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Tables of Contents for Teaching and Learning Elementary and Middle School Mathematics
Chapter/Section Title
Page #
Page Count
Preparing to Teach Mathematics
1
15
Philosophical Considerations
4
1
What Is Mathematics?
4
1
What Does It Mean to Know Mathematics?
4
1
Implications of These Philosophical Considerations
5
1
Influences on the School Mathematics Curriculum
5
3
Professional Organizations
5
1
Principles and Standards for School Mathematics
6
1
Mathematics Textbooks
6
1
Assessment Procedures
7
1
State Governmental Bodies
8
1
Looking Ahead
8
2
NCTM Standards
8
1
Developing Skills
8
1
The Math Program
9
1
Communicating
9
1
Connecting
9
1
Assessing Mathematics Learning
9
1
Something for Everyone
10
1
Teaching Considerations
10
2
Key Ideas
12
1
Discussion Questions
12
1
References
12
3
Children and Mathematics
15
20
A Constructivist View of Learning
18
1
The Children's World
19
4
Children Have Many Number Experiences
19
1
Children Are Active in Their World
20
1
Children Observe Relationships in Their World
20
1
Children Learn Mathematics in Concert with Other Subjects
20
1
Children's Feelings Affect Their Ability to Learn
21
2
Psychological Considerations in Teaching Mathematics
23
6
Logical and Psychological Approaches to Mathematics
23
1
Sources of Information about How Children Learn Mathematics
24
1
How Children Form Mathematical Concepts
25
1
Dealing with Concepts Once Formed
26
1
Children's Thinking
26
1
Children's Communication of Mathematical Concepts
27
2
Teaching Children Mathematics
29
2
Teachers' Attitudes about Children
29
1
Teaching Style
29
1
Enhancing and Guiding Learning
30
1
Key Ideas
31
1
Discussion Questions
32
1
References
32
3
Solving and Creating Problems, Estimating, and Mental Calculating
35
28
Problem Solving
38
11
What Is a Problem?
38
1
Solving and Creating Problems
39
1
Characteristics of Good Problem Solvers and Good Problem Creators
40
1
Influences on a Person Trying to Solve or Create Problems
40
1
Heuristics or Strategies Used in Solving and Creating Problems
41
7
Problem Solving in Projects
48
1
Estimating
49
1
Weekly Estimations
49
1
Mental Calculating
50
2
Warm-Ups for a Math Lesson
50
2
Grouping Students for Problem Solving, Estimating, and Mental Calculating
52
1
Communicating in Problem Solving
53
1
Connecting Learning of Problem Solving, Estimating, and Mental Calculating
53
1
Assessing Learning of Problem Solving, Estimating, and Mental Calculating
53
6
Something for Everyone
59
1
Key Ideas
59
1
Discussion Questions
59
1
References
60
3
Technology in Teaching and Learning Mathematics
63
18
Calculators
66
5
How Should Calculators Be Used?
67
3
What Types of Calculators Should Be Purchased?
