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

Cover type: PaperbackEdition: 7TH 06

Copyright: 2006

Publisher: Merrill Education/Prentice Hall

Published: 2006

International: No

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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.

**PART I METHODS OF TEACHING SECONDARY MATHEMATICS 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

Writing

**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**

Calculators

Computers

**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

**PART II 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 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

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 p

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: ax2 + 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 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

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 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

Fractals

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Summary

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

**PART I METHODS OF TEACHING SECONDARY MATHEMATICS 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

Writing

**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**

Calculators

Computers

**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

**PART II 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 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

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 p

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: ax2 + 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 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

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 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

Fractals

Publisher Info

Publisher: Merrill Education/Prentice Hall

Published: 2006

International: No

Published: 2006

International: No

**PART I METHODS OF TEACHING SECONDARY MATHEMATICS 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

Writing

**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**

Calculators

Computers

**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

**PART II 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 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

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 p

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: ax2 + 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 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

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 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

Fractals