Teaching Mathematics : A Sourcebook of Aids, Activities, and Strategies

by Sobel, Max A.; Maletsky, Evan M.

• ISBN13: 9780205292561
• ISBN10: 0205292569
• Edition: 3rd
• Format: Paperback
• Copyright: 1998-11-17
• Publisher: Pearson

Summary

The art of teaching math lies in the ability of the instructor to motivate and inspire individuals to look beyond the numbers and understand the concepts. This book is designed to revive this art, focusing more on the aspects of learning the ideas behind the math rather than the sheer mechanics of mathematical operation.This text addresses the art of teaching mathematics while also providing specific aids and activities in arithmetic, geometry, algebra and probability and statistics for use in the classroom. The authors pay close attention to the role, importance, methods and techniques of motivation. They present ideas that will generate attention, interest, and surprise among students, and will thus foster creative thinking. The material in the text is based on talks given by the authors at professional meetings, as well as the actual application of their ideas in undergraduate and graduate classes they taught. Additionally, many laboratory and discovery activities have been used by authors in teaching junior and senior high school math classes.Instructors of mathematics, school administrators, math specialists, and parents.

Table of Contents

Preface	ix
Chapter 1: The Art of Teaching	1	(32)
1.1 Start the Period in an Interesting Way	1	(3)
1.2 Use Historical Topics When Appropriate	4	(8)
1.3 Make Effective Use of Manipulative Aids	12	(4)
1.4 Make Provisions for Student Discovery	16	(7)
1.5 End the Period with Something Special	23	(6)
1.6 Conclusion	29	(1)
Exercises	30	(1)
Activities	31	(2)
Chapter 2: Motivating Mathematical Learning	33	(32)
2.1 Provide Opportunities for Guessing and Estimating	34	(2)
2.2 Make Use of "Mathemagical" Novelties	36	(4)
2.3 Introduce Unusual Arithmetic Explorations	40	(3)
2.4 Make Use of Geometric Challenges	43	(8)
2.5 Stimulate Interest with Mathematical Recreations	51	(3)
2.6 Use Bulletin Board Displays to Generate Interest	54	(4)
2.7 Discuss Applications of Mathematical Concepts	58	(2)
2.8 Conclusion	60	(1)
Exercises	61	(3)
Activities	64	(1)
Chapter 3: Motivating Problem-Solving Instruction	65	(24)
3.1 An Introduction to Problem Solving	66	(3)
3.2 Strategy for Problem Solving: Trial and Error	69	(3)
3.3 Strategy for Problem Solving: Use an Aid, Model, or Sketch	72	(4)
3.4 Strategy for Problem Solving: Search for a Pattern	76	(3)
3.5 Strategy for Problem Solving: Act It Out	79	(2)
3.6 Strategy for Problem Solving: Make a List, Table, or Chart	81	(3)
3.7 Conclusion	84	(1)
Exercises	85	(2)
Activities	87	(2)
Chapter 4: Activities with Numerical Concepts	89	(39)
4.1 Reviewing Basic Numerical Concepts	89	(2)
4.2 Fractions and Decimals	91	(7)
4.3 Percent	98	(2)
4.4 Computational Curiosities and Games	100	(1)
4.5 Number-Pattern Experiments	101	(7)
4.6 Magic Squares Activities	108	(7)
4.7 More Numerical Aids and Activities	115	(7)
4.8 Calculator Applications	122	(3)
Exercises	125	(1)
Activities	126	(2)
Chapter 5: Activities in Algebra	128	(35)
5.1 Motivation in Algebra	128	(4)
5.2 Solving Equations	132	(3)
5.3 Graphing and the Graphing Calculator	135	(4)
5.4 Sequences and Series Activities	139	(5)
5.5 Algebraic Models to Manipulate	144	(4)
5.6 More Aids and Activities	148	(3)
5.7 Overhead Projector Ideas	151	(4)
5.8 Calculator Applications	155	(4)
Exercises	159	(2)
Activities	161	(2)
Chapter 6: Activities in Geometry	163	(44)
6.1 Motivation in Geometry	163	(3)
6.2 Polygons	166	(7)
6.3 Polyhedrons	173	(6)
6.4 Constructing Models	179	(4)
6.5 Conic Sections	183	(8)
6.6 Visualization Activities	191	(7)
6.7 Measurement Experiments	198	(6)
Exercises	204	(1)
Activities	205	(2)
Chapter 7: Activities in Probability and Statistics	207	(29)
7.1 Motivation in Probability and Statistics	207	(3)
7.2 Counting and Probability	210	(5)
7.3 Probability Experiments	215	(6)
7.4 Statistical Activities	221	(3)
7.5 Games of Chance	224	(4)
7.6 Making Connections to Other Topics	228	(1)
7.7 Calculator Simulations	229	(4)
Exercises	233	(1)
Activities	234	(2)
Chapter 8: Iteration Activities and Fractal Patterns	236	(35)
8.1 Iteration Activities	236	(7)
8.2 Patterns from Triangles	243	(5)
8.3 Patterns from Squares	248	(5)
8.4 Constructing Fractal Patterns	253	(5)
8.5 Fractal Curves	258	(4)
8.6 Connections	262	(5)
Exercises	267	(2)
Activities	269	(2)
Epilogue	271	(4)
Answers to Odd-Numbered Exercises	275	(6)
Index	281