| Preface |
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xiii | |
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PART I A Journey toward Mathematical Success |
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1 | (100) |
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1 | (2) |
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1 | (1) |
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The Discipline of Mathematics |
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2 | (1) |
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2 | (1) |
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2 | (1) |
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3 | (2) |
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Professional Support: NCTM |
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3 | (1) |
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Principles and Standards for School Mathematics |
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3 | (1) |
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3 | (1) |
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3 | (2) |
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5 | (1) |
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5 | (1) |
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Making the NCTM Connection |
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6 | (1) |
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6 | (1) |
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Research Resources and Readings |
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6 | (3) |
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Chapter 0 Learning about Learning: Zero---A Real Starting Point |
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9 | (25) |
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9 | (1) |
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9 | (1) |
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Internal Representations That Match External Representations |
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10 | (2) |
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12 | (10) |
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12 | (1) |
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13 | (1) |
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14 | (4) |
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18 | (1) |
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Learning Styles and Modalities |
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19 | (1) |
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19 | (1) |
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19 | (1) |
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20 | (1) |
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Integrating Theoretical Views |
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21 | (1) |
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Formulating Learning Fundamentals |
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22 | (5) |
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Putting the Fundamentals to Work: An Instructional Sketch |
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27 | (1) |
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27 | (1) |
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27 | (1) |
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Making the NCTM Connection |
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28 | (1) |
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28 | (1) |
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29 | (1) |
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Research Resources and Readings |
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30 | (4) |
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Chapter 1 Thinking about Thinking: Identifying Problem-Solving Abilities |
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34 | (21) |
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34 | (1) |
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34 | (1) |
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35 | (1) |
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What is High-Level Thinking? |
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35 | (1) |
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35 | (1) |
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Zooming in on a Framework |
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36 | (1) |
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High-Level Cognitive Abilities |
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36 | (9) |
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Translating or Restating Communication |
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37 | (1) |
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Finding Properties, Identifying Similarities/Differences, Sorting, and Classifying |
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38 | (1) |
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Determining Sufficient and Necessary Conditions |
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39 | (1) |
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Finding Equivalent Conditions |
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40 | (1) |
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Recognizing When Conditions are Independent |
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41 | (1) |
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Extending a Pattern, Finding a Rule Based on Observations |
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41 | (1) |
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Detecting Faulty Thinking, Noting Contradictions |
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42 | (1) |
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Finding Needed Information |
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43 | (1) |
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Generating Cases or Alternatives |
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43 | (1) |
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44 | (1) |
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Elaborating, Extending, or Finding Analogous Ideas |
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44 | (1) |
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Planning Teaching/Learning Experiences |
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45 | (2) |
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Conditions of the Learner |
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45 | (1) |
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Teaching through High-Level Cognitive Thinking |
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46 | (1) |
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46 | (1) |
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Key Mathematics Thinking Abilities: A Chart |
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46 | (1) |
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47 | (1) |
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Introducing the MGB Portal |
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47 | (2) |
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48 | (1) |
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48 | (1) |
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49 | (1) |
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49 | (1) |
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50 | (1) |
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Research Resources and Readings |
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51 | (4) |
