX-85GT Plus scientific
calculators, allowing teachers to show the whole class step-by-step
instructions on how to perform calculations and get the most out of
their scientific. |
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This course is an extension of Algebra, Geometry and Trigonometry with the inclusion of a unique set of definitions. This course deals with domain, range, inverse functions, sequence, Binomial expansion, Matrices, Vectors in 2 and 3 dimensions, Integration and Application of integration, probability and statistics, basic coverage of differential calculus, and more.
Class time will be used to review homework questions, introduce "new" concepts, discuss the significance of the concepts, and apply the concepts to solve problems. In addition to learning concepts and solving problems, the students will learn to become comfortable with presenting their problems solving in a methodical manner.
COURSE REQUIREMENTS & REQUIRED MATERIALS
1. TEXT: HAESE & HARRIS, Third edition, ( Mathematics SL)
2. A scientific calculator (graphics if possible)
3. A full-size binder for the purpose of organizing ALL class notes, class handouts, homework assignments, quizzes, and tests.
*** These materials need to be in class with you everyday!
GOALS & OBJECTIVES
1. To be introduced to new mathematical tools and maintain an open mind while learning
3. To demonstrate responsibility, organization, and good study habits.
4. To prepare for advanced courses in both math and science.
5. To sharpen problem -solving skills
6. To begin to develop the ability to think through a solution and present it in an organized, thoughtful, and well-spoken way.
Participation: All students are required to participate in class discussions, offer solutions to problems, and demonstrate their knowledge of the subject at the board.
Homework: Homework is assigned on a daily basis and will be collected every class.
Exams: A test will be given on a weekly basis; tests follow the completion of each chapter.
GENERAL: To be a successful IB candidate you must apply yourself fully and to the best of your abilities at all times and on all assignments. Effort and the application of good work habits also contribute to a good grade. |
Calculus Functions Study Guide
Introduction
Calculus is the study of change. It is often important to know when something is increasing, when it is decreasing, and when it hits a high or low point. Much of the business of finance depends on predicting the high and low points for prices. In science and engineering, it is often essential to know precisely how fast quantities such as temperature, size, and speed are changing. Calculus is the primary tool for calculating such changes.
Numbers, which are the focus of arithmetic, are no longer the objects of our study. This is because they do not change. The number 5 will always be 5. It never goes up or down. Thus, we need to introduce a new sort of mathematical object, something that can change. These objects, the centerpiece of calculus, are functions.
Functions
A function is a way of matching up one set of numbers with another. The first set of numbers is called the domain. For each of these numbers in a set, the function assigns exactly one number from the other set, the range.
For example, the domain of the function could be the numbers 1, 4, 9, 25, and 100; and the range could be 1,2,3,5, and 10. Suppose the function takes 1 to 1,4 to 2, 9 to 3, 25 to 5, and 100 to 10. This could be illustrated by the following:
1 → 1
4 → 2
9 → 3
25 → 5
100 → 10
Because we sometimes use several functions at the same time, we give them names. Let us call the function we just mentioned by the name Eugene. Thus, we can ask, "Hey, what does Eugene do with the number 4?" The answer is "Eugene takes 4 to the number 2."
Mathematicians are notoriously lazy, so we try to do as little writing as possible. Thus, instead of writing "Eugene takes 4 to the number 2," we often write "Eugene(4) = 2" to mean the same thing. Similarly, we like to use names that are as short as possible, such as f (for function), g (for function when f is already being used), h, and so on. The trigonometric functions in Lesson 4 all have three-letter names like sin and cos, but even these are abbreviations. So let us save space and use f instead of Eugene.
Because the domain is small, it is easy to write out everything:
f(1) = 1
f(4) = 2
f(9) = 3
f(25) = 5
f(100) = 10
However, if the domain were large, this would get very tedious. It is much easier to find a pattern and use that pattern to describe the function. Our function f just happens to take each number of its domain to the square root of that number. Therefore, we can describe f by saying:
f(a number) = the square root of that number
Of course, anyone with experience in algebra knows that writing "a number" over and over is a waste of time. Why not just pick a variable to represent the number? Just as f is our favorite name for functions, little x is the most beloved of all variable names. Here is the way to represent our function f with the absolute least amount of writing necessary:
f(x) = √x
This tells us that putting a number into the function f is the same as putting it into √. Thus,
f(25) = √25 = 5 and f(4) = √4 = 2.
Parentheses Hint
It is true that in algebra, everyone is taught "parentheses mean multiplication." This means that 5(2 + 7) = 5(9) = 45. If x is a variable, then x(2 + 7) = x(9) = 9x. However, if f is the name of a function, then f(2 + 7) = f(9) = the number to which f takes 9. The expression f(x) is pronounced "f of x" and not "f times x." This can be confusing, so an apology is necessary. Mathematicians use parentheses to mean several different things and expect everyone to know the difference. Sorry!
Example 1
Find the value of g(3) if g(x) = x2 + 2.
Solution 1
Replace each occurrence of x with 3.
g(3) = 32 + 2
Simplify.
g(3)=9 + 2 = 11
Example 2
Find the value of h(–2) if h(t) = t3 –2t2 + 5.
Solution 2
Replace each occurrence of t with –2.
h(–2) = (–2)3– 2(–2)2 + 5
Simplify.
h(–2) = – 8 – 2(4) + 5 = – 8 – 8 + 5 = –11
Plugging Variables into Functions
Variables can be plugged into functions just as easily as numbers can. Often, though, they can't be simplified as much.
Example 1
Simplify f(w) if f(x) = √x + 2 x2 + 2.
Solution 1
Replace each occurrence of x with w.
f(w) = √w + 2w2 +2
That is all we can say without knowing more about w.
Example 2
Simplify g(a + 5) if g(t) = t2 – 3t +1.
Solution 2
Replace each occurrence of t with (a + 5).
g(a + 5) = (a + 5)2 – 3(a + 5) + 1
Multiply out (a + 5)2 and –3(a + 5).
g(a + 5) = a2 + 10a + 25 – 3a – 15 + 1
Simplify.
g(a + 5) = a2 + 7a + 11
Example 3
Simplify .
Solution 3
Start with what needs to be simplified.
.
Use f(x) = x2 to evaluate f(x + a) and f(x).
Multiply out (x + a)2.
.
Cancel out the x2 and the –x2.
.
Factor out an a.
.
Cancel an a from the top and bottom.
2x + a
Composition
Now that we can plug anything into functions, we can plug one function into another. This is called composition. The composition of function f with function g is written fg. This means to plug g into f like this: fg(x) = f(g(x))
It may seem that f comes first in fg(x), reading from left to right, but actually, the g is closer to the x. This means that the function g acts on the x first.
Example 1
If f(x) = √x + 2x and g(x) = 4x = 7, then what is the composition fg(x)?
Solution 1
Start with the definition of composition.
fg(x) = f(g(x))
Use g(x) = 4x + 7.
fg(x) = f(4x + 7)
Replace each occurrence of x in f with 4x + 7 .
fg(x) = √4x+ 7 + 2(4x+ 7)
Simplify.
fg(x) = √4x+ 7 + 8x + 14
Conversely, to evaluate gf(x) , we compute:
gf(x) = g (f (x))
Use f(x) = √x + 2x.
gf (x) = g(√x + 2 x)
Replace each occurrence of x in g with √x + 2x.
gf (x) = 4(√x + 2x) + 7
Simplify.
gf (x) = 4√x + 8x + 7
Notice that fg(x) and gf (x) are different. This is usually the case.
Example 2
If f(x) = x2 + 2x + 1 and g(x) = 5x + 1, then what is fg(x)?
Solution 2
Start with the definition of composition.
fg(x) = f(g(x))
Use g(x) = 5x + 1.
fg(x) = f(5x + 1)
Replace each occurrence of x in f with 5x + 1 .
fg(x) = (5x + 1)2 + 2(5x + 1) + 1
Simplify.
fg(x) = 25x2 + 20x + 4
Domains
In the beginning of the lesson, we defined the function Eugene as:
f(x) = √x
However, we left out a crucial piece of information: the domain. The domain of this function consisted of only the numbers 1,4,9,25, and 100. Thus, we should have written
f(x) = √x if x = 1,4,9,25, or 100
Usually, the domain of a function is not given explicitly like this. In such situations, it is assumed that the domain is as large as it possibly can be. The domain consists of all numbers that don't violate one of the following two fundamental prohibitions:
Never divide by zero.
Never take an even root of a negative number.
If you divide by zero, the entire numerical universe will collapse down to a single point. If dividing by zero were allowed, then all numbers would be equal. Four would equal five. Negative and positive would be equivalent. "It's all the same to me" would be the correct answer to every math question. While this might be appealing to some people, it would make calculus, the study of change, impossible. If only one number existed, there could be no change. Thus, we automatically rule out any situation where division by zero might occur.
Example 1
What is the domain of
Solution 1
We must never let the denominator x – 2 be zero, so x cannot be 2. Therefore, the domain of this function consists of all real numbers except 2.
The prohibition against even roots (like square roots) of negative numbers is less severe. An even root of a negative number is an imaginary number. Useful mathematics can be done with imaginary numbers. However, for the sake of simplicity, we will avoid them.
Example 2
What is the domain of g(x) = √3x + 2?
Solution 2
The numbers in the square root must not be negative, so 3x + 2 ≥ 0, thus . of all numbers greater than or equal to .
Do note that it is perfectly okay to take the square root of zero, since √0 = 0. It is only when numbers are less than zero that even roots become imaginary. |
Murderous Maths107135","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.49,"ASIN":"140710716X","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.49,"ASIN":"1407107119","isPreorder":0}],"shippingId":"1407107135::zm7ZSp%2BN5mXjWCwVllYdRAq868rDr25AwN6B7lOunjIfsl%2Ftiuzg3Sd%2Bwno9ceKqbEUgwh1kc5%2FeJ0ezZ9458lNDLTEcrhj5,140710716X::ds2RIYYZsCVOvnf8PzVw6V1J60JuhC82m8O%2Bg6va4xtVVIYGdAdqsYkUfMuEcQFqhykQR2Z9B8iahV9zCnHekKvU8rZQjkUb,1407107119::PbV1n0AVsNs9%2Bl8%2FnI%2BdqsWNRnm%2FyQUOg%2FwiQ%2BntDDvH9PQViqGCFQE10of0%2Bk68TFU%2BAUbHP9dXPbEdEclFiZexe4OkgRC The secret weapon 2. What is algebra? 3. The Slaught-o-Mart equations 4. The father of algebra 5. Packing, unpacking and the panic button 6. The mechanics of magic 7. The Murderous Maths testing laboratory 8. The bank clock 9. Axes, plots and the flight of the loveburger 10. Double trouble 11. The zero proof
written in a variety of fonts in the usual Kjartan Poskitt entertaining style, e.g.:-
'You haven't seen me before and, after this book, I hope for your sake we never meet again, because I'm dangerous to be seen with. In fact, just to be safe, before you read on check there's no one looking over your shoulder. All clear? Right then, here's the situation. Maths is one long fierce battle in which we're all being attacked by an army of different problems. Luckily, most of them are little sums that you can solve in your head. Then for the really tough sums, you can bang the numbers into a calculator and read off the answer. But sometimes you have to do sums and you aren't told what the numbers are! How can you put a number into a calculator when you don't know what it is? What do you do when you're facing the UNKNOWN? It's usually a job for ...... the Phantom X..........' |
An introduction to the methods used to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings, and toric varieties. It applies a combinatorial description of the integral closure of the corresponding monomial subring to graph theory. more...
