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Teaching Secondary School Mathematics : Techniques and Enrichment Units,9780136748052
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Teaching Secondary School Mathematics : Techniques and Enrichment Units

by ;
Edition:
5th
ISBN13:

9780136748052

ISBN10:
0136748058
Format:
Paperback
Pub. Date:
1/1/1999
Publisher(s):
Prentice Hall

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Summary

Using NCTM Standards as a foundation, this practical text once again leads the way in secondary mathematics instruction with unique enrichment units, technology updates, and a highly readable style. This book offers current and future instructors the nuts 'n bolts that are needed to improve mathematics instruction at the secondary level. It provides step-by step techniques on preparing lessons and tests, motivating students, designing assignments, and organizing the classroom. Also included are hands-on activities enrichment units, teaching strategies, and pre- and post-tests that are cross-referenced to methods presented earlier in the text.

Table of Contents

1 The Mathematics Teacher Today
1(5)
A Concise History of American Mathematics Education
2(2)
The Standards-A Vision for the Future
4(1)
Summary
4(2)
2 Planning Lessons, Assigning Homework, and Using Cooperative Learning
6(45)
The Unit Plan
7(1)
Long-Range Planning
7(1)
Short-Range Planning
8(4)
Performance Objectives
12(1)
Using Performance Objectives
12(1)
What Is Cooperative Learning?
12(1)
How to Structure Small Learning Groups
13(3)
The Teacher's Role in Managing Small Group Learning
16(1)
How to Incorporate Small Group Learning into Mathematics Class
17(1)
Assigning Homework
17(6)
Format of the Homework Assignment
23(1)
Reviewing the Homework Assignment
24(2)
Checking Homework Assignments
26(1)
Summary
27(4)
Sample Core Lessons
31(10)
Sample Before-Standards Lessons
41(7)
Creating Challenging Tasks
48(3)
3 Teaching More Effective Lessons
51(47)
SECTION I Teaching Sensitivity
52(2)
Concretizing Mathematics
52(1)
Competition in Mathematics Class
52(1)
Creating a Positive Learning Climate for All Students
52(1)
Summary
53(1)
SECTION 2 Strategies for Teaching More Effective Lessons
54(21)
Using Tree Diagrams, or Branching
54(1)
Using Paper Folding or Cutting
55(2)
A Picture Is Worth a Thousand Words
57(2)
Recognizing Patterns
59(2)
Using Mathematical Models and Manipulatives
61(6)
Using an Overhead Projector
67(2)
Extending Familiar Concepts
69(4)
Using a Graphing Calculator
73(1)
Summary
74(1)
SECTION 3 Classroom Questioning
75(11)
Classroom Questioning Features to Develop
76(1)
Some Precautionary Considerations for Improving Classroom Questioning
77(2)
Ten Types of Questions to Avoid
79(3)
Classroom Questioning as a Means to Generate Higher-Order Thinking
82(2)
Summary
84(2)
SECTION 4 Motivational Techniques
86(7)
What Is Motivation?
86(1)
Motivating Students: Eight Techniques
86(5)
Summary
91(2)
SECTION 5 Writing in the Mathematics Classroom
93(5)
Student Logs
93(1)
Student Journals
93(1)
Exposition
93(1)
Criteria for Evaluation Student Writing Samples
94(1)
Benefits of Writing Activities in the Mathematics Classroom
95(1)
Summary
96(2)
4 The Role of Problem-Solving Strategies in Teaching Mathematics
98(37)
A Psychological View of Problems Solving
101(1)
Problem Solving Preliminaries
102(2)
Problem Solving in Mathematics
104(5)