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Chapter 2 Problem Solving: A Way of Life |
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55 | (19) |
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55 | (1) |
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55 | (1) |
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55 | (2) |
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Using Problem-Solving Strategies |
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56 | (1) |
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Using Physical Aids, Props, or Tools |
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56 | (1) |
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Exhausting Possibilities or Cases |
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56 | (1) |
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Working a Problem Backward |
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57 | (1) |
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The Four-Step Problem-Solving Model |
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57 | (2) |
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Step 1 Understand the Problem |
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57 | (1) |
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Step 2 Devise at Least One Plan |
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57 | (1) |
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Step 3 Carry Out the Plan |
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58 | (1) |
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Step 4 Evaluate Your Plan and Solutions |
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58 | (1) |
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Using the Four-Step Problem-Solving Model |
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59 | (8) |
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Problem 1 Your Age May Win a Free Ice Cream Cone |
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59 | (1) |
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Problem 2 A Problem of Selection |
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60 | (1) |
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Problem 3 The T-Shirt Problem |
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61 | (1) |
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Problem 4 Calories Galore |
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62 | (1) |
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Problem 5 Working with Triangular Numbers |
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63 | (1) |
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Problem 6 Making Some Small Moves |
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63 | (1) |
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Problem 7 It's Not What Meets the Eye |
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64 | (1) |
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Problem 8 Sneaky Old Dogs |
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65 | (2) |
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Building a Problem-Solving Environment |
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67 | (1) |
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67 | (1) |
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67 | (1) |
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68 | (1) |
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It Looks Harder Than it is |
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68 | (1) |
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Developing Skills through Problem Solving |
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68 | (1) |
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69 | (1) |
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69 | (1) |
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69 | (1) |
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70 | (1) |
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70 | (1) |
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70 | (2) |
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Research Resources and Readings |
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72 | (2) |
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Chapter 3 What's Math Anyway? Unifying Ideas |
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74 | (27) |
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75 | (1) |
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Numbers and Classification |
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75 | (3) |
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75 | (1) |
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Set Ideas and Activities for Children |
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76 | (2) |
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78 | (5) |
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Where Did Numbers Come From? |
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78 | (1) |
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78 | (1) |
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Are There Different Kinds of Numbers? |
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79 | (1) |
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How Did the Arithmetic Operations Get Started? |
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80 | (1) |
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Zero: The Mathematical Big Bang |
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81 | (1) |
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81 | (1) |
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Implications for Teaching |
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82 | (1) |
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Doing and Thinking in Algebra |
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83 | (7) |
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Representation and Structure |
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84 | (1) |
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Relationships and Formulas |
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85 | (1) |
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85 | (1) |
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What Does Equal to Really Mean? |
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86 | (1) |
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87 | (1) |
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Searching for Patterns and Relationships |
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88 | (2) |
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Functions, Iterations, and Recursions |
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90 | (4) |
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90 | (2) |
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92 | (1) |
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93 | (1) |
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94 | (1) |
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94 | (1) |
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94 | (1) |
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The Literature Connection |
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95 | (1) |
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95 | (1) |
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95 | (1) |
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96 | (2) |
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Research Resources and Readings |