This text gives a basic introduction and unified approach to algebra and geometry, two of the cornerstones of undergraduate mathematics. The emphasis is constantly on the interaction between these topics. For ease of use by students, the text is divided into short chapters, with exercises at the end of each. more...
Drawn from papers presented at the their September 2004 gathering in honor of Edgar Earle Enoch, contributors describe here their work on such subjects as Warfield's hom and tensor relations, HFDs and UFDs, a counter example for a question on pseudo-calculation rings, creating co-local subgroups of Abelian groups, associated primes of the local coh more...
"The Maple Book" offers encyclopedic coverage of the latest version of this software package, Maple 7.0, and provides a tutorial that extends from high school algebra to advanced topics in mathematics. more...
The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has become prominent. This book talks about the number theory, geometry, and physics. It is divided into three parts: Random matrices, Zeta functions, and Dynamical systems. |
061822176X
9780618221769 visual approach, strongly influenced by both NCTM and AMATYC standards, begins with the presentation of a concept followed by the examination and development of a theory, verification of the theory through deduction, and finally, application of the principles to the real world.Videotapes, professionally produced for this text and hosted by Dana Mosely, offer a valuable resource for further instruction and review."Reminder" marginal notes reinforce theorems or formulas from previous chapters to help students progress through the course.Enhanced Chapter Openers introduce students to the principle notion of the chapter and provide real-world context. «Show less... Show more»
Rent Elementary Geometry for College Students 3rd Edition today, or search our site for other Alexander |
was written with the goal of having students succeed in this course, and gain a foundation to succeed in further mathematics courses. To that end, the authors have written a text with a theme (showing the connections between the zeros, x-intercepts, and solutions), with a series of side-by-side features (designed to show examples being solved algebraically and graphically), and with the knowledge that many students are using graphing technology to help them learn the key concepts in this course (and so the book automatically comes bun... MOREdled with a free graphing calculator manual). Thus, the approach of this text is more interactive than most texts and the authors feel that, accordingly, more students will succeed in this course. (Pearson Education) A two-part packaged set comprised of a college-level algebra textbook and corresponding graphing calculator manual. Both emphasize graphic methods in algebra, with real data applications and an easy-to-follow theme. DLC: Algebra.
Introduction to Graphs and the Graphing Calculator
1
(13)
Basic Concepts of Algebra R
The Real-Number System
14
(6)
Integer Exponents, Scientific Notation, and Order of... MORE Operations |
Probability Tutorials - Noel Vaillant
An online course on measure theory, lebesgue integration and probability, with tutorials (in PDF format) designed as a set of simple exercises, leading gradually to the establishment of deeper results. Proved theorems, as well as clear definitions, areRational Number Tutorial - Joseph L. Zachary
A tutorial that explores the nature of rational numbers, the significance of the minimum and maximum integers in a rational number system, and the meaning of overflow. Includes a Java applet that opens in a separate window, for use alongside the tutorial.Roman Numerals 101 - Oliver Lawrence
The Romans used only seven letters; the combination of a letter and its position could represent any number. They also used a line above the letter, so the numbering system actually represents our own very closely, with fourteen different symbols. The
...more>>
Shelley's Mathematics Articles - Shelley Walsh
"Little self-contained articles [that] write up more than you can normally fit in a lecture, and ... hopefully put together enough explanation so that there's something for a great variety of different ways of thinking." Organized into Geometry; Analytic
...more>>
SketchMad - Nathalie Sinclair
An archived resource, not currently updated: A resource center devoted to using The Geometer's Sketchpad in the classroom. Includes tips, strategies, lesson plans, and sketches for beginning and intermediate Sketchpad teachers, stories from the classroom
...more>>
Snowflakes - Kenneth G. Libbrecht
"Your online guide to snowflakes, snow crystals, and other ice phenomena." Snow activities include instructions for using everday objects and dry ice to make your own snowflakes; for using glue to make plastic snowflake replicas ("snowflake fossils")
...more>>
Software Carpentry - Software Carpentry
Basic computing skills for scientists through self-paced online instruction or short, intensive workshops ("boot camps" at universities and research facilities in the US, UK, and Canada). See, in particular, the free outlines and video lectures on MATLAB,
...more>>
olving Quadratic Equations - Prakash Sukhu
Introduces the general form of the quadratic equation, and shows how to solve the quadratic equation step by step. Includes methods of factorisation and completing the square, questions to test your knowledge, and an online equation solver with which
...more>>
The SPSS Decision Maker - Maurits Kaptein
This is a website that guides you through a number of steps to select a statistical technique. Developed for those who do know the basic concepts of research statistics and experimental design but need help determining the final test.
...more>>
Statistical Assessment Service (STATS)
STATS is a non-profit, non-partisan resource on the use and abuse of science and statistics in the media. Its goals are to correct scientific misinformation in the media and in public policy resulting from bad science, politics, or a simple lack of information
...more>>
Statistics How To - Stephanie
A resource which includes step-by-step instructions for undergraduate statistics students for specific problem types, reference tables, and visual calculators that actually explain how computations are performed using the student's own inputted data.
...more>>
Statistics Tutorials - TexaSoft
Brief explanations of the use and interpretation of standard statistical analysis techniques. Examples are given using the WINKS program (for Windows). Pearson's Correlation Coefficient; Simple Linear Regression; Single Sample t-test; Independent Group
...more>>
Stock Options - The Animated Tutorial - Jerry Marlow
A fast and easy way to teach and to learn about stock options, option prices, stock-market volatility, and Black-Scholes options pricing theory. CD and Book $39.95. The theory provides a sophisticated way of analyzing and understanding the relations among
...more>>
Study Economics
Online copies of N. Gregory Mankiw's books Principles of Macroeconomics and Principles of Microeconomics and a tutorial by Daniel Christiansen on calculus and economics.
...more>>
StudyJams! - Scholastic Inc.
An online service that complements the school math and science curriculum for grades 3 - 6. Aligned with state curriculum standards, StudyJams! takes math and science problems and presents them using relevant, real-world examples students can easily understand.
...more>> |
Course Syllabus for Elementary Algebra
Materials Required: Textbook – Elementary Algebra,
Third Edition, by Tussy and Gustafson. You will also need a scientific
calculator that can performexponent , square and cube root , and provide the
ability to use parentheses and scientific notation.
Course Features and Policies
1. Academic honesty – all work must be your own
effort and not copied from another. Cheating will result in an F grade for the
assignment or test.
2. Class participation and attendance – you are
expected to arrive on time, remain in class the entire period, ask questions,
provide constructive feedback, and participate in all class activities.
3. Missed assignments or exams – no late
assignments will be accepted. Please speak with your instructor and make
arrangements ahead of time if you are not able to attend class on the day of a
scheduled exam.
4. Financial Aid students – should ALWAYS check
with Financial Aid prior to withdrawing, signing an incomplete contract,
changing to an audit, or receiving an F as the final grade in any class.
Instructional Methods and Expectations.
1.
Evaluation:
Grade Scale:
Attendance = 20%
A = 94 – 100%
A- = 90 – 93%
Class projects/Participation = 20%
B+ = 86 – 89%
B = 82 – 85%
Homework assignments = 20%
B- = 78 – 81%
C = 74 – 77%
Tests = 20%
C- = 70 – 73%
D+= 66 – 69%
Final = 20%
D = 62 - 65%
D- = 58 – 61%
2. Incomplete: Because of extenuating
circumstances, the instructor may consider issuing an Incomplete. The student is
eligible if the student is halfway through the course, is earning at least a C ,
and is able to complete the course by working with the instructor no later than
the subsequent quarter.
3. Please make use of these available services, if
required: a. Math Center – tutoring provided free of charge to enrolled students
b. Disability Support Services -- special testing accommodations |
However, they're not diving into axing algebraic manipulation from the curriculum yet; rather Computer Based Math (abbreviated CBM) is planning to "rewrite key years of school probability and statistics from scratch". This is a reasonable first step given statistics is often taught computer based or at least calculator based these days (my colleague who teaches AP Statistics next door does so) and it does feel very silly to work through a passel of "figure out the standard deviation" problems by hand.
However, I'm going to play devil's advocate again with a thought experiment. Since algebraic manipulation is not being removed at this time, these questions aren't going to be applicable to Estonia yet, but presuming Computer Based Math continues working with them it should come up soon.
Suppose you are in a curriculum where you are used to algebraic manipulations being done by a CAS system. You are learning about statistics and come across these formulas:
What is necessary to use the formulas conceptually? What understandings might someone lack by not having experienced the algebra directly? Is it possible to understand the progressive nature and relations with these formulas just by looking at them? Is it necessary (to be well-educated in statistics) to do so? If it is necessary, what specific errors could somebody potentially make in a statistics calculation? Could this be mitigated by the text? Could this be mitigated by steps taking during the CAS portion of the education that while not leading to lengthy practice in "manipulate the algebra" problems will still allow understanding of the text above?
Is it possible to explain something too well? That is, something appears very clear to students after it is explained, so they don't practice (or at least pay attention to their practice because they assume they already understand the topic), and then the lack of practice means they forget what was explained? I'm not meaning "they never learned it in the first place" but rather "they learned it so well that they forgot it because they assumed the memory was permanent". (This is a slightly different issue than students who assume they learn something but really just keep their misconceptions.)
Are there circumstances where practice can actually lessen understanding; for example, when a student who learns a "trick" that works for an entire worksheet may attempt the same trick in circumstances where it doesn't work? Thus it may be a bad idea at times to have a student practice a topic without all the special cases? (Specific example: suppose a student practices integer addition using only a positive with a negative number, but doesn't attempting adding negative numbers with negative numbers until later. Will their earlier practice hinder their learning in the new situation?)
Each of the TED-Ed videos is meticulously animated and represents, I am sure, many many (many) hours of effort. Knowing this made the TED-Ed take on logarithms rather painful to watch:
Oof. Let me attempt to sort my thoughts:
1. The hook baffled me.
A hook should, optimally, be incorporated into the topic being learned. This hook was simply a preview of a future part of the video, and didn't carry much interest on its own. The "red eyes" made me think it was referring to the eye-bleedingly long numbers being presented.
While my own logarithm video isn't perfect (also not entirely comparable since it's about the addition property in particular) I do at least manage a hook that's useful in the explanation of the topic.
2. "…small numbers and in some cases extremely large numbers leading us to the concept of logarithms."
Logarithms come out of the inverse concept of an exponential. The numbers don't have to be large or small. (If you want to get historical, they were often used as a method to multiply quickly by turning the operation into addition.) While a logarithmic scale can be used to handle large or small numbers, I don't see how that leads to the statement in the video.
3. "the exponent p is said to be the logarithm of the number n"
Math videos often are on the glacially slow side, but this part was presented so fast parts of my brain melted.
Look: Logarithms represent, in essence, the first new mathematical operation students have had to reckon with since grade school. They cause intuitions to fail. I have seen students who have never had problems with mathematics before have them for the first time with logarithms.
It's worthwhile, then, to spend a little more than five seconds on your definition.
The definition is confusing, anyway; a logarithm is a function. It applies from one number to another number in a specific way. It is not simply an extract from an exponential equation. While the video mentions that (sort of) it waffles on the implications of introducing a new mathematical operation.
4. "…log base 10 is used so frequently in the sciences that it has the honor of having its own button."
First off, no: the sciences often use base e (given how much continuous growth and decay happens in real life). Base 10 logarithms do still get used for logarithmic scales, but the statement as given in the video is just confusing.