Strategies for Solving Problems
109(7)
Standard Algebraic Problems
116(2)
Standard Geometric Problems
118(3)
Nonroutine Problems
121(4)
Creating Mathematical Problems
125(1)
Summary
126(9)
5 Using Technology to Enhance Mathematics Instruction
135(39)
Using Technology to Enrich Instruction
136(1)
Calculators
136(5)
Enrichment in the 21st Century
141(1)
Pseudo-Calculators
141(1)
Computers
141(4)
Computer Literacy
145(2)
Computer Classroom Management
147(6)
The Geometer's Sketchpad: Software to Explore Geometry Dynamically
153(1)
A Brief Overview of The Geometer's Sketchpad
154(1)
The Geometer's Sketchpad In the Classroom
155(7)
A Quick Start with The Geometer's Sketchpad
162(8)
The Geometer's Sketchpad and Enrichment Units
170(1)
Summary
171(3)
6 Alternative Student Assessments and Grading Strategies
174(20)
Constructing a Class Test
175(7)
Administering a Test
182(1)
Grading a Test
183(2)
Interpreting Test Results
185(1)
Multiple Choice Tests
185(1)
Student Responsibilities
186(1)
Parental Responsibilities
187(1)
Determining the Course Grade
187(1)
Adjusted Classroom Tests and Quizes for Post-Standards Assessments
188(1)
Creating New Tests from Old
188(1)
Other Grading Schemes
189(1)
Summary
189(5)
7 Enriching Mathematics Instruction
194(22)
Enriching Mathematics Instruction with a Historical Approach
195(7)
Enrichment Techniques for All Levels
202(1)
The Gifted Student
203(3)
Using Calculators to Enrich Instruction
206(2)
Models and Manipulatives that Enrich Instruction
208(4)
Summary
212(4)
8 Extracurricular Activities in Mathematics
216(16)
The Mathematics Club
217(1)
Mathematics Teams
217(2)
Mathematics Contests
219(1)
Mathematics Projects
219(2)
The Mathematics Fair
221(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
223(1)
The Computer
224(1)
The Bulletin Board
224(1)
Summary
224(8)
9 The Learning Environment, Teacher Sensitivity, and Mathematics Teachers as Professionals
232(14)
The Professional Teacher
233(3)
Evaluation of the Teacher
236(1)
Summary
237(9)
10 Enrichment Units for the Secondary School Classroom
246(242)
1 Constructing Odd Order Magic Squares
253(2)
2 Constructing Even Order Magic Squares
255(2)
3 Introduction to Alphametics
257(2)
4 A Checkerboard Calculator
259(2)
5 The Game of Nim
261(2)
6 The Tower of Hanoi
263(2)
7 What Day of the Week Was It?
265(5)
8 Palindromic Numbers
270(1)
9 The Fascinating Number Nine
271(2)
10 Unusual Number Properties
273(2)
11 Enrichment with a Hand-Held Calculator
275(2)
12 Symmetric Multiplication
277(2)
13 Variations on a Theme-Multiplication
279(2)
14 Ancient Egyptian Arithmetic
281(2)
15. Napier's Rods
283(1)
16 Unit Pricing
284(1)
17 Successive Discounts and Increases
285(2)
18 Prime and Composite Factors of a Whole Number
287(1)
19 Prime Numeration System
288(2)
20 Repeating Decimal Expansions
290(2)
21 Peculiarities of Perfect Repeating Decimals
292(1)
22 Patterns in Mathematics
293(2)
23 Googol and Googolplex
295(2)
24 Mathematics of Life Insurance
297(2)
25 Geometric Dissections
299(2)
26 The Klein Bottle
301(1)
27 The Four Color Map Problem
302(2)
28 Mathematics on a Bicycle
304(3)
29 Mathematics and Music
307(2)
30 Mathematics in Nature
309(2)
31 The Birthday Problem
311(1)
32 The Structure of the Number System
312(2)
33 Excursions in Number Bases
314(2)
34 Raising Interest
316(2)
35 Reflexive, Symmetric, and Transitive Relations
318(2)
36 Bypassing an Inaccessible Region
320(1)
37 The Inaccessible Angle