70
1
Computers
71
6
Other Technology
77
1
Overhead Projectors
77
1
Lettering Machines
77
1
Videotapes and Cameras
78
1
Slides and Cameras
78
1
Interactive Video, Telecommunications, and Other Newer Technologies
78
1
Key Ideas
78
1
Discussion Questions
78
1
References
79
2
Thinking Mathematically
81
36
Developing Concepts
85
11
Observing and Inferring
85
2
Comparing
87
1
Classifying
87
6
Sequencing
93
1
Relationships
93
3
Developing and Practicing Skills
96
9
Carroll Diagrams
96
3
Tree Diagrams
99
3
Venn Diagrams
102
3
Estimating
105
2
Solving and Creating Problems
107
3
Grouping Students for Mathematical Thinking
110
1
Communicating Learning of Mathematical Thinking Processes
110
1
Connecting Learning of Mathematical Thinking
111
1
Assessing Learning of Mathematical Thinking
111
3
Something for Everyone
114
1
Key Ideas
114
1
Discussion Questions
115
1
References
115
2
Attaching Meaning to Numbers
117
34
Developing Number Concepts
121
10
Conservation
122
2
Combinations
124
1
Zero
124
1
One-to-One Correspondence and Counting
125
1
Measuring Length
125
2
Grouping
127
4
Developing and Practicing Number Skills
131
9
Matching Numerals to Sets
131
1
Writing Numerals
132
1
Rational Counting
132
3
Number Names
135
1
Place Value
135
5
Estimating
140
1
Solving and Creating Problems
141
4
Grouping Students for Learning the Meaning of Numbers
145
1
Communicating Understanding of the Meaning of Numbers
145
1
Connecting Number Learning
146
1
Assessing Number Learning
146
1
Something for Everyone
147
1
Key Ideas
147
1
Discussion Questions
148
1
References
148
3
Teaching and Learning Addition and Subtraction
151
40
Developing Addition and Subtraction Concepts
155
9
Operations
156
1
Addition
157
4
Subtraction
161
3
Developing and Practicing Addition and Subtraction Skills
164
13
Basic Addition and Subtraction Facts
165
5
Addition and Subtraction Algorithms
170
7
Estimating and Mental Calculating
177
3
Solving and Creating Problems
180
6
Grouping Students for Learning Addition and Subtraction
186
1
Communicating Learning of Addition and Subtraction
186
1
Connecting Learning of Addition and Subtraction
186
1
Assessing Learning of Addition and Subtraction
187
1
Something for Everyone
188
1
Key Ideas
188
1
Discussion Questions
189
1
References
189
2
Teaching and Learning Multiplication and Division
191
38
Developing Multiplication and Division Concepts
194
7
Multiplication
195
3
Division
198
3
Developing and Practicing Multiplication and Division Skills
201
17
Basic Multiplication and Division Facts
201
5
Multiplication and Division Algorithms
206
12
Estimating and Mental Calculating
218
2
Solving and Creating Problems
220
3
Grouping Students for Learning Multiplication and Division
223
1
Communicating Learning of Multiplication and Division
223
1
Connecting Learning of Multiplication and Division
224
1
Assessing Learning of Multiplication and Division
225
1
Something for Everyone
226
1
Key Ideas
227
1
Discussion Questions
227
1
References
228
1
Attaching Meaning to Rational Numbers
229
32
Developing Rational Number Concepts
233
10
Part-Whole Model for a Common Fraction
233
3
Ratio Model for a Common Fraction
236
2
Using Common Fractions to Indicate Division
238
1
Decimal Fractions
239
2
Percent
241
1
Equivalent Fractions
241
1
Ordering Fractions
242
1
Developing and Practicing Rational Number Skills
243
8
Renaming Common Fractions
243
3
Reading and Writing Decimal Fractions
246
1
Renaming Common Fractions, Decimal Fractions, and Percents
247
1
Ordering Common and Decimal Fractions
248
1
Proportions
249
2
Estimating and Mental Calculating
251
1
Solving and Creating Problems
252
1
Grouping Students for Learning Rational Number Concepts
253
1
Communicating Learning of Rational Number Concepts
253
3
Connecting Learning of Rational Numbers
256
1
Assessing Learning of Rational Numbers
256
2
Something for Everyone
258
1
Key Ideas
258
1
Discussion Questions
258
1
References
259
2
Teaching and Learning Operations with Rational Numbers
261
42
Developing Concepts of Operations with Rational Numbers
265
22
Addition of Common Fractions
265
2
Addition of Decimal Fractions
267
4
Subtraction of Common Fractions
271
2
Subtraction of Decimal Fractions
273
1
Multiplication of Common Fractions
274
3
Multiplication of Decimal Fractions
277
2
Multiplication with Percent
279
1
Division of Common Fractions
280
3
Division of Decimal Fractions
283
4