Also, that's a TI graphing calculator? Which one of has a logarithm button but not a natural logarithm button? Even the TI-81 has one.
5. "If the calculator will figure out logarithms for you, why study them?"
The answer the video gives … is so you can figure out a logarithm base 2.
That's a terribly weak answer, given a.) yes there are many applications of logarithms where understanding the mathematics is both good and necessary, and the video even goes into one application immediately after making this statement b.) the answer doesn't really answer the question (since it doesn't explain where the computer science-related equation came from) c.) with the current operating system, Texas Instruments calculators are perfectly capable of putting in alternate bases without a change of base formula (The video incidentally doesn't mention the change of base formula even though one of the questions in the post assessment asks what it is.) and d.) The statement presumes the use of a calculator in the first place (computer-based systems are also perfectly capable of doing logarithms with alternate bases).
6. The video then wants to show how useful logarithms are by giving a formula from science.
Based on the post-test, I'm guessing this part is here merely to show how logarithms are used in "real life".
In the master catalog of Ways to Convince Students Why Something is Useful, "look, a formula that shows up in science!" ranks somewhere between "because math is good for you" and "so you can get into a good college".
By cooperative learning tasks I mean giving particular "jobs" to students during group work; here's a sampling from this website:
Checker: Checks team members for understanding and agreement
Datakeeper: Keeps track of information generated by group
Helper: Gives help in reading, spelling, problem solving, or using materials
Questioner: Asks questions of instructor or other groups
Reporter: Gives oral reports to the total group
Summarizer: Sums up what the group did or the conclusions the group came to
Validator: Paraphrases what is said for clarity
Writer/Recorder: Writes down ideas and records the task
I tried experimenting with them last year (based on the urging of several people) but I've been distinctly unhappy. It feels like the jobs segment up the work in a rote sort of way which gives a student permission to "shut down" when they aren't needed for something in particular. I've still had some luck with engineering-like projects which involve building, but this sort of thing fails for me in general. For example, today I'm having my Algebra I students work on these questions in groups:
You have an a row by b column matrix
and want to multiply by a x row by y column matrix.
1. When is this multiplication impossible?
2. If the multiplication is possible, what is the size of the new matrix?
3. When multiplying 2×2 matrices, there is an identity operation (just like multiplying by 1 is an identity operation in arithmetic). What is it?
4. What about for nxn matrices?
5. Give an example (with all work) that shows that multiplying 2×2 matrices is in general not a commutative operation.
6. Even though the commutative law doesn't apply in general there are specific cases where it works. Give an example of a matrix A and B such that AB = BA.
My time this summer was mostly occupied with a secret project which should be revealed very soon. I can say it has to do with Common Core.
I also have been working on my book project. I'm currently calling it How Algebra Works and it is totally crazy.
It is targeted at adults who had algebra class in the past but it's now a tangled muddle of memories they barely understand. Every problem given is a puzzle — that is, it wouldn't be out of sorts in a Martin Gardner book or the World Puzzle Championship. Given I am not fussing over standard schoolbook curriculum, I am doing my best to rethink everything from scratch with the goal of explaining how it works rather than providing technical proficiency.
So, yeah — easy to crash and burn. Hence I won't talk about it any more until I'm ready for beta testers (both for the text and for the puzzles).
. . . all knowledge of any depth, not only philosophizing, begins with amazement. If that is true, then everything depends upon leading the learner to recognize the amazing qualities, the mirandum, the "novelty" of the subject under discussion. If the teacher succeeds in doing this, he has done something more important than and quite different from making knowledge entertaining and interesting. He has, rather, put the learner on the road to genuine questioning.
This invention is designed to assist the accountant in adding long columns of figures by registering the addition of two or more figures the aggregate sum of which is less than ten, thus relieving him from memorizing or carrying in his mind a greatly-accumulated result, nothing less than tens being registered, while the units are carried in the mind.
Also of note:
Should the accountant become interrupted, and be obliged to discontinue the count of a column of figures, he may register the units at the thousands-aperture by turning the milled head of the thousands-wheel, which is rarely employed, few columns of figures being of such length as to require its use. The accountant would then make a dot with the pencil at the figure last counted, and on recommencing the count carry the units thus indicated at the thousands-aperture to the next figure of the row. |
Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? Head First Statistics brings this typically dry subject to life, teaching you everything you want and need to know about statistics through engaging, interactive, and thought-provoking material, full of puzzles, stories, quizzes, visual aids, and real-world examples.
Whether you're a student, a professional, or just curious about statistical analysis, Head First's brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more.
polynomials.
Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.
Wouldn't it be great if there were a physics book that showed you how things work instead of telling you how? Finally, with Head First Physics, there is. This comprehensive book takes the stress out of learning mechanics and practical — aThis completely revised Fourth Edition of the book, appropriate for all engineering under-graduate students, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications. The book focuses clearly on teaching students numerical methods and in helping them to develop problem-solving skills.
A distinguishing feature of the present edition is that it provides references to MATLAB, IMSL and Numerical Recipes program libraries for implementing the numerical methods described in the book. Several exercises are included to illustrate the use of these libraries.
Additional worked examples and exercises have been added for better appreciation and understanding of the material. Answers to some selected exercises have been provided. |
We are now ready to approach our motivating problem.
This chapter is about graphs, and graphing.
A graph is a mathematical object; we must first take this
ideal object and form a corresponding object that can be
mechanically produced. We do not dwell on the issue; our
discourse remains lofty, as we will continue to exploit our
abstract models. The abstract models we exploit are, however, grounded
in concepts that are realizable.
Practical graphing concerns are addressed in [7]. |
Using Laptops in the Classroom: Faculty Experiences
Laptops in the Classroom
by MAJ James A. Glackin
The United States Military Academy (USMA) is currently conducting an experiment with laptop computers. Thirty-two cadets were issued laptop computers for use in MA205, Multivariable Calculus and SS201, Economics. They were also asked to use their laptop in the barracks instead of their desktop computer. While the Academy focused on deciding if the laptop is a viable alternative to desktops, the Department of Mathematical Sciences focused on how to use this additional technology in the classroom. Particularly, how could we use Mathcad to increase cadet discovery and understanding? We also wanted to find ways this experiment could help those without laptops.
Every classroom at West Point is equipped with a computer and projection device. Often during class instructors use Mathcad to help teach cadets how to use the program and to aid in visualizing a problem. Although better than nothing, this technique left several cadets very unfamiliar and unconfident in their ability to use technology to help solve problems. The reason for this was the time delay between seeing things in class and trying to execute the commands back in the barracks. When cadets got back to their rooms they had often forgotten the required syntax.
With laptops in the classroom there is no time delay. Cadets watch me perform operations on Mathcad and can follow along, ensuring they get the same results. If they don't, they can immediately ask me to take a look at their worksheet. The difference is evident in student attitudes, "Before I saw the use of Mathcad as a chore and was even afraid to use it... Now I am not only more confident with Mathcad, but I enjoy using Mathcad and see the advantages."
Although my initial focus was to make cadets confident in their ability to use Mathcad, I quickly realized this was an intermediate step. What I really wanted was for cadets to better understand Multivariable Calculus by using Mathcad to perform tedious time consuming calculations or to aid in visualizing a problem. To do this I would create a worksheet and email it to cadets the day before class. As part of their assignment I asked them to "play with" the worksheet before class. During class they could ask questions and I would bring out the concepts I wanted to emphasize. This technique can also be used with students who solely have desktops.
Parametric Equations: When we study parametric equations we spend a few minutes learning the concepts, then spend several hours doing "stubby pencil" work. By using worksheets Mathcad did the "stubby pencil" work in seconds. Cadets then use the extra time to explore what affects changes in the parametric equations have on the plot. Here are a few simple examples changing the coefficients, start, and stop points. Cadets can do dozens of changes in minutes |
Carnegie Learning develops textbooks that support a collaborative, student-centered 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 sense-making skills.
Program Components Click icons for details »
Program Components Click icons for details »
Supplemental & Intervention Solutions
Some students will need additional support and intervention to meet the high expectations of state standards. Carnegie Learning can help you implement tiered interventions in mathematics. In addition to the core instruction we provide in our textbooks, we provide interactive math instruction in our Cognitive Tutor software.
Our Algebra Readiness curriculum is a one-year course designed to remediate students who have completed a middle school math sequence of instruction but still exhibit gaps in their math knowledge and skills. The course covers the five major NCTM strands: Number and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability.
Whitepapers
In 28 years of teaching, I would have to say that I've seen more students be successful, I've seen more students know mathematics than I ever have before. And I think it wouldn't be possible without the integrated curriculum and without the materials provided by both the state and Carnegie Learning that we are using. |
This course provides students with a combined foundation in introductory and intermediate algebra topics that are NECESSARY skills for the study of a college-level mathematics course. Topics include real numbers, equations and inequalities, coordinate grid topics, exponents and polynomials, factoring, rational expressions, roots and radicals, systems of equations and quadratic equations. |
Error Patterns in Comput your students learn about mathematical operations and methods of computation, they may adopt erroneous procedures and misconceptions, despite your best efforts. This engaging book was written to model how you, the teacher, can make thoughtful analyses of your student's work, and in doing so, discover patterns in the errors they make. The text considers reasons why students may have learned erroneous procedures and presents strategies for helping those students. You will come away from the reading with a clear vision of how you can use student error patterns to gain more specific knowledge of their strengths on which to base your future instruction. Book jacket. |
This Foundation Year is designed for students who have shown that they have the ability, but do not possess the necessary qualifications, for direct entry into Stage 1 of Mathematics and Statistics at Newcastle.
The Foundation Year is a full-time programme of study covering core mathematics and statistics topics including differential calculus and complex numbers, as well as problem solving skills.
Successful completion of the Foundation Year leads to guaranteed progression to Stage 1 of any of our mathematics and statistics BSc degrees. See our A-Z list for details.
Quality and ranking
The quality of the mathematics and statistics study experience at Newcastle is recognised with an overall student satisfaction score of 91% in the 2012 National Student Survey.
School of Mathematics and Statistics
We run an induction programme for first-year students including social events to help you to get to know your fellow students and the members of staff who will be teaching you. We also have a 'buddy scheme', which begins before you even arrive at the University.
As well as the support of a personal tutor, you will be encouraged to join our extremely active student society, MathSoc. MathSoc organises a range of social events throughout the year to help you get to know people on your course and beyond.
Visit the School's website to take a virtual tour of the Herschel Building, which is on the central campus and a two-minute walk from the city centre. |
Algebra I is a class that introduces the mathematical branch of Algebra. Working with Real Numbers, Solving Equations and Problems, Polynomials, Factoring Polynomials, Fractions and their applicational use, Introduction to Functions, Systems of Linear Equations, and Inequalities are among the first topics learned about in this class. |
MAT
230
- Discrete Mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. That is, in contrast to the real numbers that vary continuously, the objects of study in discrete mathematics take on distinct, separated values. Topics include operations on sets, logic, truth tables, counting, relations and digraphs, functions, trees and graph theory. A significant goal of this course is to improve students' critical-thinking and problem-solving skills. |
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I'd call this book perfect for middle school on up if you plan to use it as is. For many younger children (lower than 4th grade)to teach the material, you'd have to be willing to present the concepts in examples you've rewritten. Examples: [In Chapter 1] 160 divided by 1/3 = 53 1/3. In Chapter 3, Level 1 problem 1 is simple subtraction...but if a student doesn't already know that a straight line = 180 degrees, he or she will just get frustrated that a number is "missing". And later in the book there are some variables and exponents. My son is entering 5th; his math level is just out of pre-algebra/getting into "real" algebra (I've supplemented at home)...if I were relying only upon what children learn through fourth grade at school, he would be too distracted by the computation to get the problem solving benefit out of it. I don't think the book is presented as being for elementary students. But if you purchase this book to use [as is] for someone comfortable with fractions and some basic pre-algebra concepts...you'll have no regrets.
