Teaching Secondary Mathematics:Techniques and Enrichment Units

List 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

1. Constructing Odd-Order Magic Squares
2. Constructing Even-Order Magic Squares
3. Introduction to Alphametics
4. A Checkerboard Calculator
5. The Game of Nim
6. The Tower of Hanoi
7. What Day of the Week Was It?
8. Palindromic Numbers
9. The Fascinating Number Nine
10. Unusual Number Properties
11. Enrichment with a Handheld Calculator
12. Symmetric Multiplication
13. Variations on a Theme—Multiplication
14. Ancient Egyptian Arithmetic
15. Napier's Rods
16. Unit Pricing
17. Successive Discounts and Increases
18. Prime and Composite Factors of a Whole Number
19. Prime Numeration System
20. Repeating Decimal Expansions
21. Peculiarities of Perfect Repeating Decimals
22. Patterns in Mathematics
23. Googol and Googolplex
24. Mathematics of Life Insurance
25. Geometric Dissections
26. The Klein Bottle
27. The Four-Color Map Problem
28. Mathematics on a Bicycle
29. Mathematics and Music
30. Mathematics in Nature
31. The Birthday Problem
32. The Structure of the Number System
33. Excursions in Number Bases
34. Raising Interest
35. Reflexive, Symmetric, and Transitive Relations
36. Bypassing an Inaccessible Region
37. The Inaccessible Angle
38. Triangle Constructions
39. The Criterion of Constructibility
40. Constructing Radical Lengths
41. Constructing a Pentagon
42. Investigating the Isosceles Triangle Fallacy
43. The Equiangular Point
44. The Minimum-Distance Point of a Triangle
45. The Isosceles Triangle Revisited
46. Reflective Properties of the Plane
47. Finding the Length of a Cevian of a Triangle
48. A Surprising Challenge
49. Making Discoveries in Mathematics
50. Tessellations
51. Introducing the Pythagorean Theorem
52. Trisection Revisited
53. Proving Lines Concurrent
54. Squares
55. Proving Points Collinear
56. Angle Measurement with a Circle
57. Trisecting a Circle
58. Ptolemy's Theorem
59. Constructing π
60. The Arbelos
61. The Nine-Point Circle
62. The Euler Line
63. The Simson Line
64. The Butterfly Problem
65. Equicircles
66. The Inscribed Circle and the Right Triangle
67. The Golden Rectangle
68. The Golden Triangle
69. Geometric Fallacies
70. Regular Polyhedra
71. An Introduction to Topology
72. Angles on a Clock
73. Averaging Rates—The Harmonic Mean
74. Howlers
75. Digit Problems Revisited
76. Algebraic Identities
77. A Method for Factoring Trinomials of the Form: ax² + bx + c
78. Solving Quadratic Equations
79. The Euclidean Algorithm
80. Prime Numbers
81. Algebraic Fallacies
82. Sum Derivations With Arrays
83. Pythagorean Triples
84. Divisibility
85. Fibonacci Sequence
86. Diophantine Equations
87. Continued Fractions and Diophantine Equations
88. Simplifying Expressions Involving Infinity
89. Continued Fraction Expansion of Irrational Numbers
90. The Farey Sequence
91. The Parabolic Envelope
92. Application of Congruence to Divisibility
93. Problem Solving—A Reverse Strategy
94. Decimals and Fractions in Other Bases
95. Polygonal Numbers
96. Networks
97. Angle Trisection—Possible or Impossible?
98. Comparing Means
99. Pascal's Pyramid
100. The Multinomial Theorem
101. Algebraic Solution of Cubic Equations
102. Solving Cubic Equations
103. Calculating Sums of Finite Series
104. A General Formula for the Sum of Series of the Form ∑ t^r 
105. A Parabolic Calculator
106. Constructing Ellipses
107. Constructing the Parabola
108. Using Higher Plane Curves to Trisect an Angle
109. Constructing Hypocycloid and Epicycloid Circular Envelopes
110. The Harmonic Sequence
111. Transformations and Matrices
112. The Method of Differences
113. Probability Applied to Baseball
114. Introduction to Geometric Transformations
115. The Circle and the Cardioid
116. Complex-Number Applications
117. Hindu Arithmetic
118. Proving Numbers Irrational
119. How to Use a Computer Spreadsheet to Generate Solutions to Certain Mathematics Problems
120. The Three Worlds of Geometry
121. πie Mix
122. Graphical Iteration
123. The Feigenbaum Plot
124. The Sierpinski Triangle
125. Fractals

Appendix
Additional Exercises
Index
About the Authors

Summary

For courses in Secondary Mathematics Methods.
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.

Product details

• Authors: Alfred S. Posamentier, Beverly S. Smith, Jay Stepelman, Jay S Stepelman
• Publisher: Pearson Academic
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2005
• EAN: 9780131185203
• ISBN: 978-0-13-118520-3
• No. of pages: 504
• Series: Allyn & Bacon; Allyn & Bacon
• Subject: Humanities, art, music > Education > Education system