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Teaching Secondary Mathematics : Techniques and Enrichment Units,9780130945143
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Teaching Secondary Mathematics : Techniques and Enrichment Units

by ;
Edition:
6th
ISBN13:

9780130945143

ISBN10:
0130945145
Format:
Paperback
Pub. Date:
1/1/2002
Publisher(s):
Prentice Hall
List Price: $93.33
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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

METHODS OF TEACHING SECONDARY MATHEMATICS 1(232)
The Challenge of Teaching
2(16)
Today's Students, Mathematics, and Society's Need
3(1)
Crisis in Math Education
3(1)
The Teacher Shortage
4(1)
Goals and Challenges for Secondary Math Teachers Today
5(3)
The Standards: Twelve Years of Growth
8(5)
Professional Development: A Teacher's Resource
13(1)
Resources for Teachers
14(1)
A Mathematics Debate
15(3)
Long-Range and Short-Range Planning
18(37)
Long-Range Planning
19(3)
Short-Range Planning
22(1)
The Daily Lesson Plan
22(4)
Examining Lesson Components More Closely
26(1)
Performance Objectives
26(2)
What Is Cooperative Learning?
28(1)
How to Structure Small Learning Groups
28(3)
The Teacher's Role in Managing Small-Group Learning
31(1)
How to Incorporate Small-Group Learning Into Mathematics Class
31(1)
Sample Lessons
32(7)
Sample Standards Lessons
39(16)
Teaching More Effective Lessons
55(41)
Motivational Techniques
56(1)
What Is Motivation?
56(1)
Motivating Students: Eight Techniques
56(6)
Classroom Questioning
62(1)
Classroom Questioning Features to Develop
63(1)
Some Precautionary Considerations for Improving Classroom Questioning
64(2)
Ten Types of Questions to Avoid
66(3)
Classroom Questioning as a Means to Generate Higher-Order Thinking
69(3)
Strategies for Teaching More Effective Lessons
72(1)
Using Tree Diagrams, or Branching
72(1)
Using Paper Folding or Cutting
73(1)
A Picture Is Worth a Thousand Words
74(2)
Recognizing Patterns
76(2)
Using Mathematical Models and Manipulatives
78(5)
Extending Familiar Concepts
83(5)
Using a Graphing Calculator
88(1)
Writing in the Mathematics Classroom
89(1)
Student Logs
89(1)
Student Journals
89(1)
Exposition
89(2)
Criteria for Evaluating Student Writing Samples
91(1)
Benefits of Writing Activities in the Mathematics Classroom
91(5)
The Role of Problem Solving
96(31)
A Psychological View of Problem Solving
99(1)
Problem-Solving Preliminaries
100(2)
An Introduction to Problem-Solving Strategies
102(6)
The Ten Problem-Solving Strategies
108(8)
Creating Mathematical Problems
116(1)
Creativity in Problem Solving
117(10)
Using Technology to Enhance Mathematics Instruction
127(30)
Calculators
128(1)
Calculators as an Aid to Problem Solving
128(1)
Examples of Calculator Activities
128(6)
Solving Equations Using Matrices
134(1)
Calculus Applications
135(2)
Computers
137(2)
Using The Geometer's Sketchpad
139(14)
The Geometer's Sketchpad and Enrichment Units
153(4)
Multiple Assessment and Grading Strategies
157(35)
Using Performance Assessment Tasks
158(1)
Using Rubrics to Evaluate Student Work
158(13)
Constructing a Class Test
171(12)
Administering a Test
183(1)
Grading a Test
184(2)
Interpreting Test Results
186(1)
Multiple Choice Tests
186(1)
Student Responsibilities
187(1)
Parental Responsibilities
187(1)
Determining the Course Grade
188(2)
Other Grading Schemes
190(2)
Enriching Mathematics Instruction
192(24)
Enriching Mathematics Instruction with a Historical Approach
193(8)
Enrichment Techniques for All Levels
201(1)
The Gifted Student
202(3)
Using Calculators to Enrich Instruction
205(2)
Models and Manipulatives That Enrich Instruction
207(9)
Extracurricular Activities in Mathematics
216(17)
The Mathematics Club
217(1)
Mathematics Teams
217(2)
Mathematics Contests
219(1)
Mathematics Projects
219(1)
The Mathematics Fair
220(2)
Cooperation With a University
222(1)
The School Mathematics Magazine
222(1)
The Mathematics Assembly Program
222(1)
Guest Speakers Program
223(1)
Class Trips of Mathematical Significance
223(1)
Peer Teaching Program
224(1)
The Computer
224(1)
The Bulletin Board
224(9)
ENRICHMENT UNITS FOR THE SECONDARY SCHOOL CLASSROOM 233(242)
Cross-Catalogue of Enrichment Units