I have a 2nd grader (who is advanced for his age) and this book is written in such a way that he can grasp the concepts without feeling overwhelmed. The "cartooning" style is easy to follow and entertaining while still being educational. We were looking for something for him to use to develop his probleming solving skills. This was an excellent place to start. |
Short description
Presents MATLAB both as a mathematical tool and a programming language, giving an introduction to its potential and power. This book illustrates the fundamentals of MATLAB with many examples from a wide range of familiar scientific and engineering areas. It includes coverage of Symbolic Math and SIMULINK. It highlights common errors and pitfalls.
Long description
This is the essential guide to MATLAB as a problem solving tool. This text presents MATLAB both as a mathematical tool and a programming language, giving a concise and easy to master introduction to its potential and power. The fundamentals of MATLAB are illustrated throughout with many examples from a wide range of familiar scientific and engineering areas, as well as from everyday life. The new edition has been updated to include coverage of Symbolic Math and SIMULINK. It also adds new examples and applications, and uses the most recent release of Matlab. Features of this title include: new chapters on Symbolic Math and SIMULINK provide complete coverage of all the functions available in the student edition of Matlab; more exercises and examples, including new examples of beam bending, flow over an airfoil, and other physics-based problems; a bibliography that provides sources for the engineering problems and examples discussed in the text; and, a chapter on algorithm development and program design. In this book, common errors and pitfalls are highlighted. It provides extensive teacher support on: solutions manual, extra problems, multiple choice questions, PowerPoint slides. It features companion website for students providing M-files used within the book.
Product details
Publisher:
Academic Press
ISBN:
9780123748836
Publication date:
October 2009
Length:
236mm
Width:
191mm
Thickness:
20mm
Weight:
821g
Edition:
4th edition
Pages:
391
Illustrated:
True
Review
This book provides an excellent initiation into programming in MATLAB while serving as a teaser for more advanced topics. It provides a structured entry into MATLAB programming through well designed exercises. - Carl H. Sondergeld, Professor and Curtis Mewbourne Chair, Mewbourne School of Petroleum and Geological Engineering, University of Oklahoma This updated version continues to provide beginners with the essentials of Matlab, with many examples from science and engineering, written in an informal and accessible style. The new chapter on algorithm development and program design provides an excellent introduction to a structured approach to problem solving and the use of MATLAB as a programming language. - Professor Gary Ford, Department of Electrical and Computer Engineering, University of California, Davis For a while I have been searching for a good MATLAB text for a graduate course on methods in environmental sciences. I finally settled on Hahn and Valentine because it provides the balance I need regarding ease of use and relevance of material and examples. - Professor Wayne M. Getz, Department Environmental Science Policy & Management, University of California at Berkeley This book is an outstanding introductory text for teaching mathematics, engineering, and science students how MATLAB can be used to solve mathematical problems. Its intuitive and well-chosen examples nicely bridge the gap between prototypical mathematical models and how MATLAB can be used to evaluate these models. The author does a superior job of examining and explaining the MATLAB code used to solve the problems presented. - Professor Mark E. Cawood, Department of Mathematical Sciences, Clemson University This has proved an excellent book for engineering undergraduate students to support their first studies in Matlab. Most of the basics are covered well, and it includes a useful introduction to the development of a Graphical User Interface. - Mr. K |
Click on the Google Preview image above to read some pages of this book!
Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well. In each lecture, the concepts, theories and methods are taken as the core. The examples serve to explain and enrich their intentions and to indicate their applications. Besides, appropriate number of test questions is available for the readers' practice and testing purpose. Their detailed solutions are also conveniently provided. The examples are not very complicated so readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions originate from many countries all over the world. This book will serve as a useful textbook of mathematical Olympiad courses, a self-study lecture notes for students, or as a reference book for related teachers and researchers.
Volume 1: Fractional Equations; Higher Degree Polynomial Equations; Irrational Equations; Indicial Functions and Logarithmic Functions; Trigonometric Functions; Law of Sines and Law of Cosines; Manipulations of Trigonometric Expressions; Extreme Values of Functions and Mean Inequality; Extreme Value Problems in Trigonometry; Fundamental Properties of Circles; Relation of Line and Circle and Relation of Circles; Cyclic Polygons; Power of a Point with Respect to a Circle; Some Important Theorems in Geometry; Five Centers of a Triangle; Volume 2: Mathematical Induction; Arithmetic Progression and Geometric Progression; Recursive Sequence; Summation of Series; Some Fundamental Theorems on Congruence; Chinese Remainder Theorem and Order of Integer; Diophantine Equation (III); Cauchy - Schwartz Inequality; Rearrangement Inequality and Jensen' Inequality; Schur Inequality; Fractional Inequality; Variable - Freezing Method; Some Methods in Counting Numbers (I); Some Methods in Counting Numbers (II); Introduction to Functional Equations. |
Creative Problem Solving (CPS) is a process that allows people to apply both creative and critical thinking to find solutions to everyday problems. It is a way to enhance creative behavior and also a systematic way to organize information and ideas in order to solve problems. The overall goal of CPS training is to improve creative behavior and problem-solving behavior. The skills involved are: ability to select relevant information ability to summarize information ability to analyze social situations, ability to think creatively to generate possible solutions, ability to evaluate options based
Each chapter contains a detailed review and many types of review exercises and problems. Solutions to PSSG questions explain answers and discuss how to approach similar types of accounting questions. Tips alert students to common problem-solving pitfalls and misconceptions.
The referred international conferences in computer scien
Problem solving is an integral part of everyday life yet few books are dedicated to this important aspect of human cognition. In each case, the problem, such as solving a crossword or writing an essay, has a goal. In this comprehensive and timely textbook, the author discusses the psychological processes underlying such goal-directed problem solving and examines both how we learn from experience of problem solving and how our learning transfers (or often fails to transfer) from one situation to another.
With the advent of computers, theoretical studies and solution methods for polynomial equations have changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasizing computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval M
This is a practical anthology of some of the best elementary problems in different branches of mathematics. They are selected for their aesthetic appeal as well as their instructional value, and are organized to highlight the most common problem-solving techniques encountered in undergraduate mathematics. Readers learn important principles and broad strategies for coping with the experience of solving problems, while tackling specific cases on their own. The material is classroom tested and has been found particularly helpful for students preparing for the Putnam exam. For easy reference, the |
Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully ... > read more
What is understanding and how does it differ from knowledge? How can we determine the big ideas worth understanding? Why is understanding an important teaching goal, and how do we know when students ... > read more |
Algebra/Who should read this book
This book is intended to (eventually) be a comprehensive look at the mathematics topic of Algebra. That said, it would be well suited for a wide variety of individuals, ranging from students (at any grade level) to adults interested in refreshing or improving their understanding of basic math. It could be used either as a primary text or a reference.
This book will avoid explaining subjects with only "rigorous" mathematical abstractions whenever possible. Math can be tricky and frustrating enough without it seeming inaccessible. So while every topic will be covered fully and correctly and in many times using "proper" mathematical terminology, there will always be a backup definition or simple explanation to complete the concept. This allows a wider variety of individuals to learn from this text, from an ambitious 12-year-old to a forgetful college professor. |
Visualizing Sequences
For those who like pictures better than formulas, we can visualize sequences on number lines and on graphs. For those who like Kit Kats, we can visualize a giant Kit Kat bar. Either way, creating an image will help us understand better how some...
Please purchase the full module to see the rest of this course
Purchase the Sequences Pass and get full access to this Calculus chapter. No limits found here. |
This playlist is for my students to use on the first day of their introduction to functions week.
All credit is passed on to Melissa Jaeger who posted this at algebra 4 all. Thank you! To download this lesson plan for ...
This presentation will present results of the presenter's doctoral dissertation. This quantitative research compared sections of college algebra using the flipped classroom methods and the traditional lecture/homework ... |
Summary
Elementary and Intermediate Algebra: A Practical Approachprovides concise, manageable treatment of the mathematics required for the combined algebra course. While emphasizing problem solving and the real-world applications of algebra, the text provides solid coverage of core mathematical concepts and essential symbol manipulation skills. Furthermore, the text encourages students to use graphing technology while still requiring them to master pencil-and-paper techniques for certain tasks. Authors Craine, McGowan, and Ruben combine their experience and expertise as a math educator and author, a math researcher, and an authority on math anxiety to deliver a balanced, targeted text that enables instructors to cover all the material for the combined course in one text. Pedagogically, the instructional material is concise, clear, and presented in a style that encourages students to read all the material and complete all the exercises. Examples focus on a particular concept and include complete worked-out solutions. Examples presented with multiple solution methods--algebraic, graphical, and/or numerical--help students with different learning styles understand solutions from various aspects. Eduspace, powered by Blackboard, for the Craine/McGowan/RubensElementary and Intermediate Algebracourse includes algorithmic exercises, test bank content in question pools, interactive tutorials and video explanations. |
The Basic Math DVD Series helps students build confidence in their mathematical knowledge, skills, and ability.
In this episode, students will learn how to solve basic equations. This lesson introduces a method for solving relatively simple linear equations of one variable, starting with simple equations such as 3x = 15 and x + 5 = 11 and eventually moving on to equations such as 3(x + 5) - 6x = 11 - 2x + 8. The importance of checking answers using the original equation is emphasized throughout the lesson. Grades 3-7. 30 minutes on DVD.
Customer Reviews for Basic Math Series: Solving Simple Equations DVD
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Extension Mathematics 2
10 Units 2000 Level Course
Available in 2012
This course requires competence in the algebraic and graphical skills developed in EPMATH153. This course aims to develop the trigonometric and calculus skills necessary for entry to an undergraduate science or mathematics degree and covers the topics of trigonometry, and differential and integral calculus, with some applications in the physical sciences.
Objectives
The course will develop: 1. trigonometric skills sufficient for the understanding and practice of calculus. 2. an understanding of differentiation, both in theory and practice, and the ability to apply it to real-world problems. 3. an understanding of integration, both in theory and practice, and the ability to apply it to real-world problems. 4. the ability to communicate mathematics, orally and in writing. 5. an understanding and correct use of mathematical notation. 6. the formulation of real-world problems in the language of mathematics, and the ability to solve them. |
The Centralia High School Math Department adopted new textbooks to supports our curriculum and to meet the new Common Core Math Standards adopted by the State of Washington. Our courses will again follow the standard sequence of Algebra (online resources), Geometry, Advanced Algebra (online resources), Pre-Calculus (online resources), and AP Calculus. As a department, we have aligned and analyzed the new textbooks to best help your student prepare for the State of Washington End-of-Course exams in Algebra and Geometry. With the new requirement to take 3 years of math, the math department is offering the classes normally taken by college bound students (Advanced Algebra, Pre-Calculus, AP Calculus) and Applied Mathematics, for students looking for the application of mathematics in their future careers. |
,... read moreVector Geometry by Gilbert de B. Robinson Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962Projective Geometry by T. Ewan Faulkner Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960Product Description:
, much more. Includes over 500 exercises.
