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Teaching Secondary Mathematics Techniques and Enrichment Units

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ISBN-10: 0130945145

ISBN-13: 9780130945143

Edition: 6th 2002

Authors: Alfred S. Posamentier, Jay S. Stepelman

List price: $93.33
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Description:

For Mathematics Methods for the Secondary School. The revision of this principal text introduces the 2000 NCTM Principles and Standards and explains their use for teaching secondary school mathematics instruction. Unlike other texts, it utilizes 125 enrichment units to provide the staples in preparing to teach mathematics. The authors provide step-by-step techniques on preparing lessons and tests, motivating students, designing assignments, and organizing the classroom. This valuable text also provides practical teaching methods for immediate use along with answers to typical questions readers have about teaching math.
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Book details

List price: $93.33
Edition: 6th
Copyright year: 2002
Publisher: Prentice Hall PTR
Publication date: 12/14/2001
Binding: Paperback
Pages: 495
Size: 8.25" wide x 10.50" long x 1.00" tall
Weight: 2.288
Language: English

Alfred S. Posamentier is professor of mathematics education and dean of the School of Education at the City College of the City University of New York. He has authored and co-authored several resource books in mathematics education for Corwin Press.

Methods of Teaching Secondary Mathematics
The Challenge of Teaching
Today's Students, Mathematics, and Society's Need
Crisis in Math Education
The Teacher Shortage
Goals and Challenges for Secondary Math Teachers Today
The Standards: Twelve Years of Growth
Professional Development: A Teacher's Resource
Resources for Teachers
A Mathematics Debate
Long-Range and Short-Range Planning
Long-Range Planning
Short-Range Planning
The Daily Lesson Plan
Examining Lesson Components More Closely
Performance Objectives
What Is Cooperative Learning?
How to Structure Small Learning Groups
The Teacher's Role in Managing Small-Group Learning
How to Incorporate Small-Group Learning Into Mathematics Class
Sample Lessons
Sample Standards Lessons
Teaching More Effective Lessons
Motivational Techniques
What Is Motivation?
Motivating Students: Eight Techniques
Classroom Questioning
Classroom Questioning Features to Develop
Some Precautionary Considerations for Improving Classroom Questioning
Ten Types of Questions to Avoid
Classroom Questioning as a Means to Generate Higher-Order Thinking
Strategies for Teaching More Effective Lessons
Using Tree Diagrams, or Branching
Using Paper Folding or Cutting
A Picture Is Worth a Thousand Words
Recognizing Patterns
Using Mathematical Models and Manipulatives
Extending Familiar Concepts
Using a Graphing Calculator
Writing in the Mathematics Classroom
Student Logs
Student Journals
Exposition
Criteria for Evaluating Student Writing Samples
Benefits of Writing Activities in the Mathematics Classroom
The Role of Problem Solving
A Psychological View of Problem Solving
Problem-Solving Preliminaries
An Introduction to Problem-Solving Strategies
The Ten Problem-Solving Strategies
Creating Mathematical Problems
Creativity in Problem Solving
Using Technology to Enhance Mathematics Instruction
Calculators
Calculators as an Aid to Problem Solving
Examples of Calculator Activities
Solving Equations Using Matrices
Calculus Applications
Computers
Using The Geometer's Sketchpad
The Geometer's Sketchpad and Enrichment Units
Multiple Assessment and Grading Strategies
Using Performance Assessment Tasks
Using Rubrics to Evaluate Student Work
Constructing a Class Test
Administering a Test
Grading a Test
Interpreting Test Results
Multiple Choice Tests
Student Responsibilities
Parental Responsibilities
Determining the Course Grade
Other Grading Schemes
Enriching Mathematics Instruction
Enriching Mathematics Instruction with a Historical Approach
Enrichment Techniques for All Levels
The Gifted Student
