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Teaching Secondary Mathematics : Techniques and Enrichment Units

Teaching Secondary Mathematics : Techniques and Enrichment Units - 7th edition

ISBN13: 978-0131185203

Cover of Teaching Secondary Mathematics : Techniques and Enrichment Units 7TH 06 (ISBN 978-0131185203)
ISBN13: 978-0131185203
ISBN10: 0131185209
Cover type:
Edition/Copyright: 7TH 06
Publisher: Merrill Education/Prentice Hall
Published: 2006
International: No

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Teaching Secondary Mathematics : Techniques and Enrichment Units - 7TH 06 edition

ISBN13: 978-0131185203

Alfred S. Posamentier, Jay Stepelman and Beverly S. Smith

ISBN13: 978-0131185203
ISBN10: 0131185209
Cover type:
Edition/Copyright: 7TH 06
Publisher: Merrill Education/Prentice Hall

Published: 2006
International: No

Teaching Secondary Mathematics: Techniques and Enrichment Units, 7th edition has been thoroughly revised to discuss current methods of teaching mathematics, considering all aspects and responsibilities of the job, beginning with a brief overview of the history of mathematics education and how it has evolved over time to include standards for teaching and assessment. The authors address how to craft rich and effective daily lesson plans, and how to use a variety of instructional tools and strategies to reach all students in a classroom. Problem solving is a key focus from its instructional underpinnings to its recreational and motivational aspects. The second part of the text provides mathematics teachers with a collection of enrichment units appropriate for the entire secondary school curriculum spectrum.

Table of Contents

Chapter 1. The Challenge of Teaching

Today's Students, Mathematics, and Society's Need

Chapter 2. Planning for Instruction

Long-Range Planning of the Curriculum
Unit Plans
Short-Range Planning
Differentiated Instruction
Cooperative Learning
Mathematical Tasks
Final Thoughts on Lesson Planning

Chapter 3. Teaching More Effective Lessons

Motivational Techniques
Classroom Questioning
Strategies for Teaching More Effective Lessons
Literacy in Mathematics

Chapter 4. The Role of Problem-Solving

A Psychnological View of Problem Solving
Problem-Solving Preliminaries
An Introduction to Problem Solving
The Ten Problem-Solving Strategies
Creating Mathematical Problems
Creativity in Problem Solving

Chapter 5. Using Technology to Enhance Mathematics Instruction


Chapter 6. Assessment

Assessment for Monitoring Student Progress
Assessment for Making Instructional Decisions
Evaluating Student Achievement

Chapter 7. 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

Chapter 8. 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


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 Handheld 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
Introducing the Pythagorean Theorem
Trisection Revisited
Proving Lines Concurrent
Proving Points Collinear
Angle Measurement with a Circle
Trisecting a Circle
Ptolemy's Theorem
Constructing p
The Arbelos
The Nine-Point Circle
The Euler Line
The Simson Line
The Butterfly Problem
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
Digit Problems Revisited
Algebraic Identities
A Method for Factoring Trinomials of the Form: ax2 + bx + c
Solving Quadratic Equations
The Euclidean Algorithm
Prime Numbers
Algebraic Fallacies
Sum Derivations With Arrays
Pythagorean Triples
Fibonacci Sequence
Diophantine Equations
Continued Fractions and Diophantine Equations
Simplifying Expressions Involving Infinity
Continued Fraction Expansion 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
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 Series of the Form ? tr
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
pie Mix
Graphical Iteration
The Feigenbaum Plot
The Sierpinski Triangle

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