Mathematics for Teachers: An Interactive Approach for Grades K-8 » (4th Edition)

Dr. Thomas Sonnabend is currently in his 17th year teaching mathematics at Montgomery College. He recently developed an expanded program of three mathematics courses for elementary teachers that began during the 2002-2003 school year. He has done in-service work with elementary school teachers and has taught grades five and nine-twelve in New York City. Having published over 23 book reviews in the MATHEMATICS TEACHER, two articles "Calculus Reform: An Interview with Tom Sonnabend" and "Cooperative Learning

Mathematics for Teachers: An Interactive Approach for Grades K-8 actively involves students in developing and explaining mathematical concepts and how the topics relate to NCTM Standards and Curriculum focal points. The text includes coverage of reasoning, sets, arithmetic, geometry, measurement, algebra, statistics, and probability. The carefully organized, interactive lesson format promotes student involvement and gradually leads the student to a deeper understanding of mathematical ideas.

Introduction. 1. MATHEMATICAL REASONING. Inductive Reasoning. Deductive Reasoning. Inductive and Deductive Reasoning. Patterns. Problem Solving. Problem Solving Strategies and Skills. 2. SETS AND FUNCTIONS. Sets. Operations on Two Sets. Functions and Relations. 3. WHOLE NUMBERS. Numeration Systems. Addition and Subtraction of Whole Numbers. Multiplication and Division of Whole Numbers. Properties of Whole-Number Operations. Algorithms for Whole-Number Addition and Subtraction. Algorithms for Whole-Number Multiplication and Divisions. Whole Numbers: Mental Computation and Estimation. Place Value and Algorithms in Other Bases. 4. NUMBER THEORY. Factors. Divisibility. Prime and Composite Numbers. Common Factors and Multiples. 5. INTEGERS. Addition and Subtraction of Integers. Multiplication and Division of Integers. Properties of Integer Operations. 6. RATIONAL NUMBERS AS FRACTIONS. Rational Numbers. Addition and Subtraction of Rational Numbers. Multiplication and Division of Rational Numbers. Rational Numbers: Properties, Estimation, and Error Patterns. 7. DECIMALS, PERCENTS AND REAL NUMBERS. Decimals: Place Value, Estimation and Mental Computation. Decimal Arithmetic and Error Patterns. Ratio and Proportion. Percents. Percents: Mental Computation, Estimation and Change. Rational, Irrational, and Real Numbers. 8. INTRODUCTORY GEOMETRY. Beginning Geometry. Polygons. Triangles, Quadrilaterals and Circles. Angle Measures of Polygons. Three-Dimensional Geometry. Viewing and Drawing Solid Figures. 9. CONGRUENCE, SYMETRY AND SIMILARITY. Transformations and Congruence. Applications of Transformations. Constructions and Congruence. Symmetry. Similarity and Dilations. 10. MEASUREMENT. Systems of Measurement. Perimeter and Area. Area of Quadrilaterals, Triangles, and Circles. The Pythagorean Theorem. Surface Area. Volume. Lengths, Areas, and Volumes of Similar Figures. 11. ALGEBRA AND GRAPHING. The Language of Algebra. Solving Equations and Inqualities. Linear Functions. Non-Linear Functions. 12. STATISTICS. Observational Studies and Experiments. Statistical Graphs and Tables. Misleading Graphs and Statistics. Mode, Median, and Mean. Measuring Spread. Standardized Test Scores. 13. PROBABILITY. Experimental and Theoretical Probability. Probability Rules and Simulations. Counting. Independent and Dependent Events. Expected Values and Odds.