Reprint of A Course for Geometry for Colleges and Universities, Cambridge University Press, Cambridge, England, 1970 |
Synopsis your skills, with detailed answers and explanations to show you exactly how to improve • A cheat sheet of key formulas |
The math department offers many different courses starting with Algebra I. The Honors program is designed for those students that are math oriented and can maintain grades of B- or better. Anyone completing this series will be well qualified for any college program requiring a strong math background. The department also offers a regular curriculum for those students that will pursue post secondary education but may not be math oriented. Its basis is the CORE 40 curriculum set up by the State of Indiana.
In order to continue taking courses in the Honors curriculum of mathematics, students must complete the Honors above it on the chart above and be recommended by the teacher. For example, students may not take Geometry and then Algebra II Honors.
Algebra I shall appear on the transcript per state requirement but not count for credit or in the GPA for students in the class of 2012 who enter high school taking Geometry.
Any 8thgrade math student (starting with the class of 2013) who have maintained at least a B average in Algebra I and have enrolled in Geometry (at the high school level) may earn 2 high school math credits. The awarding of these credits will be contingent upon the successful completion of Geometry A or B and recommendation of Department
Chair. Individual grades received in Algebra I then will become part of the student's high school transcript.
Click here to visit the Academic Handbook for more detailed information regarding this area. |
Math
Designed for students from kindergarten though the 12th grade, BJU Math Textbooks and Homeschool Curriculum strengthens your child's reasoning and problem-solving skills and develops their understanding of math as a tool of commerce, the language of science, and a means for solving everyday problems. From basic math through algebra. geometry and even pre-calculus, BJU Math Textbooks and Homeschool curriculum will help students understand the relevance of math and its biblical basis from beginning to end. Mardel carries the complete line of BLU Math Homeschool Curriculum and Teacher Resources. |
Comment: This copy of "GCSE Maths Complete Revision & Practice contains all-in-one exam preparation resources for Higher Level GCSE Maths, including a free Online Edition to use on a PC, Mac or tablet device. Every topic is clearly explained in CGP's informal, straightforward style, with plenty of tips and worked examples. Each mini-section is rounded off with a quick warm-up test and a selection of exam-style questions, with detailed answers at the back. At the end of the book, you'll find two full practice exam papers - you can watch fully worked video solutions to these papers once you've accessed the Online Edition of the book. Please note: this book covers every major GCSE exam board. Separate editions are also available for the AQA (9781847621771) and Edexcel (9781847622082) courses |
Intermediate 2 Maths Course Notes - Leckie (Paperback)
Specifically designed to support Intermediate 2 students, this text is divided into three units for a succinct approach to topics assessed in Units 1, 2 and 3 of the exam. New formulae and problem-solving methods are explained step-by-step to reinforce knowledge and understanding and enable students to review what they have learned in class. All topics are accompanied by questions with worked examples to allow students to assess their learning and to target areas of weakness for exam success. In addition, the comprehensive topic index supports quick and easy reference in the approach to exams. (Applications of Maths is not covered by this title.) |
Bootstrap is a computing curriculum that engages students with animation, targets core skills in algebra and coordinate geometry, and is vertically integrated with the Program by Design high-school and college curriculum. Both Bootstrap and Program by Design align with state mathematics standards.
We express animations using algebra, rather than more traditional styles of programming. We want to exploit the connection between computing and algebra to motivate kids to stick with math through high-school and to excite them about computing. This reinforces essential material underlying many TEM and computing careers and enables integration into a conventional middle-school curriculum. |
This text and CD-ROM are designed to make algebra interesting and relevant to the student. The focus is shifted from learning a set of discrete mathematical rules to exploring how algebra is used in ... |
In Practise
mode, the students solve questions by performing their own calculations. If
they don't know what to do, they can request a companion to make a
suggestion or a calculation step. Aplusix automatically verifies the students'
calculations and the completion of questions.
In Test
mode,
students work for 30 minutes without any feedback. At the end of
the test, they get a score and can enter Self-correcting mode.
In Self-correction
mode, students review their own work.
Correct and incorrect calculations are clearly marked and they can see whether they have completed
the question or not. They can correct their calculations with the same level of feedback
as in Practise mode, including the use of companions.
In Review mode, students review their work. Correct and incorrect calculations are
clearly marked and they can see whether they have completed the question or not.
A replay system is also available to them.
Many exercises, covering most aspects of the Number and Algebra strands of the UK National Curriculum
and a lot of the algebraic content of Foundation and Higher GCSE, allow to practise, understand,
and become efficient: numerical calculations, expansions and simplifications, factorising,
solving equations and inequalities, simultaneous equations.
In addition to the provided exercises, it is possible to do homework and to practise with exercises
given by the teacher (e.g. from textbooks or worksheets).
Scientific
experiments led in several countries, under the control of
mathematical education researchers, have shown that with Aplusix
students work more, become
self-confident and independent,
and improve their skills. |
Systems of Equations Unit PlanThis 92 page unit plan includes 11 days of lessons on Solving Linear Systems by graphing, substitution, and elimination with multiplication. Also included are special types of linear systems. Each daily plan includes a warm up and the notes / worksheets / activities for the day. There is a quiz and a final assessment. Answer keys for everything are included!
Don't need a full unit plan? Purchase just the resources instead!
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Video Description: There is more than one type of integral in multivariable calculus. In this lesson, Herb Gross defines and discusses line integrals. He reviews integration with respect to a curve (line) as distinguished from an integral as an area computation (double ...
Video Description: Herb Gross illustrates the equivalence of the Fundamental Theorem of the Calculus of one variable to the Fundamental Theorem of Calculus for several variables. Topics include: The anti-derivative and the value of a definite integral; Iterated integrals. Instructor/speaker: ...
Video Description: With our knowledge of matrix algebra to help, Herb Gross teaches how to find the local maxima and minima of functions of several real variables. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross defines the directional derivative and demonstrates how to calculate it, emphasizing the importance of this topic in the study of Calculus of Several Variables. He also covers the definition of a gradient vector. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross discusses the topic of equations of lines and planes in 3-dimensional space. Topics include: The normal vector to a plane; Parallel planes; Equation of a plane; Equation of a line in space. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross describes the "game" of matrices — the rules of matrix arithmetic and algebra. He also covers non-singularity and the inverse of a matrix. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross shows examples of the chain rule for several variables and develops a proof of the chain rule. He also explains how the chain rule works with higher order partial derivatives and mixed partial derivatives. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross show how the chain rule is involved in finding some integrals involving parameters. He computes the derivatives of integrals with constant limits, as well as derivatives of integrals with variable limits of integration (chain rule). ...
Video Description: Herb Gross reviews the definition of vectors — objects that have magnitude, direction, and sense. He also defines equality of vectors, their components, and rules of arithmetic. Vector arithmetic shares many structural properties with scalar arithmetic including a zero ...
Video Description: Herb Gross teaches us how to calculate infinite double (multiple) sums (for topics in calculus of several variables). This topic is analogous to the use of infinite sums in calculus of a single variable. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross introduces the topic of vector functions of scalar variables and explains why the result is a vector (since the inputs are scalars). He then reviews limits (definition and related theorems) and presents the topic of differentiation of ...
Video Description: Herb Gross defines and demonstrates the use of polar coordinates. He describes the non-uniqueness of polar coordinates and how to calculate the slope of a curve, which depends on the angle the curve makes with the radius vector. Finally, he computes the area (in terms of ... |
As mentioned, all kinds of Math are important as a general point, I'm of the opinion problem solving is likely going to make you better than branching into learning a bunch of math for the sake of becoming a better programmer.
However, Discrete Math is probably a good starting point. – mjsabbyJan 16 '10 at 11Boolean Algebra. Of all the math
courses I ever did understanding
boolean logic stands out as by far
the most useful. Just formally
knowing the basics, such as NOT A
AND NOT B == NOT(A OR B) will get
you far. This is the one math subject that justifies the question
Linear Algebra is surprisingly
useful too. I've done a
considerable amount of 3D work so
that is essential there, but it pops
up all over the place to some
degree.
Statistics. Everyone should have
some grasp of basic stats
And finally one off the wall - Fractal algebra. Partly because it's just fun, but also because understanding what turbulence is and knowing to reach for a Perlin noise function or similar when otherwise you might just use white noise is a major win.
Algebra is a must for anyone aiming to be good at mathematics but for a CS student, discrete mathematics is a must. For the sake of algorithm analysis, you should study statistics along with differential equations and calculus. Also if you intend to study DSP, Fourier analysis is a must.
Even if you plan to never go outside the realm of algorithms and data structures, some math is really useful.
Discrete maths and number theory is a must imho.
An entry level (linear) algebra class is always useful. As noted above, algebra pops up everywhere.
Statistics is a must no matter what you intend to do(within CS).
Calculus, well, nice to have, but I would prioritize the discrete, statistics, number theory and algebra first(in that order).
All in all, most entry level math classes are probably good to have. Then you can build upon that later if you find you like it and/or need it. It's great that you already are thinking about math. Too many underestimate the usefulness of mathematics.
I think knowledge of Probability and Statistics is a must in every field of computer, including software development. Sooner or later, a developer needs to profile his/her program and analyze the statistical results and then this knowledge comes really essential.
It sounds as though you already know that all programmers, web developers or otherwise, could benefit from giving their brains a bit of a maths work out. Studying maths is unlikely to inform your hands-on-technical knowledge but it will refine your logical thinking skills.
I'd agree with Mark Harrison on studying Discrete Maths, a great subject encompassing a lot of concepts used in computer science. I'd second the book that Mark recommends - its actually the one that I used in my undergraduate studies. It was pretty good back then and such textbooks generally improve through subsequent editions.
Discrete Maths is a big topic however, and its very difficult to work one's way through such a meaty textbook. One way of jumpstarting your studies could be via a book of Discrete Maths puzzles with solutions. (I have this book and its written in an engaging and fun style). Work through the puzzles and if you get stuck then explore the new concepts in greater depth using the Grimaldi book.
All programmers will benefit from studying Algorithms too. I stumbled across some video lectures from an MIT course on Algorithms. I learnt a lot from these!
The ability to collect, analyze and present data to others is a skill that you can always use whether you're a programmer or you move on to other things like management. I currently develop software, and in the past hardware, that is always very speed/performance critical. When debugging and looking for bottlenecks, it is easy to point fingers and make wild assumptions. When you have data to back your argument, it is easy to prove your point.
Just a few of the cases where I have used statistics:
determining data flow volumes to aid in making hardware/IT purchase decisions for new sites
analyzing lab and fields results to determine precision and accuracy of equipment
You don't need to be able to do high-level calculus to utilize statistics. You just need to understand, and then apply the concepts. It helps to know how to use a few tools too, like Excel or R, so that you don't have to roll your own scripts.
I think maths in general is quite important as I think it helps you think in a structured and logical way that would help you if you want to be a developer.
For the time being I am finding anll the maths, calculus and also statistics very useful. I am currently doing a Masters in Biometrics and all the years of learning maths and statistics if truely proving very helpful.
Regards
Shivam |
General Site Search
Mathematics (AQA GCSE Level 2)
Course Overview
The College runs the AQA GCSE Modular Mathematics course. This course gives candidates the opportunity to take exams in three smaller chunks rather than one big exam at the end of the course. GCSE Maths is taken as one of two tiers (levels) enabling learners to achieve grades G to C on Foundation, and D to A* on Higher.
Entry Requirements
We run the GCSE Mathematics course over a year, which means the pace of lessons is quite high. For this reason we have the following requirements for entry onto the course:
Candidates wishing to study the Foundation course will either be asked to take an assessment prior to starting the course, or must have already achieved a D grade in the subject. If you do not meet the entry requirements, but have other relevant qualifications or experience your application will be considered independently.
