This text has been written to help prospective teachers of preschool through grade 8 understand how children in these grades learn mathematics and how they themselves might teach the subject. It is based on the National Council of Teachers of Mathematics (NCTM) Principles and Standards 2000 and grounded in the belief that before one can become a confident and competent teacher of mathematics, one must first become a competent and confident learner of mathematics.
Table of Contents
1. New Standards for Learning and Teaching Mathematics. The Goals of Mathematics Education. The Nature of the PreK-2 Learner. Teaching the Young Child. Teaching Children from Ages 8-13. Summary. 2. Standards For Number And Numeration. Planning for Instruction. Factors Affecting the Mathematical Achievement of Students. Constructivism in the Mathematics Classroom. Number and Operation for Children in Grades PreK-2. Number and Operation for Grades 3-5. Number and Operation for Grades 6-8. Summary. 3. Standards For Whole Numbers: Addition And Subtraction. Operations for Grades PreK-2. Basic Facts of Addition and Subtraction. Addition and Subtraction of Multi-Digit Numbers. Summary. 4. Standards For Whole Numbers: Multiplication And Division. Operations of Multiplication and Division. Basic Multiplication and Division. Multiplication and Division of Multi-Digit Numbers. Number and Operation for Grades 6-8. Summary. 5. Standards For Geometry. Geometry and Spatial Sense for Grades PreK-2. Observation, Description and Classification. Connecting Geometry to Other Mathematical Ideas. Geometry and Spatial Sense for Students in Grades 3-5. Summary. 6. Continuing The Study Of Geometry. Geometry as Measurement. Geometry and Spatial Sense for Grades 6-8. Geometric Drawing Utilities. Transformational Geometry. Geometry and Spatial Sense for Grades 6-8. Summary. 7. Standards For Extending Number Line. Number and Operation for Grades PreK-2 and 3-5. Adding and Subtracting with Fractions and Decimals. Linear Measurement. Summary. 8. Standards For Multiplication And Division Of Fractions And Decimals. Multiplying and Dividing with Fractions and Decimals. Number and Operations for Grades 3-5. Measurement for Mass and Volume. Proportional Thinking. Summary. 9. Standards For Patterns And Relationships. Simple Patterns, Functions, and Algebra. More Complex Patterns, Functions, and Algebra. Summary. 10. Standards For Data Analysis, Statistics, And Probability. Graphing and Data Analysis. Focus Areas for Grades Pre-K-2 Introducing Concepts of Chance. Probability for Grades 3-5. Summary. 11. Further Investigations Into Data Analysis, Statistics, And Probability. Focus Areas for Grades 6-8. Theoretical and Experimental Probability. Summary. Appendix A. Masters. Appendix B. NCTM Document Summary. Index.