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98 | (3) |
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PART II From Counting to Division: Whole Numbers |
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101 | (196) |
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Types of Learning Activities |
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101 | (1) |
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101 | (1) |
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102 | (1) |
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102 | (1) |
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Problem-Solving Activities |
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102 | (1) |
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Drill and Practice Activities |
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102 | (1) |
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102 | (1) |
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102 | (1) |
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102 | (1) |
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The MGB Learning Resource |
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103 | (1) |
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103 | (1) |
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Research Resources and Readings |
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103 | (2) |
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Chapter 4 Getting Ready for a Good Beginning: Number Sense, Classification, and Counting |
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105 | (25) |
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106 | (1) |
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Helping Children Develop Pre-Number Concepts |
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106 | (7) |
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106 | (1) |
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Helping Children Learn to Classify |
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107 | (2) |
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Finding the Relation between Two Sets |
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109 | (2) |
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111 | (1) |
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Classifying on the Basis of Relations |
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112 | (1) |
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112 | (1) |
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Ordering Sets Using More Than or Less Than |
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112 | (1) |
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113 | (1) |
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Learning the Numbers 1 through 10 |
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113 | (5) |
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Naming a Family of Sets with a Number |
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113 | (1) |
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Making Sets with One More or One Less |
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114 | (1) |
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114 | (1) |
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115 | (1) |
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116 | (1) |
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117 | (1) |
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117 | (1) |
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117 | (1) |
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Getting Ready to Add and Subtract |
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118 | (2) |
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Matching Representations with Problem Situations |
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119 | (1) |
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Introducing the Idea of Function |
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119 | (1) |
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120 | (1) |
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121 | (1) |
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A Little about Fractions and Rational Numbers |
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122 | (1) |
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122 | (1) |
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123 | (1) |
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124 | (1) |
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125 | (1) |
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The Literature Connection |
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125 | (1) |
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125 | (1) |
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125 | (1) |
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126 | (1) |
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126 | (1) |
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126 | (2) |
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Research Resources and Readings |
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128 | (2) |
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Chapter 5 100s, 10s, Is, ... The Best Yet: Our Base-Ten Numeration System |
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130 | (29) |
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130 | (1) |
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Head and Shoulders above the Rest |
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130 | (3) |
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What is a Numeration System? |
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131 | (1) |
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Base-Five: An Analogous System |
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131 | (2) |
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Understanding the Base-Ten System of Numeration |
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133 | (4) |
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Ten Symbols and a Place Value Code |
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133 | (1) |
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Using Exponents and Powers of Ten |
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134 | (1) |
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134 | (1) |
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Reading and Writing Larger Numbers |
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134 | (1) |
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Extension to Decimal Fractions |
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135 | (1) |
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135 | (1) |
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136 | (1) |
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Finding Nonstandard Representations |
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136 | (1) |
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137 | (1) |
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Constructing Place Value Concepts |
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137 | (9) |
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Place Value Models for the Early Grades |
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137 | (1) |
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Strategies and Activities for the Early Grades |
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138 | (3) |
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141 | (2) |
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143 | (1) |