If you wish to study the Higher course we ask that you are already in possession of a C grade at GCSE. Again, if you have other relevant qualifications or experience your application may still be accepted.
College policy is to recruit with integrity, so if you do not have the entry requirements or you have other relevant qualifications your application will be considered independently. All applicants undertake initial diagnostic tests and a personal interview before being accepted on the course.
Duration
32 Weeks
Course Contents
For both levels of the GCSE Mathematics course, lessons will be taught in a classroom environment with the group then being allowed time to practice what they have learned. All electronic teaching materials will be made available to learners on the internet via the College website.
Assessment
The course is split into 3 units:
Unit 1 - Statistics and Number - This unit is worth 27% of the final grade, and the exam is taken in November
Unit 2 - Number and Algebra - This unit is worth 33% of the final grade, and the exam is taken in March
Unit 3 - Geometry and Algebra - This unit is worth 40% of the final grade, and the exam is taken in June
Progression Route
Completion of the Foundation level GCSE at grade C will enable learners to advance onto the Higher level GCSE the following year, which will allow them to gain a grade up to an A*. Attainment of a grade C at either level is often a requirement for entry onto higher level College or University courses. Job prospects are also greatly improved upon gaining a grade C |
Saltire is host to a variety of math software that teaches
though exploration. From algebra and geometry through calculus,
students can explore and reflect on problems to gain new insights
to mathematics.
For
years Saltire have been developing educational software. Now
the company also provides materials, sensors and associated
software to make data-gathering a simple and reliable task
for teachers and students from the early grades through high
school. These new products are sold under the name
Saltire Scientific. All the new products are designed
to work particularly well with Casio Data Analyzers and graphing
calculators, further enhancing student's educational experiences.
The
Casio ClassPad 300
is the natural evolution of the graphing calculator. This
pen input calculator comes packed with an impressive collection
of applications that support self-study, like 3D Graph, Geometry,
eActivity, and lots more. A big 160 x 240-dot LCD touch screen
enables easy and intuitive stylus-based operation. Learn how
the Classpad can be used in the classroom with free Classpad explorations.
Saltire's
Geometry Gallery is a collection of Java applets
showing interesting geometry configurations. All applets are
dynamic in that user input can cause the configuration to
change. In some cases, points can be dragged. In other cases
dimensions can be changed via edit controls. Some of the applets
feature animation.
Math
Xpander is an application that resulted from investigations
within laboratories at Hewlett Packard. It supports real time
interactions between users and mathematical objects with a
stylus in multiple representations: graphic, symbolic, and
numeric. Saltire Software contributed a geometry engine
that supports geometric constructions in the application.
math Xpander is available as a free
download for Pocket PC devices running Windows CE.
Saltire specializes in the development of software with
high mathematical content. Our current areas of mathematical
expertise include: interactive geometry, symbolic mathematics,
mechanism design and optimization. Assisted by a series of
National Science Foundation grants we are applying these core
technologies to a variety of areas in mathematics education.
We have contributed to educational projects sponsored by Casio,
Hewlett Packard, as well as Texas Instruments. more... |
introduction is based on a workshop given by Eric Bainville at CabriWorld 2004. The first part introduces a few important features of Cabri 3D. This is followed by activities involving constructi... More: lessons, discussions, ratings, reviews,...
Cabri 3D is interactive solid geometry software based on 3rd generation Cabri technology. It enables users to build and manipulate figures in 3D. It is entirely designed and developed by Cabrilog, and... More: lessons, discussions, ratings, reviews,...
The intent of each activity in this brief book is to allow students to use the TI-83 Plus and TI-84 Plus families of graphing calculators to explore and make conjectures related to key geometry concep... More: lessons, discussions, ratings, reviews,...
A rotation around a point is one of three types of rigid transformations. It is a transformation that turns a figure a certain number of degrees about a certain point. This activity explores the prope |
Learning and Teaching for the 21st Century Search the website: Leagan Gaeilge
Overview of Project Maths
Project Maths involves the introduction of revised syllabuses for both
Junior and Leaving Certificate Mathematics. It involves changes to what
students learn in mathematics, how they learn it and how they will be
assessed.
Project Maths aims to provide for an enhanced student learning experience
and greater levels of achievement for all. Much greater emphasis will
be placed on student understanding of mathematical concepts, with increased
use of contexts and applications that will enable students to relate
mathematics to everyday experience.
The initiative will also focus on developing students' problem-solving
skills. Assessment will reflect the different emphasis on understanding
and skills in the teaching and learning of mathematics.
Led by the NCCA the initiative began in September 2008, with the start-up
of Project Maths in an initial group of 24 schools. These schools are
key players in the process of curriculum development. Their work helps
the NCCA to learn from schools how the proposed revisions to the syllabus
work in classrooms. Their work leads to the development of teaching
and learning resources and assessment instruments.
The Mathematics syllabuses will be introduced by strand as follows:
1. Statistics and Probability
2. Geometry and Trigonometry
3. Number
4. Algebra
5. Functions
The first two strands which have been worked on in the 24 schools
will be introduced nationally for incoming first year and fifth year
students in September 2010.
WHAT'S IN IT FOR STUDENTS?
According as the revised strands are introduced, students will experience
mathematics in a new way, using examples and applications that are meaningful
for them. These will also allow students to appreciate how mathematics
relates to daily life and to the world of work. Students will develop
skills in analysing, interpreting and presenting mathematical information;
in logical reasoning and argument, and in applying their mathematical
knowledge and skills to solve familiar and unfamiliar problems.
JUNIOR CERTIFICATE MATHEMATICS
In the junior cycle, a more investigative approach will be used which
will build on and extend students' experience of mathematics in the
primary school. To provide better continuity with primary school mathematics,
a bridging framework is being developed that links the various strands
of mathematics in the primary school to topics in the Junior Certificate
mathematics syllabuses.
A common introductory course in mathematics at the start of the junior
cycle will make it possible for students to delay their choice of syllabus
level until a later stage. Two revised syllabus levels will be implemented
at Junior Certificate, Ordinary level and Higher level, with a targeted
uptake of 60% of the student cohort for Higher-level mathematics. This
is expected to facilitate increased uptake of Leaving Certificate Higher-level
mathematics.
Initially, a Foundation level examination, based on the revised Ordinary
level syllabus, will also be provided. As the revised syllabuses and
the targeted uptake become established, the necessity for the Foundation
level examination will be kept under review.
LEAVING CERTIFICATE MATHEMATICS
In the senior cycle, students' experience of mathematics will enable
them to develop the knowledge and skills necessary for their future
lives as well as for further study in areas that rely on mathematics.
Leaving Certificate Mathematics will be provided at three syllabus levels,
Foundation, Ordinary and Higher, with corresponding levels of examination
papers. An uptake of 30% at Higher level is targeted. The issue of the
status of the Foundation level course and the examination grades achieved
by candidates in terms of acceptability for some courses at third level
will be explored.
As the revised syllabus strands are introduced, there will be incremental
changes to the examination papers.
The table below sets out the schedule for the introduction of revised
syllabus strands. |
Specification
Aims
To develop understanding of modern methods of numerical linear algebra for
solving linear systems, least squares problems and the
eigenvalue problem.
Brief Description of the unit
This module treats the main classes of problems
in numerical linear algebra:
linear systems, least square problems, and eigenvalue problems,
covering both dense and sparse matrices.
It provides analysis of the problems along with algorithms for their solution.
It also introduces MATLAB as tool for expressing and implementing
algorithms and describes some of the key ideas used in developing
high-performance linear algebra codes (blocking, BLAS).
Applications will be introduced throughout the module.
Learning Outcomes
On successful completion of this course unit students will
understand the concepts of efficiency and stability of algorithms
in numerical linear algebra;
understand the importance of matrix factorizations,
and know how to construct some key factorizations using
elementary transformations;
be familiar with some important methods for
solving linear systems, least squares problems, and the eigenvalue
problem;
appreciate the issues involved in the choice of algorithm for particular
problems (sparsity, structure, etc.);
appreciate the basic concepts involved
in the efficient implementation of algorithms in a high-level language. |
Book Description: Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. In this textbook, João Hespanha covers the key topics of the field in a unique lecture-style format, making the book easy to use for instructors and students. He looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization, and examines advanced foundational topics such as multivariable poles and zeros, and LQG/LQR.The textbook presents only the most essential mathematical derivations, and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these important tools. The balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Solutions to the theoretical and computational exercises are also available for instructors.Easy-to-use textbook in unique lecture-style format Sidebars explain topics in further detail Annotated proofs and discussions of MATLAB commands Balanced chapters can each be taught in two hours of course lecture Solutions to exercises available to instructors |
An introduction to variables. The number-line is labeled and the different types of numbers are defined. Students manipulate simple equations, and practice constructing equations based on real world applications. |
Eric Robinson
Above all else, mathematics is a way of thinking. Eric Robinson, the director of COMPASS*--an NSF-sponsored program to implement new secondary mathematics curricula-- talks about the real-world advantages that students gain by learning to think with math concepts.
Why was COMPASS established?
In our efforts to improve the mathematics experience for pre-college students, there has been a realization that change needed to occur in all areas of the classroom: the way math was taught, what math was taught, what students were expected to be doing, what students were expected to get out of their mathematical experience, and how students were assessed.
So, our purpose is to provide support and advice to schools and districts as they implement mathematics education reform, and particularly to help them consider and implement mathematics curricula that reflect this new approach to mathematics education. COMPASS focuses on five high school, multi-year curricula that were developed with funds from the National Science Foundation and which support the vision of school mathematics set forth by the National Council of Teachers of Mathematics.
In what ways have the goals of mathematics education changed?
For one thing, we live in a new age. A strong understanding of mathematics that goes beyond computation is not just for future college math majors in today's world. It is important for all school students. Society is much more dependent on mathematics. Math affects almost every career--sometimes subtly and sometimes very apparently.
Let's look back a bit at the Industrial Age. If you worked on an assembly line, you were given a certain process and you just did the process over and over again. The world is not like that anymore. What we need, in the business world as well as in the professional world of mathematicians, scientists and engineers, is people who able to deal with open-ended situations, problems that are non-routine, and problems that aren't very well formulated. People have to be creative about their solutions, and draw on a variety of different sources to solve problems.
The mathematics curriculum needs to train students to do those things. It's not good enough to be able to solve just template problems. It's creative stuff. It's in a world that is changing almost every 24 hours in terms of what tools we have to work with and, what information and how quickly we get that information.
Maybe we should clarify what is meant by the term "mathematics"?
Well, there are several ways to talk about what mathematics is.
Certainly, it is a collection of facts. For example, all isosceles triangles have equal base angles.
It also contains a collection of operations, algorithms and procedures where, if you follow a certain sequence of computational steps, you get a guaranteed answer.
But to me, as a mathematician, far more important than any of those is that mathematics is a way of thinking. It's a method of inquiry.
More than once I've heard students say "I don't understand what they want me to do, but tell me what to do and I'll do it." They might have had the ability to do the procedures or memorize the facts, but they didn't have the ability to see where their facts were important, when to do the procedures or what the procedures meant.
To me, that's the antithesis of mathematics. The whole idea of doing mathematics is figuring out how to approach a problem. And then, of course, you have to have the ability to do some procedures. We do have to know how to do the computations---sometimes facilitated by the use of technology. But being able to do computations alone doesn't mean we know mathematics.
Doing mathematics includes lots of things. It can include looking at specific examples, trying to find patterns or making comparisons to situations that we already understand. It includes making conjectures. It includes figuring out how simpler situations work and seeing if we can then generalize to more complicated situations. It includes being able to abstract mathematical properties out of real situations. And it includes being able to reason logically.