Developing and Practicing Skills in Operations with Rational Numbers
287
5
Addition and Subtraction of Common Fractions
287
2
Addition and Subtraction of Decimal Fractions
289
1
Multiplication and Division of Common Fractions
290
1
Multiplication and Division of Decimal Fractions
291
1
Operations with Percents
292
1
Estimating and Mental Calculating with Rational Number Operations
292
2
Solving and Creating Problems
294
1
Grouping Students for Learning Rational Number Operations
295
1
Communicating Learning of Rational Number Operations
296
1
Connecting Learning of Rational Number Operations
296
1
Assessing Learning of Rational Number Operations
297
1
Something for Everyone
297
2
Key Ideas
299
1
Discussion Questions
299
1
References
300
3
Teaching and Learning Probability, Statistics, and Graphing
303
28
Developing Concepts of Probability, Statistics, and Graphing
306
12
Probability Concepts
306
3
Statistics Concepts
309
5
Graphing Concepts
314
4
Developing Skills in Probability and Graphing
318
3
Probability Skills
318
2
Graphing Skills
320
1
Estimating and Mental Calculating
321
1
Solving and Creating Problems
322
2
Grouping Students for Learning Probability, Statistics, and Graphing
324
1
Communicating Learning of Probability, Statistics, and Graphing
324
1
Connecting Learning of Probability, Statistics, and Graphing
325
1
Assessing Learning of Probability, Statistics, and Graphing
325
1
Something for Everyone
326
1
Key Ideas
327
1
Discussion Questions
327
1
References
327
4
Teaching and Learning Geometry
331
50
Developing Geometric Concepts
335
27
Young Children's Views of the World
337
2
Projective Geometry
339
2
Plane Figures and Their Properties
341
8
Symmetry and Motion
349
6
Space Figures
355
3
Fractal Geometry
358
4
Developing and Practicing Geometric Skills
362
6
Identifying Shapes
362
1
Copying and Inventing Shapes
362
1
Constructing Shapes
363
5
Estimating
368
2
Solving and Creating Problems
370
5
Grouping Students for Learning Geometry
375
1
Communicating Learning of Geometry
376
1
Connecting Learning of Geometry
376
1
Assessing Learning of Geometry
377
1
Something for Everyone
378
1
Key Ideas
378
1
Discussion Questions
378
1
References
378
3
Teaching and Learning Measurement
381
40
Developing Measurement Concepts
384
7
Length and Distance
385
1
Area
386
1
Weight and Mass
387
1
Time
388
1
Volume and Capacity
389
1
Temperature
389
1
Angle
390
1
Developing and Practicing Measurement Skills
391
23
Measuring Length
391
6
Measuring Area
397
3
Measuring Weight and Mass
400
3
Measuring Time
403
2
Measuring Volume and Capacity
405
3
Measuring Temperature
408
2
Measuring Angles
410
4
Estimating
414
1
Solving and Creating Problems
414
2
Grouping Students for Learning Measurement
416
1
Communicating Learning of Measurement
417
1
Connecting Learning of Measurement
417
1
Assessing Learning of Measurement
418
1
Something for Everyone
418
1
Key Ideas
419
1
Discussion Questions
419
1
References
420
1
Introducing Algebra
421
28
Developing Algebraic Concepts
425
16
Patterns and Relationships
425
2
Integers and Their Operations
427
3
Functions, Variables, Equations, and Inequalities
430
9
Solving Equations and Inequalities
439
2
Developing and Practicing Algebraic Skills
441
1
Estimating and Mental Calculating
442
1
Solving and Creating Problems
442
1
Grouping Students for Algebraic Learning
443
1
Communicating Learning of Algebraic Skills
443
1
Connecting Learning of Algebraic Concepts
443
1
Assessing Learning of Algebraic Concepts and Skills
444
1
Something for Everyone
444
1
Key Ideas
445
1
Discussion Questions
445
1
References
446
3
Organizing for Mathematics Instruction
449
28
Fitting Instruction to Students' Differing Needs and Styles
452
4
Planning for Teaching
453
1
Cooperative Learning
454
2
Assessing, Recording, and Reporting Students' Progress
456
6
Assessing Students' Progress
457
4
Recording Students' Progress
461
1
Reporting Students' Progress
461
1
Children with Special Needs
462
3
Children with Special Problems
462
1
Children with Special Mathematical Talents
463
2
Arranging the Classroom
465
4
Providing Learning Aids
469
5
Commercial Materials
469
2
Teacher-Made Learning Aids
471
3
Student-Made Learning Aids
474
1
Constructing Learning Aids
474
1
Key Ideas
474
1
Discussion Questions
475
1
References
475
2
Appendix A Suppliers of Manipulative Materials and Computer Software
477
4
Appendix B Blackline Masters
481
33
Index
514