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Getting Ready to Round Numbers |
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144 | (1) |
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Place Value for Numbers through 1000 |
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144 | (1) |
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Using Teacher-Made and Commercial Aids |
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145 | (1) |
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Beyond Funny Faces: Place Value |
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146 | (6) |
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Using Bigger and Better Models |
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146 | (1) |
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Using Other Applications to Reinforce Place Value Ideas |
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147 | (1) |
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147 | (1) |
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148 | (1) |
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Reading and Writing Large Numbers |
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148 | (1) |
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Number Sense Explorations for Large Numbers |
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149 | (1) |
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Strategies for Ordering and Rounding Numbers |
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150 | (1) |
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Using Calculators to Teach Place Value |
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150 | (2) |
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152 | (1) |
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153 | (1) |
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154 | (1) |
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The Literature Connection |
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154 | (1) |
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154 | (1) |
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Problem-Solving Snapshots |
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154 | (1) |
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155 | (1) |
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155 | (1) |
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155 | (3) |
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Research Resources and Readings |
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158 | (1) |
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Chapter 6 Addition and Subtraction of Whole Numbers: Constructing Meaning |
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159 | (33) |
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159 | (1) |
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160 | (1) |
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160 | (1) |
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160 | (4) |
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Using Many Aids to Explore Addition |
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162 | (1) |
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The Interpretations for Addition |
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162 | (2) |
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Learning the Basic Facts of Addition |
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164 | (9) |
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164 | (3) |
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167 | (1) |
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168 | (1) |
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Systematic Strategies for Teaching the Basic Facts |
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169 | (4) |
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Constructing Meaning for Subtraction |
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173 | (9) |
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The Interpretations for Subtraction |
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173 | (2) |
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Strengthening Subtraction Concepts and Writing Number Sentences |
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175 | (3) |
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178 | (1) |
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Relating the Basic Facts of Addition to Subtraction |
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178 | (2) |
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180 | (2) |
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182 | (1) |
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183 | (1) |
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183 | (1) |
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184 | (2) |
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186 | (1) |
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186 | (1) |
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The Literature Connection |
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186 | (1) |
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Problem-Solving Snapshots |
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187 | (1) |
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187 | (1) |
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187 | (1) |
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188 | (1) |
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Research Resources and Readings |
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189 | (3) |
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Chapter 7 Addition and Subtraction, Whole Number Algorithms: Building, Understanding, Applying, and Estimating |
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192 | (20) |
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192 | (1) |
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192 | (1) |
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193 | (1) |
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Counting by 2s, 5s, and 10s |
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193 | (1) |
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Exploring "How Many in All?" |
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193 | (1) |
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194 | (5) |
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195 | (1) |
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195 | (4) |
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Exploring Ways to Subtract |
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199 | (1) |
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Developing a Subtraction Algorithm |
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200 | (4) |
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Subtraction Involving Numbers Greater Than 1000 |
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202 | (1) |
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Other Computational Ideas |
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203 | (1) |
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204 | (1) |
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Using Number Families and Doubles |
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204 | (1) |
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204 | (1) |
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Subtracting or Adding Equals |
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205 | (1) |