Real mathematics requires all of these things. It requires mucking along, as well as knowing immediately what to do in some cases. But I know with too many students there's been a tendency to look at a problem and then, if there isn't an understanding of what to do immediately, they skip the problem and ask the teacher the next day. We're not helping kids build in a sense of persistence or build in a sense of exploration that they're going to need to have to solve problems in the real world.
Is there other evidence that indicated a need for change?
Other evidence includes the Second International Mathematics and Science Study and the Third International Mathematics and Science Study. Both of them showed clearly that, internationally, we weren't competing well.
There was also the problem that students were leaving the study of mathematics in droves. As soon as students reached a level where mathematics was no longer required, half of them would quit. Then, the next year, half of the ones who were left would quit. And so on.
That trend of course is exactly contrary to increased need for mathematical ability in society. We were funneling everybody into mathematics courses at the beginning of school and getting a very, very small residue of those who would pursue it beyond high school.
For a whole variety of reasons we had to do better. Some of these reasons I have already mentioned. Others include the need to update the mathematical content of our courses and incorporate the use of new technology that allows us to examine mathematical concepts on a deeper level as well as utilize mathematical tools that remain primarily theoretical without the use of technological computational power. And so early in the 1990's the National Science Foundation put out a call for proposals to update the mathematics curriculum, incorporating not only a more complete approach to learning mathematics, but also based on the knowledge we had gained about how students learn and effective ways to teach.
And the result was?
The result was the development of new comprehensive curriculum materials at elementary, secondary and high school levels.
At the time, at the high school level, by and large across the country schools were committed to an algebra, geometry, advanced algebra, pre-calculus sequence. But when you look at how math is used in the real world, very often real world problems come without the content nicely separated like that.
A problem often can involve algebra and geometry and maybe some probability.
So, with the NSF support, out came high school level programs of three-year length or four-year length in which algebra, geometry and so on were intermixed.
These programs focus on mathematics as a process of reasoning, of thinking. They develop concepts so that there's an understanding of why, rather than simply being able to compute. Students develop a deeper mathematical understanding. And also they develop a deeper way to apply mathematics, such in as multi-step problems. These programs require students to synthesize ideas. And they require students to use math concepts and skills in places other than at the end of the chapter in which they're discussed.
What else was different about these materials?
For a long time mathematics educators adopted what I might loosely call the Euclidean approach. If you go back to Euclid's Elements, which was produced about 300 BC, the organization of the information was first, a statement, and then, a rationalization for it. So you had the answer first. Then, you got an understanding of why it worked.
Math education up through the early '80s was very much in the same spirit. Present some mathematical concepts, maybe some definitions, present the justification for those, present certain formulas and then the explanation of those formulas, do some examples of problems, and then practice with problems that were similar to the problems done in the text.
While this way may be an efficient way to present known results, it is not the best way to engage students in mathematical thinking. What we've learned is that it's more effective if you don't present quite so much to the student up front. Now, we try to present the questions before we give the answers so you get the kids' attention and interest. You get them hooked on pursuing understanding. And then you let them figure out how to get an answer. And when the students come up with the approach, they not only have a much better understanding, they retain their understanding better, too.
Retention, by the way, has long been a major problem in US math education. That's why a lot of topics in the US repeated year after year after year, because there was no retention of what was done. Now we have found that we can really improve retention, by putting the development of mathematics in a context that has some meaning for students. Very often, that takes the form of a real world situation. Real world context can be a wonderful way to provide meaning and mental "glue" for mathematical ideas and concepts.
What about the idea that some students will not be as good at developing inquiry skills, and will fall behind?
Well, it's true that some students will go further than others. But what we've seen is that every student can improve his ability to do mathematics and learn mathematics with this approach. Whereas with earlier approaches, students who did not grasp every new definition or procedure as it was presented to them would not be able to keep up at all with subsequent material.
If the curriculum is engaging, students will come along and will use each problem as an opportunity to exercise their ability to think. Their study of mathematics becomes a process of learning what they can do, not what they can't do.
What's supposed to happen as a result of having these new curricula?
Well, I think, personally, it would be wonderful if these five new curricula were adopted in every school across the country. But that is not just a simple matter of changing textbooks. It often requires a lengthy process, because it involves having teachers and other stakeholders really look at their beliefs and assumptions about what kind of mathematical education they want their high school students to get. It requires significant understanding by all concerned of the aspects and ramifications of such change. And it requires district administrative support for professional development of teachers who want to improve the educational experiences of their students in mathematics. Systemic change is not easy.
Of course these five programs are not the only answer--but they represent five different models that demonstrate an approach math education in the way we've been talking about
Some schools are going to transition in slower ways and will more gradually change their curriculum. But generally I do think we are seeing a continuous motion in the direction suggested by the NCTM standards and successful programs in other countries.
Anything else you'd like to say?
Just that I am very encouraged when I look at all the activities at improving mathematics education—including the valuable resource and promise of the Futures Channel. Because, to my mind, we are getting to the root of what mathematics is. In the world that our children are growing up into, we do need clear thinkers, we do need critical thinkers, we do need creative thinkers. And what better place than to develop those skills than in a mathematics classroom? |
Specification
Aims
To introduce students to
the elements of set theory and its role as a foundation for classical mathematics.
Brief Description of the unit
The notion of set is one of the fundamental notions of modern
mathematics. Set Theory was initiated by Cantor over a hundred years ago. He
developed a revolutionary theory of transfinite numbers that can be
used to compare the `sizes' of possibly infinite sets. The first part
of the course unit will be concerned with Cantor's theory. A naive
approach to set theory leads to paradox and Zermelo initiated an
axiomatic approach that puts set theory on a sound rigorous basis.
Axiomatic set theory can be viewed as a foundation of mathematics in
the following sense. All mathematical notions can be defined in
purely set theoretical terms and their properties can be proved using
only the set theoretical axioms. Also the language of set theory has
played a central unifying role in modern mathematics. These topics
will be examined in the second part of the course unit.
Learning Outcomes
On successful completion of this course unit students will have acquired
facility with the notions of elementary set theory;
a sound knowledge of the basic properties of the cardinal and
ordinal numbers;
familiarity with the axiom system ZF
and its role as a foundation for mathematics,
an understanding of the axiom of choice and some of its applications.
Future topics requiring this course unit
None.
Syllabus
Part I: The size of sets [15 lectures]
Standard set notation for elementary set theory; naive and not so
naive set theory; finite and countable sets; cardinal and ordinal
numbers - their ordering and arithmetic.
Part II: Axiomatic Set Theory [15 lectures]
The reduction of mathematical notions to purely set theoretic ones;
the ZF axioms for pure sets; the axiom of choice and the well-ordering
principle; the cumulative hierarchy.
Textbooks
There is no recommended textbook to cover the course. The
following are some good books to consult. |
To meet the demands of the world in which they will live, students
will need to adapt to changing conditions and to learn independently.
They will require the ability to use technology effectively and
the skills for processing large amounts of quantitative information.
TCT's mathematics curriculum prepares students for their tomorrows.
It equips them with essential mathematics knowledge and skills;
with skills of reasoning, problem solving, and communication; and,
most importantly, with the ability and the incentive to continue
learning on their own. |
Letter to Parents
Math Lab
by Rob Schultz
The purpose of Math Lab is to assist students in strengthening math skills necessary for success in assigned math classes. Various tools, projects, and in-class assignments will be used to support student understanding of math concepts. We will also discuss numerous strategies that students can use in the classroom for taking notes, taking tests, etc.
Algebra 2
by Rob Schultz
Algebra 2 is designed to build on concepts learned in Algebra 1 while continuing to develop mathematical and problem solving skills. Throughout the course, we will explore functions (linear, quadratic, exponential and logarithmic), graphing (with and without a graphing calculator), matrices, and systems of equations.
Scholarship PreCalculus
by Rob Schultz
Scholarship PreCalculus is designed to build on concepts learned in Algebra II while continuing to develop mathematical and problem solving skills. In addition to the function families introduced in Algebra 2, students will explore advanced function families including trigonometric, parametric, and polar functions, as well as conic sections. Basic calculus concepts will be introduced at the end of the year as time permits.
Intro Computer Science
by Rob Schultz
The Intro Computer Science course is designed to serve as a prerequiste to the AP Computer Science course. Students will explore basic programming techniques and object-oriented programming using Alice and the Java programming language.
AP Computer Science
by Rob Schultz
The AP Computer Science course is designed to be comparable to a college/university level, entry year computer science class using the JAVA programming language. Completion of Intro Computer Science or a comparable course is REQUIRED for enrollment in this course! |
calculator.com - Athera Corporation
Free access to online calculators to help you solve problems and answer questions in the home, office, and school. There are calculators for finance, business, and science, cooking, hobbies, and health. Some solve problems, some satisfy curiosity, and
...more>>
calculator.org - Flow Simulation Ltd.
A collection of calculator-related resources, including an online scientific
calculator, recommendations for hardware calculators, books about calculators, links to other online resources, and a free download of Calc98, a scientific,
engineering,Calculus: an Overview - Paul Pollack
Written by a 16-year-old, this site-in-progress contains brief summaries of topics for the advanced high school student. Available pages include: Functions: a review; Limits: what they mean and how to find them; Integration practice problems; Taylor and
...more>>
The Calendar Zone - Janice McLean
A collection of links about calendars, organized by topic: celestial, cultural, geographic, historic, etc. Includes an extensive list of calendar software for a 3000 Years Calendar (look through Julian, Gregorian, Hebrew and Islamic calendars to see conformity
...more>> |
Students will need the following materials to complete the course:
The necessary computer hardware as defined at the APEX website
Speakers to access the audio of the text.
A printer for the worksheets and a notebookDescription
The second semester of Algebra 2 covers the following mathematical topics: radical functions, exponential and logarithmic functions, probability and statistics, systems of equations and inequalities, matrices, conic sections, and sequences and series. Students enrolled in this course will complete an online curriculum called Compass Learning Odyssey (CLO). High School Math focuses on foundational skills to support learners, emphasizes repetition and practice of key skills, reinforces study habits, including note-taking, to sharpen students� comprehension, and covers National Mathematics Advisory Panel�s concepts for success in algebra. |
Courses found
- Mathcad
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In this course, you will learn the basics Mathcad Prime. You will learn about Mathcad Prime's extensive functionality such as opening and working with Mathcad files, navigating workspaces, defining variables and expressions, and solving equations. Further, you will learn how to plot graphs, solving for roots and manipulating data.
Nearest classes to your location
Virtual Class
Class Details (00159265)
Address
Registration Deadline
This course introduces the essentials of Mathcad, including its unique whiteboard interface, and math toolbars. It reinforces Mathcad's extensive functionality using clear, straightforward, trainer-led instruction and examples.
In this course, you will learn about Mathcad's advanced formatting capabilities. Using clear, straightforward instruction and examples, you will learn how to use Mathcad's formatting features such as creating headers and footers, hyperlinks, referencing a worksheet, embedding an object, protecting calculations, and adding metadata.
No classes available within the selected area
Currently, there are no classes available for this course within the area you selected. If you are interested in this class, please select another location or request the class below.
In this course, you will learn the essentials of Mathcad, including its unique whiteboard interface, and math toolbars. It reinforces Mathcad's extensive functionality using clear and concise trainer-led instruction and examples.
No classes available within the selected area
Currently, there are no classes available for this course within the area you selected. If you are interested in this class, please select another location or request the class below.