233(242)
Constructing Odd-Order Magic Squares
240(2)
Constructing Even-Order Magic Squares
242(2)
Introduction to Alphametics
244(2)
A Checkerboard Calculator
246(2)
The Game of Nim
248(2)
The Tower of Hanoi
250(2)
What Day of the Week Was It?
252(5)
Palindromic Numbers
257(1)
The Fascinating Number Nine
258(2)
Unusual Number Properties
260(2)
Enrichment with a Hand-Held Calculator
262(2)
Symmetric Multiplication
264(2)
Variations on a Theme---Multiplication
266(2)
Ancient Egyptian Arithmetic
268(2)
Napier's Rods
270(1)
Unit Pricing
271(1)
Successive Discounts and Increases
272(2)
Prime and Composite Factors of a Whole Number
274(1)
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(2)
Geometric Dissections
286(2)
The Klein Bottle
288(1)
The Four Color Map Problem
289(2)
Mathematics on a Bicycle
291(3)
Mathematics and Music
294(2)
Mathematics in Nature
296(2)
The Birthday Problem
298(1)
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(1)
The Inaccessible Angle
308(2)
Triangle Constructions
310(2)
The Criterion of Constructibility
312(2)
Constructing Radical Lengths
314(1)
Constructing a Pentagon
315(1)
Investigating the Isosceles Triangle Fallacy
316(2)
The Equiangular Point
318(1)
The Minimum Distance Point of a Triangle
319(2)
The Isosceles Triangle Revisited
321(2)
Reflective Properties of the Plane
323(2)
Finding the Length of a Cevian of a Triangle
325(2)
A Surprising Challenge
327(2)
Making Discoveries in Mathematics
329(1)
Tessellations
330(2)
Introducing the Pythagorean Theorem
332(2)
Trisection Revisited
334(2)
Proving Lines Concurrent
336(2)
Squares
338(1)
Proving Points Collinear
339(2)
Angle Measurement with a Circle
341(2)
Trisecting a Circle
343(1)
Ptolemy's Theorem
344(2)
Constructing π
346(2)
The Arbelos
348(2)
The Nine-Point Circle
350(1)
The Euler Line
351(2)
The Simson Line
353(1)
The Butterfly Problem
354(2)
Equicircles
356(2)
The Inscribed Circle and the Right Triangle
358(2)
The Golden Rectangle
360(2)
The Golden Triangle
362(2)
Geometric Fallacies
364(2)
Regular Polyhedra
366(2)
An Introduction to Topology
368(1)
Angles on a Clock
369(2)
Averaging Rates---The Harmonic Mean
371(2)
Howlers
373(2)
Digit Problems Revisited
375(1)
Algebraic Identities
376(2)
A Method for Factoring Trinomials of the Form: ax2 + bx + c
378(1)
Solving Quadratic Equations
379(2)
The Euclidean Algorithm
381(2)
Prime Numbers
383(2)
Algebraic Fallacies
385(2)
Sum Derivations with Arrays
387(2)
Pythagorean Triples
389(2)
Divisibility
391(2)
Fibonacci Sequence
393(2)
Diophantine Equations
395(1)
Continued Fractions and Diophantine Equations
396(2)
Simplifying Expressions Involving Infinity
398(2)
Continued Fraction Expansions of Irrational Numbers
400(2)
The Farey Sequence
402(2)
The Parabolic Envelope
404(2)
Application of Congruence to Divisibility
406(2)
Problem Solving---A Reverse Strategy
408(3)
Decimals and Fractions in Other Bases
411(1)
Polygonal Numbers
412(3)
Networks
415(2)
Angle Trisection---Possible or Impossible?
417(1)
Comparing Means
418(2)
Pascal's Pyramid
420(2)
The Multinomial Theorem
422(2)
Algebraic Solution of Cubic Equations
424(2)
Solving Cubic Equations
426(2)
Calculating Sums of Finite Series
428(2)
A General Formula for the Sum of a Series of the Form
430(3)
A Parabolic Calculator
433(2)
Constructing Ellipses
435(2)
Constructing the Parabola
437(2)
Using Higher Plane Curves to Trisect an Angle
439(2)
Constructing Hypocycloid and Epicycloid Circular Envelopes
441(2)
The Harmonic Sequence
443(1)
Transformations and Matrices
444(3)
The Method of Differences
447(1)
Probability Applied to Baseball
448(2)
Introduction to Geometric Transformations
450(2)
The Circle and the Cardioid
452(3)
Complex Number Applications
455(2)
Hindu Arithmetic
457(2)
Proving Numbers Irrational
459(1)
How to Use a Computer Spreadsheet to Generate Solutions to Certain Mathematics Problems
460(2)
The Three Worlds of Geometry
462(3)
πie Mix
465(1)
Graphical Iteration
466(2)
The Feigenbaum Plot
468(2)
The Sierpinski Triangle
470(2)
Fractals
472(3)
Appendix A Additional Exercises 475(6)
Appendix B Assigning Homework 481(11)
Index 492(4)
About the Authors 496


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