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Estimation for Addition and Subtraction |
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205 | (1) |
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Problem Solving with Addition and Subtraction |
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206 | (1) |
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207 | (1) |
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207 | (1) |
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208 | (1) |
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208 | (1) |
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The Literature Connection |
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208 | (1) |
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209 | (1) |
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209 | (1) |
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209 | (1) |
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209 | (1) |
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209 | (2) |
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Research Resources and Readings |
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211 | (1) |
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Chapter 8 Multiplication and Division of Whole Numbers: Constructing Meaning |
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212 | (29) |
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212 | (1) |
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Constructing Meaning for Multiplication |
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212 | (1) |
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The Interpretations for Multiplication |
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213 | (1) |
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The Additive Interpretation |
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213 | (1) |
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The Row-by-Column Interpretation |
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214 | (1) |
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The Combination Interpretation |
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214 | (1) |
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214 | (2) |
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Developmental Activities and the Multiplication Symbol |
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216 | (3) |
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Developing the Basic Facts of Multiplication |
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219 | (1) |
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Properties of Multiplication |
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220 | (3) |
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220 | (1) |
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The Commutative Property of Multiplication |
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221 | (1) |
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The Distributive Property of Multiplication over Addition |
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222 | (1) |
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The Associative Property for Multiplication |
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223 | (1) |
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Mastering the Basic Facts |
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223 | (3) |
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Division of Whole Numbers |
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226 | (1) |
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226 | (1) |
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Developmental Experiences for Division |
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226 | (1) |
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The Interpretations for Division |
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227 | (3) |
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The Subtractive or Measurement Interpretation |
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227 | (1) |
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The Distributive or Partition Interpretation |
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228 | (2) |
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Special Issues in Division |
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230 | (1) |
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You Don't Always Get a Whole Number |
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230 | (1) |
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230 | (1) |
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Putting it Together: The Four Operations |
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230 | (3) |
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An Introduction to Symbols of Inclusion |
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231 | (1) |
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Problem Solving with the Operations |
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232 | (1) |
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Reaching Out for New Connections |
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233 | (2) |
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233 | (1) |
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234 | (1) |
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More Than a Problem, a Project |
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234 | (1) |
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Investigations and Logical Thinking |
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234 | (1) |
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235 | (1) |
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235 | (1) |
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236 | (1) |
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The Literature Connection |
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236 | (1) |
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236 | (1) |
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237 | (1) |
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237 | (1) |
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237 | (2) |
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Research Resources and Readings |
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239 | (2) |
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Chapter 9 Multiplication and Division, Whole Number Algorithms: Building, Understanding, Estimating, and Applying |
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241 | (20) |
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241 | (1) |
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Operation Sense: Understanding Algorithms |
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241 | (1) |
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Products and Quotients of Multiples of 10 |
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242 | (2) |
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Exploring Computational Procedures for Multiplication |
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244 | (2) |
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Developing the Standard Multiplication Algorithm |
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246 | (1) |
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When to Teach What in Multiplication |
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247 | (1) |
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Exploring Computational Procedures for Division |
