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| Preface | |
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| What Does It Mean to "Do," "Teach," and "Learn" Mathematics? | |
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| Mathematics as a Process | |
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| National and International Assessment Data | |
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| The Need for Reform | |
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| "Doing" Mathematics | |
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| Problem Solving | |
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| Reasoning and Proof | |
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| Communication | |
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| Connections | |
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| Representation | |
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| Learning Theories and Psychology in Mathematics Education | |
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| Research in Mathematics Education | |
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| Quantitative and Qualitative Methods | |
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| Experimental and Descriptive Research | |
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| Learning Theories in Mathematics | |
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| Bruner's Stages of Representation | |
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| The van Hiele Model | |
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| The Inquiry Approach and Constructivist Model | |
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| Inductive versus Deductive Teaching | |
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| Motivation | |
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| The Mathematics Curriculum | |
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| Curricular Models | |
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| NCTM Curriculum Standards | |
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| State Models | |
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| The Core Curriculum | |
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| Traditional versus Integrated Sequences | |
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| Implementing a Course of Study | |
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| The Course of Study | |
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| Writing Goals and Objectives | |
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| Classifying Objectives | |
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| Affective Objectives | |
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| Cognitive Objectives | |
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| Selection and Organization of Resources | |
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| Textbooks | |
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| Print Resources | |
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| The Internet | |
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| Organizing a Resource File | |
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| Sample Recommended Resource Books | |
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| COMAP "Hi-Map" (High School Mathematics) Teaching Modules | |
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| NCTM Navigations Series | |
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| NCTM Addenda Series Resource Books | |
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| NSF-Funded Curricular Materials | |
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| Teaching Mathematics | |
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| Planning for Instruction | |
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| Unit Planning | |
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| Lesson Planning | |
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| General Considerations | |
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| Goals and Objectives | |
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| Materials and Resources | |
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| Motivation | |
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| Lesson Procedure | |
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| Closure | |
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| Extension | |
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| Assessment | |
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| Sample Lesson Plans | |
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| Lesson Imaging versus Lesson Planning | |
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| Reflecting on a Lesson | |
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| Teaching Tools and Strategies | |
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| Teaching Standards and Principles | |
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| The NCTM Professional Teaching Standards | |
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| The Teaching and Learning Principles | |
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| Selecting Activities and Problems | |
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| Classroom Tools | |
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| Hands-On Manipulative Materials | |
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| Use of Technology | |
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| Diagrams, Graphs, and Other Discussion Starters | |
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| Classroom Discourse | |
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| Student and Teacher Roles | |
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| Questioning Skills | |
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| Cooperative Learning | |
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| Learning Environment | |
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| Reflective Practices | |
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| Teaching Specific Mathematics Content | |
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| The Teaching of Algebra | |
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| Algebra--Sample Lesson Plan | |
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| Algebra--Activities Sampler | |
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| The Teaching of Geometry | |
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| Geometry--Sample Lesson Plan | |
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| Geometry--Activities Sampler | |
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| The Teaching of Data Analysis and Probability | |
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| Data Analysis and Probability--Sample Lesson Plan | |
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| Data Analysis and Probability--Activities Sampler | |
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| The Teaching of Discrete Mathematics | |
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| Discrete Mathematics--Sample Lesson Plan | |
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| Discrete Mathematics--Activities Sampler | |
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| Assessment in Mathematics | |
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| The Role of Assessment | |
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| What Is Assessment? | |
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| Purposes for Assessment | |
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| Test Construction | |
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| Preparing Items | |
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| Ensuring Validity and Reliability | |
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| Scoring Student Work | |
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| Including Review Items | |
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| Limitations to Written Tests | |
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| Alternate Strategies for Assessing Student Progress | |
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| Journals | |
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| Open-Ended Questions and Rubrics | |
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| Individual and Team Projects | |
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| Observations and Checklists | |
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| Interviews | |
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| Portfolios | |
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| Principles of Assessment Practices | |
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| NCTM Recommendations on Assessment | |
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| The Assessment Standards | |
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| The Assessment Principle | |
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| Equity and Assessment | |
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| Homework Assignments | |
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| Homework Amount and Frequency | |
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| Checking Homework Assignments | |
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| Using Homework Assignments in Assessment | |
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| Evaluation: Determining Final Grades | |
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| Meeting Individual Student and Teacher Needs | |
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| Meeting the Needs of All Students | |
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| Defining and Achieving Equity | |
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| Students with Special Needs | |
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| Gender | |
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| Ethnic and Cultural Issues | |
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| General Suggestions for Meeting Diverse Student Needs | |
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| The Teacher of Mathematics in the School Community | |
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| Working with Parents | |
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| The Supervision and Evaluation of Teachers | |
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| Functioning in a Department | |
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| Ongoing Professional Development | |
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| Making the Case for Long-Term Development | |
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| Opportunities for Professional Development | |
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| The Professional Development Plan | |
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| Recommended Web Sites | |
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| Professional Organizations | |
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| Curriculum Projects | |
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| Activities and Lesson Plan Ideas | |
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| General Mathematics Education Sites | |
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| Cases | |
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| The Marble Line (algebra) | |
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| Chances Are (probability) | |
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| Index | |