321(2)
38 Triangle Constructions
323(2)
39 The Criterion of Constructibility
325(2)
40 Constructing Radical Lengths
327(1)
41 Constructing a Pentagon
328(1)
42 Investigation the Isosceles Triangle Fallacy
329(2)
43 The Equiangular Point
331(1)
44 The Minimum Distance Point of a Triangle
332(2)
45 The Isosceles Triangle Revisited
334(2)
46 Reflective Properties of the Plane
336(2)
47 Finding the Length of a Cevian of a Triangle
338(2)
48 A Surprising Challenge
340(2)
49 Making Discoveries in Mathematics
342(1)
50 Tessellations
343(2)
51 Introducing the Pythagorean Theorem
345(2)
52 Trisection Revisited
347(2)
53 Proving Lines Concurrent
349(2)
54 Squares
351(1)
55 Proving Points Collinear
352(2)
56 Angle Measurement with a Circle
354(2)
57 Trisecting a Circle
356(1)
58 Ptolemy's Theorem
357(2)
59 Constructing PI
359(2)
60 The Arbelos
361(2)
61 The Nine-Point Circle
363(1)
62 The Euler Line
364(2)
63 The Simson Line
366(1)
64 The Butterfly Problem
367(2)
65 Equicircles
369(2)
66 The Inscribed Circle and the Right Triangle
371(2)
67 The Golden Rectangle
373(2)
68 The Golden Triangle
375(2)
69 Geometric Fallacies
377(2)
70 Regular Polyhedra
379(2)
71 An Introduction to Topology
381(1)
72 Angles on a Clock
382(2)
73 Averaging Rates--The Harmonic Mean
384(2)
74 Howlers
386(2)
75 Digit Problems Revisited
388(1)
76 Algebraic Identities
389(2)
77 A Method for Factoring Trinomials of the Form: ax(2) + bx + c
391(1)
78 Solving Quadratic Equations
392(2)
79 The Euclidean Algorithm
394(2)
80 Prime Numbers
396(2)
81 Algebraic Fallacies
398(2)
82 Sum Derivations with Arrays
400(2)
83 Pythagorean Triples
402(2)
84 Divisibility
404(2)
85 Fibonacci Sequence
406(2)
86 Diophantine Equations
408(1)
87 Continued Fractions and Diophantine Equations
409(2)
88 Simplifying Expressions Involving Infinity
411(2)
89 Continued Fraction Expansions of Irrational Numbers
413(2)
90 The Farey Sequence
415(2)
91 The Parabolic Envelope
417(2)
92 Application of Congruence to Divisibility
419(2)
93 Problem Solving--A Reverse Strategy
421(3)
94 Decimals and Fractions in Other Bases
424(1)
95 Polygonal Numbers
425(3)
96 Networks
428(2)
97 Angle Trisection--Possible or Impossible?
430(1)
98 Comparing Means
431(2)
99 Pascal's Pyramid
433(2)
100 The Multinational Theorem
435(2)
101 Algebraic Solution of Cubic Equations
437(2)
102 Solving Cubic Equations
439(2)
103 Calculating Sums of Finite Series
441(2)
104 A General Formula for the Sum of a Series of the Form XXX t(r))
443(3)
105 A Parabolic Calculator
446(2)
106 Constructing Ellipses
448(2)
107 Constructing the Parabola
450(2)
108 Using Higher Plane Curves to Trisect an Angle
452(2)
109 Constructing Hypocycloid and Epicycloid Circular Envelopes
454(2)
110 The Harmonic Sequence
456(1)
111 Transformations and Matrices
457(3)
112 The Method of Differences
460(1)
113 Probability Applied to Baseball
461(2)
114 Introduction to Geometric Transformations
463(2)
115 The Circle and the Cardioid
465(3)
116 Complex Number Applications
468(2)
117 Hindu Arithmetic
470(2)
118 Proving Numbers Irrational
472(1)
119 How to Use a Computer Spreadsheet to Generate Solutions to Certain Mathematics Problems
473(2)
120 The Three Worlds of Geometry
475(3)
121 XXX Mix
478(1)
122 Graphical Iteration
479(2)
123 The Feigenbaum Plot
481(2)
124 The Sierpinski Triangle
483(2)
125 Fractals
485(3)
Index 488


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