A hands-on, in-depth introductory course for the novice or intermediate user. Introduces the fundamentals of Mathcad, including its unique whiteboard interface, math toolbars, entering and editing of functions and expressions, arrays and range variables, units, 2D and 3D plots, as well as calculus and symbolic calculation.
No classes available within the selected area
Currently, there are no classes available for this course within the area you selected. If you are interested in this class, please select another location or request the class below.
By taking this course users will gain a general understanding of some of the more sophisticated applications of Mathcad, including solving & optimization, programming, data exchange & statistical analysis, and differential equations.
No classes available within the selected area
Currently, there are no classes available for this course within the area you selected. If you are interested in this class, please select another location or request the class below. |
Book Description: Following conveniently displayed in the back. This book is for parents of schooled students, homeschooling parents and teachers. Parents of schooled children find that the problems give their children a "leg up" for mastering all skills presented in the classroom. Homeschoolers use the Workbook - in conjunction with the Guide - as a complete Algebra 1 curriculum. Teachers use the workbook's problem sets to help children sharpen specific skills - or they can use the reproducible pages as tests or quizzes on specific topics. Like the Algebra Survival Guide, the Workbook is adorned with beautiful art and sports a stylish, teen-friendly design |
Learning Upgrade
Online Courses Featuring Songs, Video & Games
800-998-8864
Teaching Content
Curriculum of Algebra Upgrade
The map below shows the 60 lessons that students must complete in order to finish the Algebra Upgrade course. Students begin with the basics and move up to Linear Equations, Inequalities, Functions, Systems of Equations, Polynomials, Rational Expressions, Quadratics, and Radicals. Below the map are tables listing the content of each level by level and by subject area. |
Framework Maths: Year 9: Support Homework Book
Suitable for: Year 9 students following the Framework for Teaching Mathematics in England. Users of Framework Maths.
Homework for every lesson in a handy book
This homework book is written to complement the Support objectives in Year 9, and is especially useful for students using Framework Maths 9S. The convenient format means students do not need to take home the Students' book. The book is exceptional value for money at only £3.99 for 144 pages.
Features
Homework for every lesson with a focus on problem-solving activities
Worked examples where appropriate so that the book is self-contained
Past paper SAT questions at the end of each unit, levelled so you can check students'
progress
Great value for money
"Framework Maths was voted number 1 in a TES survey of top KS3 titles |
Student must have access to a high-speed (DSL or cable) Internet connection at least 4 days weekly, including a computer with sound and Java applet support, Microsoft Excel or Google Spreadsheet, a media player that can play Windows Media Player (WMA) and RealPlayer (RM) files, and a scanner or digital camera/phone. Access to a Graphing Calculator and experience using it is essential.
Description:
Description:
This one semester Pre-Calculus/Functions course prepares students for eventual work in Calculus. The central focus of this course is functions:
· linear,
· exponential and logarithmic,
· polynomial and rational,
· discrete and continuous,
· inverses, graphs, and applications.
The course will include other topics from advanced mathematics such as analytic geometry and three-dimensional geometry. Students will develop skills in applying the concepts by solving real-world problems.
Graphing calculators are used frequently in each lesson to familiarize students with the basics of graphing calculator use, to demonstrate concepts, to facilitate problem solving, and to verify results of problems solved algebraically. SAT practice topics and problems provide a review of the prerequisite courses.
MediaKit Contents: eBook: Precalculus Enhanced with Graphing Utilities
Syllabus: This course is designed to provide students with a thorough background in the mathematics of functions. This may be the last math course that some students take, while others will continue on to Precalculus: Trigonometry. At the conclusion of this course, all students will be prepared to take an introductory course in Calculus.
Because the use of graphing utilities is a key component of this course, all students will need access to a graphing calculator. While a scanner is not required, many students find it convenient to use one to submit assignments.
Each week contains an Are You Prepared? section which reviews the mathematics needed to master the week's topics. Each student is assigned to a study group, which provides a forum to work cooperatively on problems, discuss solutions and become better acquainted with classmates.
Week 4: Functions & Graphs
- Review for the Chapter 1 Test
- Distinguish between relations and functions
- Determine the domain of a function
- Evaluate a function
- Perform operations on functions
- Identify the graph of a function
- Obtain information from graphs
- Take a quiz as a team
- Start a Calculator Challenge called Caching Up
Week 7: Quadratic Functions & Inequalities
Graph quadratic functions using vertex, axis of symmetry, intercepts, transformations
Identify the vertex & axis of symmetry
Find max or min value of a quadratic
Find a quadratic function given vertex and one point
Solve inequalities involving a quadratic function
Prepare for and take the Chapter 2 test
Make a mid-course private journal entry giving feedback on the course
Week 10: Polynomial Inequalities & Composite Functions
Solve polynomial & rational inequalities algebraically & graphically
Form a composite function
Determine the domain of a composite function
Review for the Chapter 4 test
Analyze careers that use math and report on one of them
Week 11: One-to-one, Inverse & Exponential Functions
Determine if a function is one-to-one
Find the inverse of a function defined by a map, set of ordered pairs or an equation
Obtain the graph of the inverse function from the graph of the function
Define the number e
Evaluate, graph & solve exponential equations
Prepare for & take the Chapter 4 test
Start the Geometry Calculator Challenge
Week 12: Logarithmic Functions
Change exponential statements to logarithmic and logarithmic to exponential
Determine the domain of a logarithmic function
Evaluate logarithmic expressions
Graph logarithmic functions & solve logarithmic equations
Work with properties of logarithms
Write a logarithmic expression as a sum or difference of logarithms or as a single logarithm
Evaluate & graph a logarithm whose base is neither 10 nor e
Submit the Geometry Calculator Challenge |
Ability to manipulate numbers and use simple pre-algebra formulas.
It is suggested that students have headphones for this class, but it is not required. Students will be using a voice board during this class and will need to listen to and record messages. If your school does not have the necessary equipment for this tool, students can still participate by typing their messages into the voice board.
Course Requires a Media Kit to be Purchased by Course Sponsor
(see additional details below):
No
Description:
We hear about stock market gains and losses in the news each day – but what does it all really mean? In this course, you will learn about the fundamentals of investing, and even have the chance to invest your money and compare your results with the rest of the class!
We will learn how to create a budget, learn about banks and checking accounts, and discover how quickly money can grow. What do you know about credit and credit cards? In this course you will have the opportunity to look at credit card offers and learn about the ways credit card companies get new customers.
Have you ever thought of starting a part-time business? In this class you will have the opportunity to decide what type of business you would like to own, create your own advertisements, and learn about business competition.
Finally…accounting, what is it? This course will help you understand the importance of accounting concepts and how all businesses, including yours, need them! If you are interested in business and like using math in real world situations, join us as we discover MS Business Foundations!
** This course may also be appropriate for gifted and talented 6th grade students who have met the prerequisites** |
Mathematics in Non-Math Courses
In introductory courses such as chemistry, economics, political
science, and psychology, you will often see discussions of examples
and topics that require an understanding of concepts in mathematics
such as algebra. The examples below are taken directly from different
economics textbooks and they demonstrate the kinds of skills that
you will be required to use in many non-math introductory courses.
Example
Production costs are
divided into fixed costs and variable costs. All production costs
fall within these two categories, so total costs (TC)
equal total fixed costs (TFC) plus total variable costs
(TVC), or
The example above demonstrates the use of basic algebra skills
in economics. Without the ability to substitute values for the
variables, or the ability to evaluate this equation, there would
be no meaning to this paragraph or equation.
Below is a more complex linear equation that relates the yield
of lumber to maintenance of land. |
Pre-calculus Demystified 2/E
Synopsis
Your step-by-step solution to mastering precalculus
Understanding precalculus often opens the door to learning more advanced and practical math subjects, and can also help satisfy college requisites. Precalculus Demystified,It's a no-brainer! You'll learn about:
Linear questions
Functions
Polynomial division
The rational zero theorem
Logarithms
Matrix arithmetic
Basic trigonometry
Simple enough for a beginner but challenging enough for an advanced student, Precalculus Demystified, Second Edition, Second Edition, helps you master this essential subject.
Found In
eBook Information
ISBN: 9780071778503 |
Introductory Combinatorics, Coursesmart eTextbook
Description
This best-seller emphasizes combinatorial ideas—including the pigeon-hole principle, counting techniques, permutations and combinations, Pólya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatortial structures (matchings, designs, graphs), and flows in networks. The Fifth Edition clarifies the exposition throughout and adds a wealth of new exercises. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
1. What is Combinatorics?
1.1 Example: Perfect Covers of Chessboards
1.2 Example: Magic Squares
1.3 Example: The Four-Color Problem
1.4 Example: The Problem of the 36 Officers
1.5 Example: Shortest-Route Problem
1.6 Example: Mutually Overlapping Circles
1.7 Example: The Game of Nim
2. The Pigeonhole Principle
2.1 Pigeonhole Principle: Simple Form
2.2 Pigeonhole Principle: Strong Form
2.3 A Theorem of Ramsay
3. Permutations and Combinations
3.1 Four Basic Counting Principles
3.2 Permutations of Sets
3.3 Combinations of Sets
3.4 Permutations of Multisets
3.5 Combinations of Multisets
3.6 Finite Probability
4. Generating Permutations and Combinations
4.1 Generating Permutations
4.2 Inversions in Permutations
4.3 Generating Combinations
4.4 Generating r-Combinations
4.5 Partial Orders and Equivalence Relations
5. The Binomial Coefficients
5.1 Pascal's Formula
5.2 The Binomial Theorem
5.3 Unimodality of Binomial Coefficients
5.4 The Multinomial Theorem
5.5 Newton's Binomial Theorem
5.6 More on Partially Ordered Sets
6. The Inclusion-Exclusion Principle and Applications
6.1 The Inclusion-Exclusion Principle
6.2 Combinations with Repetition
6.3 Derangements
6.4 Permutations with Forbidden Positions
6.5 Another Forbidden Position Problem
6.6 Möbius Inversion
7. Recurrence Relations and Generating Functions
7.1 Some Number Sequences
7.2 Generating Functions
7.3 Exponential Generating Functions
7.4 Solving Linear Homogeneous Recurrence Relations
7.5 Nonhomogeneous Recurrence Relations
7.6 A Geometry Example
8. Special Counting Sequences
8.1 Catalan Numbers
8.2 Difference Sequences and Stirling Numbers
8.3 Partition Numbers
8.4 A Geometric Problem
8.5 Lattice Paths and Schröder Numbers
9. Systems of Distinct Representatives
9.1 General Problem Formulation
9.2 Existence of SDRs
9.3 Stable Marriages
10. Combinatorial Designs
10.1 Modular Arithmetic
10.2 Block Designs
10.3 Steiner Triple Systems
10.4 Latin Squares
11. Introduction to Graph Theory
11.1 Basic Properties
11.2 Eulerian Trails
11.3 Hamilton Paths and Cycles
11.4 Bipartite Multigraphs
11.5 Trees
11.6 The Shannon Switching Game
11.7 More on Trees
12. More on Graph Theory
12.1 Chromatic Number
12.2 Plane and Planar Graphs
12.3 A 5-color Theorem
12.4 Independence Number and Clique Number
12.5 Matching Number
12.6 Connectivity
13. Digraphs and Networks
13.1 Digraphs
13.2 Networks
13.3 Matching in Bipartite Graphs Revisited
14. Pólya Counting
14.1 Permutation and Symmetry Groups
14.2 Burnside's Theorem
14.3 Pólya's Counting formula |
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