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248 | (1) |
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Developing a Division Algorithm |
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249 | (1) |
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When to Teach What in Division |
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250 | (1) |
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More about Mental Arithmetic |
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251 | (1) |
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251 | (2) |
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Problem-Solving Connection |
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253 | (1) |
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254 | (1) |
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255 | (1) |
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255 | (1) |
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The Literature Connection |
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255 | (1) |
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256 | (1) |
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256 | (1) |
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256 | (1) |
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256 | (2) |
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Research Resources and Readings |
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258 | (3) |
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Chapter 10 Assessing Teaching and Learning: Putting the Pieces Together |
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261 | (26) |
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261 | (1) |
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What is Assessment and What is Not Assessment? |
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262 | (1) |
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262 | (1) |
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What are the purposes of Assessment? |
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262 | (1) |
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262 | (1) |
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Improving Student Learning |
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262 | (1) |
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Analyzing Patterns of Growth |
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263 | (1) |
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Modifying Lesson Development and Learning Aids |
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263 | (1) |
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Modifying Teaching Strategies |
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263 | (1) |
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Modifying Curriculum Goals and Standards |
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263 | (1) |
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What are the Characteristics of Effective Assessment? |
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263 | (2) |
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What are the Tools of Assessment? |
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265 | (1) |
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265 | (4) |
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A Set of Criterion Categories |
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265 | (1) |
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266 | (1) |
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266 | (1) |
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266 | (2) |
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268 | (1) |
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Rubrics with Analytical Scales |
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268 | (1) |
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269 | (1) |
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269 | (3) |
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Checklists for Small Groups |
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269 | (1) |
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Checklists for Large Groups |
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270 | (1) |
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Checklists for Individual Students |
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271 | (1) |
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Checklists for Group Participation |
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271 | (1) |
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Interviews: Question-and-Answer Sessions |
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272 | (1) |
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Pencil-and-Paper Testing: A Traditional Method for Assessing Learning |
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273 | (1) |
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274 | (6) |
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Student-Prepared Journals |
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274 | (3) |
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277 | (1) |
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278 | (2) |
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Let Students Make Assessments |
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280 | (1) |
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280 | (1) |
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Assessing Their Own Work Habits and Progress |
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281 | (1) |
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Reporting Final Outcomes and Assigning Grades |
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281 | (1) |
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282 | (1) |
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282 | (1) |
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The Literature Connection |
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282 | (1) |
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282 | (1) |
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283 | (1) |
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283 | (1) |
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283 | (1) |
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Research Resources and Readings |
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284 | (3) |
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Chapter 11 A Fitting Finale for Part II: Predicting Student Difficulties |
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287 | (10) |
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287 | (1) |
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287 | (2) |
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What Learner Characteristics Can Be Diagnosed? |
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288 | (1) |
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What Skills Must the Teacher Have? |
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288 | (1) |
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Why do Students Make Errors? |
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289 | (1) |
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Place Value and Understanding the Operation |
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289 | (1) |
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Difficulty with Prerequisite Skills |
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289 | (1) |
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289 | (1) |