Using Calculators to Enrich Instruction
Models and Manipulatives That Enrich Instruction
Extracurricular Activities in Mathematics
The Mathematics Club
Mathematics Teams
Mathematics Contests
Mathematics Projects
The Mathematics Fair
Cooperation With a University
The School Mathematics Magazine
The Mathematics Assembly Program
Guest Speakers Program
Class Trips of Mathematical Significance
Peer Teaching Program
The Computer
The Bulletin Board
Enrichment Units for the Secondary School Classroom
Cross-Catalogue of Enrichment Units
Constructing Odd-Order Magic Squares
Constructing Even-Order Magic Squares
Introduction to Alphametics
A Checkerboard Calculator
The Game of Nim
The Tower of Hanoi
What Day of the Week Was It?
Palindromic Numbers
The Fascinating Number Nine
Unusual Number Properties
Enrichment with a Hand-Held Calculator
Symmetric Multiplication
Variations on a Theme--Multiplication
Ancient Egyptian Arithmetic
Napier's Rods
Unit Pricing
Successive Discounts and Increases
Prime and Composite Factors of a Whole Number
Prime Numeration System
Repeating Decimal Expansions
Peculiarities of Perfect Repeating Decimals
Patterns in Mathematics
Googol and Googolplex
Mathematics of Life Insurance
Geometric Dissections
The Klein Bottle
The Four Color Map Problem
Mathematics on a Bicycle
Mathematics and Music
Mathematics in Nature
The Birthday Problem
The Structure of the Number System
Excursions in Number Bases
Raising Interest
Reflexive, Symmetric, and Transitive Relations
Bypassing an Inaccessible Region
The Inaccessible Angle
Triangle Constructions
The Criterion of Constructibility
Constructing Radical Lengths
Constructing a Pentagon
Investigating the Isosceles Triangle Fallacy
The Equiangular Point
The Minimum Distance Point of a Triangle
The Isosceles Triangle Revisited
Reflective Properties of the Plane
Finding the Length of a Cevian of a Triangle
A Surprising Challenge
Making Discoveries in Mathematics
Tessellations
Introducing the Pythagorean Theorem
Trisection Revisited
Proving Lines Concurrent
Squares
Proving Points Collinear
Angle Measurement with a Circle
Trisecting a Circle
Ptolemy's Theorem
Constructing [pi]
The Arbelos
The Nine-Point Circle
The Euler Line
The Simson Line
The Butterfly Problem
Equicircles
The Inscribed Circle and the Right Triangle
The Golden Rectangle
The Golden Triangle
Geometric Fallacies
Regular Polyhedra
An Introduction to Topology
Angles on a Clock
Averaging Rates--The Harmonic Mean
Howlers
Digit Problems Revisited
Algebraic Identities
A Method for Factoring Trinomials of the Form: ax[superscript 2] + bx + c
Solving Quadratic Equations
The Euclidean Algorithm
Prime Numbers
Algebraic Fallacies
Sum Derivations with Arrays
Pythagorean Triples
Divisibility
Fibonacci Sequence
Diophantine Equations
Continued Fractions and Diophantine Equations
Simplifying Expressions Involving Infinity
Continued Fraction Expansions of Irrational Numbers
The Farey Sequence
The Parabolic Envelope
Application of Congruence to Divisibility
Problem Solving--A Reverse Strategy
Decimals and Fractions in Other Bases
Polygonal Numbers
Networks
Angle Trisection--Possible or Impossible?
Comparing Means
Pascal's Pyramid
The Multinomial Theorem
Algebraic Solution of Cubic Equations
Solving Cubic Equations
Calculating Sums of Finite Series
A General Formula for the Sum of a Series of the Form [characters not reproducible]
A Parabolic Calculator
Constructing Ellipses
Constructing the Parabola
Using Higher Plane Curves to Trisect an Angle
Constructing Hypocycloid and Epicycloid Circular Envelopes
The Harmonic Sequence
Transformations and Matrices
The Method of Differences
Probability Applied to Baseball
Introduction to Geometric Transformations
The Circle and the Cardioid
Complex Number Applications
Hindu Arithmetic
Proving Numbers Irrational
How to Use a Computer Spreadsheet to Generate Solutions to Certain Mathematics Problems
The Three Worlds of Geometry
[pi]ie Mix
Graphical Iteration
The Feigenbaum Plot
The Sierpinski Triangle
Fractals
Additional Exercises
Assigning Homework
Index
About the Authors