Teaching Secondary and Middle School Mathematics

I. WHAT DOES IT MEAN TO "DO," "TEACH," AND "LEARN" MATHEMATICS? 1. Mathematics as a Process National and International Assessment Data How would You React? The Need for Reform "Doing" Mathematics - Problem Solving - Reasoning and Proof - Spotlight on Technology - Communication - Connections - Classroom Dialogues - Representation Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources 2. Principles of Mathematics Education The Six Principles - Equity How Would You React? - Curriculum - Teaching Spotlight on Technology - Learning - Assessment - Technology Classroom Dialogues Connecting the Principles Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources 3. Learning Theories and Psychology in Mathematics Education Research in Mathematics Education - Quantitative and Qualitative Methods - How Would You React? - Experimental and Descriptive Research Learning Theories in Mathematics - Bruners, Stages of Representation - The van Hiele Model - The Inquiry Approach and Constructivist Model - Spotlight on Technology - Inductive versus Deductive Teaching - Classroom Dialogues - Motivation Conclusion Glossary Discussion Questions and Activities Bibliographic References and Resources II. THE MATHEMATICS CURRICULUM 4. Curricular Models NCTM Curriculum Standards NCTM Focal Points and Related Documents How Would You React? State Models The Core Curriculum Spotlight on Technology Traditional versus Integrated Sequence Classroom Dialogues Conclusion Glossary Discussion Questions and Activities Bibliographic References and Resources 5. Implementing a Course of Study The Course of Study How Would You React? Writing Goals and Objectives - Classifying Objectives - Affective Objectives - Cognitive Objectives Spotlight on Technology Selection and Organization of Resources - Textbooks - Print Resources - Classroom Dialogues - The Internet - Organizing a Resource File Conclusion Glossary Discussion Questions and Ctivities Bibliographical References and Resources Sample Recommended Resource Books COMAP "Hi-Map" (High School Mathematics) Teaching Modules. NCTM Navigation Series NSF-Funded Curricular Materials III. TEACHING MATHEMATICS 6. Planning for Instruction Unit Planning How Would You React? Lesson Planning - General Considerations - Goals and Objectives - Materials and Resources - Motivation - Lesson Procedure - Closure - Extension - Assessment - Spotlight on Technology - Sample Lesson Plans Classroom Dialogues Lesson Imaging versus Lesson Planning Reflecting on a Lesson Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources Activities-Selected Lesson Plan Ideas from The Mathematics Teacher 7. Teaching Tools and Strategies Teaching Standards and Principle - The NCM Standards for Teaching and Learning Mathematics Knowledge - The Teaching and Learning Principles Selecting Activities and Problems - How Would You React? Classroom Tools - Hands-On Manipulative Materials - Use of Technology - Spotlight on Technology - Diagrams, Graphs, and Other Discussion Starters Learning Environment Classroom Discourse - The Role of Discourse - Questioning Skills - Classroom Dialogues - Cooperative Learning Skills Reflective Practices Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources 8. Teaching Specific Mathematics Content The Teaching of Algebra - Algebra- Sample Lesson Plan - Algebra- Activities Sampler - How Would You React? The Teaching of Geometry - Geometry- Sample Lesson Plan - Geometry- Activities Sampler - Spotlight on Technology The Teaching of Data Analysis and Probability - Data Analysis and Probability- Sample Lesson Plan - Data Analysis and Probability- Activities Sampler The Teaching of Discrete Mathematics - Discrete Mathematics- Sample Lesson Plan - Classroom Dialogues - Discrete Mathematics- Activities Sampler A Word on Pre-Calculus and Calculus Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources IV. ASSESSMENT IN MATHEMATICS 9. The Role of Assessment What Is Assessment? Purposes for Assessment Test Construction - Preparing Items - Ensuring Validity and Reliability - How Would You React? - Scoring Student Work - Including Review Items - Limitations to Written Tests Alternate Strategies for Assessing Student Progress - Journals - Open-Ended Questions and Rubrics - Spotlight on Technology - Individual and Team Projects - Observations and Checklists - Interviews - Self-Assessment - Classroom Dialogues - Portfolios Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources 10. Principles of Assessment Practices NCTM Recommendations on Assessment - The Assessment Standards - How Would You React? - The Assessment Principle Equity and Assessment Homework Assignments - Homework Amount and Frequency - Spotlight on Technology - Checking Homework Assignments - Using Homework Assignments in Assessment - Classroom Dialogues Evaluation: Determining and Maintaining Final Grades Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources V. MEETING INDIVIDUAL STUDENT AND TEACHER NEEDS 11. Meeting the Needs of All Students Defining and Achieving Equity - Students with Special Needs - How Would You React? - Gender - Spotlight on Technology - Ethnic and Cultural Issues Classroom Dialogues Ideas for Meeting Diverse Student Needs - Differentiated Instruction - General Suggestions for the Classroom Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources 12. The Teacher of Mathematics in the School Community Working with Parents How Would You React? The Supervision and Evaluation of Teachers Functioning in a Department Ongoing Professional Development - Making the Case for Long-term Development - Classroom Dialogues - Opportunities for Professional Development - The Professional Development Plan Conclusion Glossary Discussion Questions and Activities Bibliographical References and Resources Appendix: Recommended Web Sites Professional Organizations Curriculum Projects Activities and Lesson Plan Idea General Mathematics Education Sites Index