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A Catalog of Difficulties |
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289 | (5) |
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290 | (1) |
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291 | (1) |
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Multiplication and Division |
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292 | (1) |
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293 | (1) |
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294 | (1) |
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294 | (1) |
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294 | (1) |
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295 | (1) |
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Research Resources and Readings |
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296 | (1) |
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PART III The Rest of the Rationals |
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297 | (110) |
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Chapter 12 Some Theory about Numbers: Factors, Multiples, Primes, and Composites |
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299 | (33) |
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299 | (1) |
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299 | (1) |
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Even Numbers and Odd Numbers |
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300 | (7) |
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Exploratory Activities for Even and Odd |
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301 | (1) |
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Developmental Activities for Even and Odd |
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302 | (1) |
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303 | (4) |
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307 | (1) |
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308 | (4) |
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Using Rainbow Diagrams to Examine the Factors of a Number |
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310 | (1) |
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311 | (1) |
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Using the Prime Factorization |
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311 | (1) |
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Using Upside-Down Division |
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311 | (1) |
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312 | (2) |
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Discovering Divisibility Rules |
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312 | (1) |
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312 | (1) |
|
Justifying Divisibility Rules |
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313 | (1) |
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Prime Factorization Revisited |
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314 | (3) |
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Greatest Common Factor: Going a Little Deeper |
|
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317 | (1) |
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The Prime Factors Approach |
|
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317 | (1) |
|
A Sure Way to Find the GCF |
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317 | (1) |
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318 | (2) |
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318 | (1) |
|
A More Systematic Way to Find the LCM |
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319 | (1) |
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320 | (1) |
|
Applications with Calculators |
|
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320 | (1) |
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Problem Solving with Number Theory |
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321 | (1) |
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Beyond Factors and Multiples |
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322 | (3) |
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322 | (1) |
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323 | (1) |
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323 | (1) |
|
Special Numbers in Number Theory |
|
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324 | (1) |
|
Logic and Careful Use of Language |
|
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324 | (1) |
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325 | (1) |
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326 | (1) |
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326 | (1) |
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326 | (1) |
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326 | (1) |
|
Problem-Solving Snapshots |
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327 | (1) |
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327 | (1) |
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327 | (1) |
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327 | (3) |
|
Research Resources and Readings |
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330 | (2) |
|
Chapter 13 Superstitious? Not Us: But We Believe in the Magic of Children |
|
|
332 | (2) |
|
Chapter 14 Not All Numbers are Whole Numbers: Representing, Adding, and Subtracting Rational Numbers |
|
|
334 | (39) |
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|
334 | (1) |
|
What is a Rational Number? |
|
|
334 | (3) |
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Fractions Can Be Used to Represent Rational Numbers |
|
|
335 | (1) |
|
Decimal Fractions Can Be Used to Represent Rational Numbers |
|
|
336 | (1) |
|
Rational Number Models and Applications |
|
|
337 | (4) |
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|
|
337 | (1) |
|
Building a Checklist for Rational Numbers |
|
|
338 | (1) |
|
Updating the Rational Number Checklist |
|
|
339 | (1) |
|
Teaching Rational Number Concepts |
|
|
339 | (1) |
|
|
|
340 | (1) |
|
Exploratory Activities: Part-Whole |
|
|
340 | (1) |
|
Learning to Use Rational Numbers |
|
|
341 | (7) |
|
|
|
341 | (2) |
|
A Structured Approach for Developing Key Concepts |
|
|
343 | (4) |
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|
347 | (1) |
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|
348 | (1) |
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|
|
348 | (1) |
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|
349 | (3) |
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|
|
349 | (1) |
|
Ordering Numbers Represented by Fractions |
|
|
350 | (1) |
|
Adding and Subtracting with Fractions and Mixed Numerals |
|
|
351 | (1) |
|
Decimals: A Better Way to Work with Rational Numbers |
|
|
352 | (4) |
|
|
|
353 | (1) |
|
|
|
354 | (2) |
|
Addition and Subtraction with Decimals |
|
|
356 | (2) |
|
|
|
358 | (3) |
|
|
|
361 | (2) |
|
|
|
363 | (1) |
|
The Power of Problem Simulation |
|
|
363 | (1) |
|
The Problem: Angelo's Model Train Business |
|
|
363 | (1) |
|
Strategies for Guiding Children through the Problem |
|
|
363 | (1) |
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|
|
364 | (2) |
|
|
|
366 | (1) |
|
|
|
366 | (1) |
|
|
|
366 | (1) |
|
|
|
367 | (1) |
|
Problem-Solving Snapshots |
|
|
367 | (1) |
|
|
|
367 | (1) |
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|
|
368 | (1) |
|
|
|
368 | (1) |
|
Research Resources and Readings |
|
|
369 | (4) |
|
Chapter 15 Security is Knowing Why: Multiplying and Dividing Rational Numbers |
|
|
373 | (34) |
|
|
|
373 | (1) |
|
