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Teaching Secondary Mathematics : Techniques and Enrichment Units,9780131185203
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Teaching Secondary Mathematics : Techniques and Enrichment Units

by ; ;
Edition:
8th
ISBN13:

9780131185203

ISBN10:
0131185209
Format:
Paperback
Pub. Date:
1/1/2010
Publisher(s):
Allyn & Bacon
List Price: $123.40
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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 book provides mathematics teachers with a collection of enrichment units appropriate for the entire secondary school curriculum spectrum.

Table of Contents

The Challenge of Teaching
1(13)
Today's Students, Mathematics, and Society's Need
2(12)
Crisis in Math Education
2(1)
The Teacher Shortage
3(1)
Goals and Challenges for Secondary Math Teachers Today
4(3)
The Standards: Twelve Years of Growth
7(3)
Professional Development: A Teacher's Resource
10(2)
Resources for Teachers
12(1)
A Mathematics Debate
12(2)
Long-Range and Short-Range Planning
14(49)
Long-Range Planning of the Curriculum
15(1)
Scope and Sequence
15(1)
Unit Plans
16(5)
Unit Planning Model
16(2)
Interdisciplinary Planning
18(1)
Planning From a Fully Developed Curriculum
18(1)
Sources to Assist in Long-Range Planning
18(3)
Short-Range Planning
21(26)
Rationale for Planning Model
21(1)
Daily Lesson Planning
21(1)
Lesson Plan Template
21(6)
Assigning Homework
27(6)
Format of the Homework Assignment
33(1)
Reviewing the Homework Assignment
34(2)
Checking Homework Assignments
36(1)
Another Sample Lesson Plan
37(3)
Spiraling Content
40(6)
Reflecting on Your Lesson
46(1)
Differentiated Instruction
47(1)
Cooperative Learning
48(4)
What Is Cooperative Learning?
48(1)
How to Structure Small Learning Groups
48(3)
The Teacher's Role in Managing Small Group Learning
51(1)
Mathematical Tasks
52(2)
Final Thoughts on Lesson Planning
54(9)
Teaching More Effective Lessons
63(46)
Motivational Techniques
64(10)
What Is Motivation?
64(1)
Motivating Students: Ten Techniques
64(10)
Classroom Questioning
74(10)
Classroom Questioning Features to Develop
74(2)
Some Precautionary Considerations for Improving Classroom Questioning
76(2)
Ten Types of Questions to Avoid
78(3)
Classroom Questioning as a Means to Generate Higher Order Thinking
81(3)
Strategies for Teaching More Effective Lessons
84(17)
Using Tree Diagrams, or Branching
84(1)
Using Paper Folding or Cutting
85(1)
A Picture Is Worth a Thousand Words
86(2)
Recognizing Patterns
88(2)
Using Mathematical Models and Manipulatives
90(5)
Extending Familiar Concepts
95(5)
Using a Graphing Calculator
100(1)
Literacy in Mathematics
101(3)
Language Acquisition
101(1)
Comprehension
102(1)
Semantic Mapping
103(1)
Guided Reading
103(1)
Rich Mathematical Literacy Environment
104(1)
Writing
104(5)
Criteria for Evaluating Student Writing Samples
106(1)
Benefits of Writing Activities in the Mathematics Classroom
107(2)
The Role of Problem Solving
109(26)
A Psychological View of Problem Solving
112(1)
Problem-Solving Preliminaries
113(2)
An Introduction to Problem-Solving Strategies
115(6)
The Ten Problem-Solving Strategies
121(11)
Creating Mathematical Problems
132(1)
Creativity in Problem Solving
132(3)
Using Technology to Enhance Mathematics Instruction
135(31)
Calculators
136(10)
Appropriate Use of Calculators in the Mathematics Classroom
136(1)
Calculators as an Aid to Problem Solving
137(1)
Examples of Calculator Activities
137(6)
Solving Equations Using Matrices
143(2)
Calculus Applications
145(1)
Computers
146(20)
Appropriate Use of Computer Technology in the Mathematics Classroom
146(1)
Some Examples of Using the Computer to Enhance Instruction
147(4)
Introduction to Dynamic Geometry and The Geometer's Sketchpad
151(1)
Using The Geometer's Sketchpad
152(11)
Dynamic Data Analysis and Fathom
163(1)
Computer Algebra Systems
163(1)
Mathematical Equation Editors
163(1)
Multimedia
163(1)
Course Management Systems
163(3)
Assessment
166(31)
Assessment for Monitoring Student Progress
167(1)
Assessment for Making Instructional Decisions
167(1)
Evaluating Student Achievement
168(29)
Using Performance Assessment Tasks
169(1)
Using Rubrics to Evaluate Student Work
169(13)
Constructing a Rubric
182(1)
Constructing a Class Test
182(8)
Administering a Test
190(1)
Grading a Test
191(1)
Interpreting Test Results
192(1)
Multiple-Choice Tests
193(1)
Determining the Course Grade
193(2)
Final Thoughts on Evaluating Student Achievement
195(2)
Enriching Mathematics Instruction
197(20)
Enriching Mathematics Instruction with a Historical Approach
198(8)
Enrichment Techniques for All Levels
206(1)
The Gifted Student
207(3)
Using Calculators to Enrich Instruction
210(2)
Models and Manipulatives That Enrich Instruction
212(5)
Extracurricular Activities in Mathematics
217(14)
The Mathematics Club
218(1)
Mathematics Teams
218(2)
Mathematics Contests
220(1)
Mathematics Projects
220(2)
The Mathematics Fair
222(1)
Cooperation with a University
222(1)
The School Mathematics Magazine
222(2)
The Mathematics Assembly Program
224(1)
Guest Speakers Program
224(1)
Class Trips of Mathematical Significance
224(1)
Peer Teaching Program
225(1)
The Computer
225(1)
The Bulletin Board
226(5)
ENRICHMENT UNITS FOR THE SECONDARY SCHOOL CLASSROOM
231(260)
Cross-Catalogue of Enrichment Units
232(6)
Constructing Odd-Order Magic Squares
238(2)
Constructing Even-Order Magic Squares
240(2)
Introduction to Alphametics
242(2)
A Checkerboard Calculator
244(2)
The Game of Nim
246(2)
The Tower of Hanoi
248(2)
What Day of the Week Was It?
250(5)
Palindromic Numbers
255(2)
The Fascinating Number Nine
257(2)
Unusual Number Properties
259(2)
Enrichment with a Handheld Calculator
261(2)
Symmetric Multiplication
263(2)
Variations on a Theme---Multiplication
265(2)
Ancient Egyptian Arithmetic
267(2)
Napier's Rods
269(1)
Unit Pricing
270(1)
Successive Discounts and Increases
271(2)
Prime and Composite Factors of a Whole Number
273(2)
Prime Numeration System
275(2)
Repeating Decimal Expansions
277(2)
Peculiarities of Perfect Repeating Decimals
279(1)
Patterns in Mathematics
280(2)
Googol and Googolplex
282(2)
Mathematics of Life Insurance
284(1)
Geometric Dissections
285(2)
The Klein Bottle
287(2)
The Four-Color Map Problem
289(2)
Mathematics on a Bicycle
291(2)
Mathematics and Music
293(2)
Mathematics in Nature
295(2)
The Birthday Problem
297(2)
The Structure of the Number System
299(2)
Excursions in Number Bases
301(2)
Raising Interest
303(2)
Reflexive, Symmetric, and Transitive Relations
305(2)
Bypassing an Inaccessible Region
307(2)
The Inaccessible Angle
309(1)
Triangle Constructions
310(2)
The Criterion of Constructibility
312(2)
Constructing Radical Lengths
314(2)
Constructing a Pentagon
316(1)
Investigating the Isosceles Triangle Fallacy
317(2)
The Equiangular Point
319(2)
The Minimum-Distance Point of a Triangle
321(2)
The Isosceles Triangle Revisited
323(2)
Reflective Properties of the Plane
325(2)
Finding the Length of a Cevian of a Triangle
327(2)
A Surprising Challenge
329(1)
Making Discoveries in Mathematics
330(1)
Tessellations
331(3)
Introducing the Pythagorean Theorem
334(3)
Trisection Revisited
337(2)
Proving Lines Concurrent
339(2)
Squares
341(1)
Proving Points Collinear
342(2)
Angle Measurement with a Circle
344(2)
Trisecting a Circle
346(2)
Ptolemy's Theorem
348(2)
Constructing π
350(2)
The Arbelos
352(2)
The Nine-Point Circle
354(1)
The Euler Line
355(2)
The Simson Line
357(2)
The Butterfly Problem
359(2)
Equicircles
361(2)
The Inscribed Circle and the Right Triangle
363(2)
The Golden Rectangle
365(3)
The Golden Triangle
368(2)
Geometric Fallacies
370(2)
Regular Polyhedra
372(2)
An Introduction to Topology
374(2)
Angles on a Clock
376(2)
Averaging Rates---The Harmonic Mean
378(2)
Howlers
380(2)
Digit Problems Revisited
382(1)
Algebraic Identities
383(2)
A Method for Factoring Trinomials of the Form: ax2 + bx + c
385(2)
Solving Quadratic Equations
387(2)
The Euclidean Algorithm
389(2)
Prime Numbers
391(2)
Algebraic Fallacies
393(2)
Sum Derivations With Arrays
395(2)
Pythagorean Triples
397(3)
Divisibility
400(2)
Fibonacci Sequence
402(2)
Diophantine Equations
404(2)
Continued Fractions and Diophantine Equations
406(2)
Simplifying Expressions Involving Infinity
408(2)
Continued Fraction Expansion of Irrational Numbers
410(3)
The Farey Sequence
413(1)
The Parabolic Envelope
414(3)
Application of Congruence to Divisibility
417(2)
Problem Solving---A Reverse Strategy
419(3)
Decimals and Fractions in Other Bases
422(1)
Polygonal Numbers
423(3)
Networks
426(2)
Angle Trisection---Possible or Impossible?
428(2)
Comparing Means
430(2)
Pascal's Pyramid
432(2)
The Multinomial Theorem
434(2)
Algebraic Solution of Cubic Equations
436(2)
Solving Cubic Equations
438(3)
Calculating Sums of Finite Series
441(3)
A General Formula for the Sum of Series of the Form Σ
444(3)
A Parabolic Calculator
447(2)
Constructing Ellipses
449(2)
Constructing the Parabola
451(2)
Using Higher Plane Curves to Trisect an Angle
453(2)
Constructing Hypocycloid and Epicycloid Circular Envelopes
455(2)
The Harmonic Sequence
457(2)
Transformations and Matrices
459(3)
The Method of Differences
462(2)
Probability Applied to Baseball
464(1)
Introduction to Geometric Transformations
465(3)
The Circle and the Cardioid
468(2)
Complex-Number Applications
470(2)
Hindu Arithmetic
472(2)
Proving Numbers Irrational
474(2)
How to Use a Computer Spreadsheet to Generate Solutions to Certain Mathematics Problems
476(1)
The Three Worlds of Geometry
477(3)
πie Mix
480(1)
Graphical Iteration
481(3)
The Feigenbaum Plot
484(2)
The Sierpinski Triangle
486(2)
Fractals
488(3)
Appendix Additional Exercises 491(5)
References 496(20)
Index 516(4)
About the Authors 520


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