Constructing Meaning for Multiplication |
|
|
373 | (6) |
|
The Additive Interpretation |
|
|
373 | (4) |
|
A Special Relationship: The Reciprocal |
|
|
377 | (1) |
|
The Area Interpretation for Multiplication |
|
|
378 | (1) |
|
Algorithms for Multiplication with Fractions |
|
|
379 | (1) |
|
Multiplication with Decimals |
|
|
380 | (2) |
|
Division of Rational Numbers |
|
|
382 | (3) |
|
|
|
382 | (1) |
|
Developing and Justifying an Algorithm for Division with Fractions |
|
|
383 | (1) |
|
Using the Equivalent Fraction Rule to Justify the Division Algorithm |
|
|
384 | (1) |
|
|
|
385 | (5) |
|
|
|
385 | (1) |
|
Developing and Justifying an Algorithm for Division with Decimals |
|
|
386 | (2) |
|
Terminating and Repeating Decimals |
|
|
388 | (2) |
|
|
|
390 | (1) |
|
|
|
391 | (1) |
|
|
|
391 | (1) |
|
|
|
391 | (1) |
|
The Finishing Touches: Positive and Negative |
|
|
392 | (5) |
|
Adding and Subtracting Integers with Links |
|
|
393 | (1) |
|
Multiplying and Dividing Integers with Links |
|
|
393 | (1) |
|
Other Models for Integers |
|
|
394 | (3) |
|
Finally, Rational Numbers |
|
|
397 | (1) |
|
The Problem-Solving Connection |
|
|
397 | (2) |
|
|
|
399 | (1) |
|
|
|
400 | (1) |
|
|
|
400 | (1) |
|
The Literature Connection |
|
|
400 | (1) |
|
|
|
400 | (1) |
|
Problem-Solving Snapshots |
|
|
401 | (1) |
|
|
|
401 | (1) |
|
|
|
401 | (1) |
|
|
|
402 | (2) |
|
Research Resources and Readings |
|
|
404 | (3) |
|
PART IV Beyond Arithmetic |
|
|
407 | (114) |
|
Chapter 16 Seeing is Believing: Constructing Geometric Ideas |
|
|
409 | (38) |
|
|
|
409 | (1) |
|
Research and Models for Learning Geometry |
|
|
409 | (2) |
|
|
|
411 | (1) |
|
Children's Development of Geometric Ideas before Age 4: Forming Topological Impressions |
|
|
412 | (2) |
|
Children's Development of Geometric Ideas from Ages 4 to 7: Developing Euclidian Concepts |
|
|
413 | (1) |
|
Geometry Experiences for Kindergarten through Second Grade |
|
|
414 | (2) |
|
Activities for the Development of Topological Concepts |
|
|
415 | (1) |
|
Activities for Teaching about Plane Figures |
|
|
416 | (12) |
|
Activities for Teaching about Space Figures |
|
|
420 | (1) |
|
|
|
421 | (1) |
|
Children's Development of Geometric Ideas from Ages 7 to 9 |
|
|
422 | (1) |
|
Geometry Experience for Grades 2 through 4 |
|
|
423 | (1) |
|
Activities for Teaching about Plane Figures |
|
|
423 | (4) |
|
Activities for Teaching about Space Figures |
|
|
427 | (1) |
|
Children's Development of Geometric Ideas from Ages 9 to 13 |
|
|
428 | (1) |
|
Geometry Experience for Grades 4 through 8 |
|
|
429 | (6) |
|
|
|
429 | (1) |
|
|
|
429 | (1) |
|
Using a Coordinate System |
|
|
430 | (2) |
|
|
|
432 | (1) |
|
Finding Cross Sections of Space Figures |
|
|
432 | (1) |
|
Ruler and Compass Constructions |
|
|
433 | (1) |
|
Long-Term Projects or Investigations |
|
|
434 | (1) |
|
The Problem-Solving Connection |
|
|
435 | (1) |
|
|
|
436 | (2) |
|
Visualization and Assessment |
|
|
436 | (1) |
|
Analyzing Properties and Assessment |
|
|
436 | (1) |
|
Assessment for Informal Induction and Deduction |
|
|
437 | (1) |
|
|
|
438 | (1) |
|
|
|
438 | (1) |
|
The Literature Connection |
|
|
438 | (1) |
|
|
|
439 | (1) |
|
|
|
439 | (1) |
|
|
|
439 | (1) |
|
|
|
440 | (1) |
|
|
|
440 | (2) |
|
Research Resources and Readings |
|
|
442 | (5) |
|
Chapter 17 Sizing it Up: Attributes of Measurement and the Measurement of Attributes |
|
|
447 | (46) |
|
|
|
447 | (1) |
|
|
|
448 | (1) |
|
Attributes of Measurement |
|
|
448 | (1) |
|
Using Metric Units of Measure |
|
|
449 | (3) |
|
|
|
452 | (1) |
|
|
|
453 | (11) |
|
|
|
453 | (2) |
|
Planning Activities for Children |
|
|
455 | (9) |
|
|
|
464 | (6) |
|
|
|
464 | (1) |
|
Area Activities for Children |
|
|
465 | (5) |
|
|
|
470 | (3) |
|
|
|
470 | (1) |
|
Deciding on Measurement Experiences |
|
|
471 | (2) |
|
|
|
473 | (2) |
|
|
|
475 | (1) |
|
Measuring Time and Temperature |
|
|
476 | (2) |
|
|
|
476 | (2) |
|
|
|
478 | (1) |
|
|
|
478 | (1) |
|
|
|
479 | (1) |
|
Extending Developmental Ideas |
|
|
480 | (3) |
|
Working with Irregular Figures |
|
|
481 | (1) |
|
Measurement and Ratio Ideas |
|
|
481 | (1) |
|
Discovering Relationships Involving Measurement |
|
|
481 | (1) |
|
Discovering Special Numbers |
|
|
482 | (1) |
|
The Problem-Solving Connection |
|
|
483 | (1) |
|
|
|
484 | (1) |
|
|
|
484 | (1) |
|
|
|
485 | (1) |
|
The Literature Connection |
|
|
485 | (1) |
|
|
|
486 | (1) |
|
|
|
486 | (1) |
|
|
|
486 | (1) |
|
|
|
486 | (1) |
|
|
|
487 | (3) |
|
Research Resources and Readings |
|
|
490 | (3) |
|
Chapter 18 Making Numbers Count: Analyzing Data and Using Probability |
|
|
493 | (28) |
|
|
|
493 | (1) |
|
|
|
494 | (1) |
|
Collecting and Organizing Data |
|
|
495 | (1) |
|
Recording and Representing Data |
|
|
496 | (6) |
|
|
|
496 | (1) |
|
The Frequency Distribution |
|
|
496 | (1) |
|
|
|
496 | (1) |
|
|
|
497 | (1) |
|
Some Important Points about Graphs |
|
|
497 | (1) |
|
Finding the Right Average |
|
|
498 | (1) |
|
Finding the Arithmetic Average, or Mean |
|
|
499 | (1) |
|
Finding the Median and the Mode |
|
|
500 | (2) |
|
Using Small Samples to Predict |
|
|
502 | (2) |
|
|
|
504 | (3) |
|
|
|
505 | (1) |
|
Listing Possible Outcomes |
|
|
505 | (2) |
|
Determining the Probability of an Event |
|
|
507 | (3) |
|
The Problem-Solving Connection |
|
|
510 | (2) |
|
|
|
510 | (1) |
|
The Most Often Used Letters in the Alphabet |
|
|
511 | (1) |
|
|
|
511 | (1) |
|
|
|
512 | (2) |
|
|
|
512 | (1) |
|
|
|
512 | (1) |
|
|
|
513 | (1) |
|
|
|
513 | (1) |
|
|
|
513 | (1) |
|
A Checklist for Facilitating Group Learning |
|
|
513 | (1) |
|
|
|
514 | (1) |
|
|
|
514 | (1) |
|
The Literature Connection |
|
|
514 | (1) |
|
|
|
515 | (1) |
|
|
|
515 | (1) |
|
|
|
515 | (1) |
|
|
|
516 | (2) |
|
Research Resources and Readings |
|
|
518 | (3) |
|
PART V Technology and the Children That We Teach |
|
|
521 | (53) |
|
Chapter 19 Technology and Mathematics Instruction: Status and Direction |
|
|
523 | (21) |
|
|
|
523 | (1) |
|
Technology for the Classroom |
|
|
524 | (1) |
|
Understanding the Characteristics of Promising Technologies |
|
|
524 | (2) |
|
|
|
524 | (1) |
|
The Internet and the World Wide Web |
|
|
525 | (1) |
|
Using Technology to Advance Instruction |
|
|
526 | (12) |
|
Computer-Directed Instruction (CDI) |
|
|
527 | (2) |
|
Computer-Managed Instruction (CMI) |
|
|
529 | (1) |
|
Technology-Enhanced Instruction (TEI) |
|
|
530 | (6) |
|
|
|
536 | (2) |
|
Programming and Unique Learning Environments |
|
|
538 | (1) |
|
|
|
538 | (2) |
|
|
|
540 | (1) |
|
|
|
540 | (1) |
|
|
|
540 | (1) |
|
Research Resources and Readings |
|
|
541 | (3) |
|
Chapter 20 Teaching in the Real World: After Formal Preparation |
|
|
544 | (30) |
|
|
|
544 | (2) |
|
Children with Special Needs |
|
|
546 | (10) |
|
Children with Learning Disabilities |
|
|
546 | (9) |
|
|
|
555 | (1) |
|
Children with Physical Disabilities |
|
|
556 | (1) |
|
Teaching Children of Poverty |
|
|
556 | (2) |
|
Multiculturalism and Mathematics |
|
|
558 | (2) |
|
|
|
560 | (1) |
|
Strategies for Implementing Multicultural Learning Environments |
|
|
561 | (1) |
|
|
|
562 | (1) |
|
Mathematics, Equity, and Gender |
|
|
563 | (1) |
|
Understanding the Problem |
|
|
563 | (1) |
|
Evaluating and Adjusting Your Own Attitudes and Beliefs |
|
|
564 | (1) |
|
Guidelines for Conquering Gender Bias in Mathematics |
|
|
564 | (1) |
|
|
|
564 | (3) |
|
|
|
567 | (1) |
|
The Literature Connection |
|
|
567 | (1) |
|
|
|
567 | (1) |
|
|
|
567 | (1) |
|
Research Resources and Readings |
|
|
568 | (6) |
| Appendix A NCTM Standards and Expectations |
|
574 | (11) |
| Appendix B The MGB Resource |
|
585 | (7) |
| Appendix C Selected Answers to ThinkTank Exercises |
|
592 | (13) |
| Index |
|
605 | |
