by Calvin T. Long and Richard Millman
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The fifth edition ofMathematical Reasoning for Elementary Teachers,with new co-author Richard Millman, focuses on mathematical knowledge needed for teaching--constantly showing future teachers why they are learning math content and when they will use this information in the classroom. To decide whether the methods or ideas of elementary students are right or wrong and be able to explainwhyto them is one of the most important aspects of teaching, and is the emphasis of this fantastic text for future teachers.
1. Thinking Critically 1.1 An Introduction to Problem Solving. 1.2 Poacute;lya's Problem-Solving Principles. 1.3 More Problem-Solving Strategies. 1.4 Algebra as Problem-Solving Strategy 1.5 Additional Problem-Solving Strategies 1.6 Reasoning Mathematically
2. Sets and Whole Numbers 2.1 Sets and Operations on Sets. 2.2 Sets, Counting, and the Whole Numbers. 2.3 Addition and Subtraction of Whole Numbers. 2.4 Multiplication and Division of Whole Numbers.
3. Numeration and Computation 3.1 Numeration Systems Past and Present. 3.2 Nondecimal Positional Systems. 3.3 Algorithms for Adding and Subtracting Whole Numbers. 3.4 Algorithms for Multiplication and Division of Whole Numbers. 3.5 Mental Arithmetic and Estimation. 3.6 Getting the Most Out of Your Calculator.
4. Number Theory 4.1 Divisibility of Natural Numbers. 4.2 Tests for Divisibility. 4.3 Greatest Common Divisors and Least Common Multiples. 4.4 Codes and Credit Card Numbers: Connections to Number Theory.
5. Integers 5.1 Representations of Integers. 5.2 Addition and Subtraction of Integers. 5.3 Multiplication and Division of Integers.
6. Fractions and Rational Numbers 6.1 The Basic Concepts of Fractions and Rational Numbers. 6.2 Addition and Subtraction of Fractions 6.3 Multiplication and Division of Fractions 6.4 Properties and Applications of Rational Numbers
7. Decimals, Real Numbers, and Proportional Reasoning 7.1 Decimals and Real Numbers 7.2 Computations with Decimals. 7.3 Proportional Reasoning 7.4 Percent.
8. Algebraic Reasoning 8.1 Expressions, Functions, and Equations 8.2 Graphing Functions in the Cartesian Plane
9. Statistics: The Interpretation of Data 9.1 Graphical Representation of Data. 9.2 Measures of Central Tendency and Variability. 9.3 Statistical Inference and Sampling
10. Probability 10.1 Empirical Probability. 10.2 Principles of Counting. 10.3 Permutations and Combinations 10.4 Theoretical Probability
11. Geometric Figures 11.1 Figures in the Plane. 11.2 Curves and Polygons in the Plane. 11.3 Figures in Space. 11.4 Networks.
12. Measurement 12.1 The Measurement Process. 12.2 Area and Perimeter. 12.3 The Pythagorean Theorem. 12.4 Surface Area and Volume.
13. Transformations, Symmetries, and Tilings 13.1 Rigid Motions and Similarity Transformations. 13.2 Patterns and Symmetries. 13.3 Tilings and Escher-like Design.
14. Congruence, Constructions, and Similarities 14.1 Congruent Triangles. 14.2 Constructing Geometric Figures. 14.3 Similar Triangles.
Calvin T. Long and Richard Millman
ISBN13: 978-0321460844The fifth edition ofMathematical Reasoning for Elementary Teachers,with new co-author Richard Millman, focuses on mathematical knowledge needed for teaching--constantly showing future teachers why they are learning math content and when they will use this information in the classroom. To decide whether the methods or ideas of elementary students are right or wrong and be able to explainwhyto them is one of the most important aspects of teaching, and is the emphasis of this fantastic text for future teachers.
Table of Contents
1. Thinking Critically 1.1 An Introduction to Problem Solving. 1.2 Poacute;lya's Problem-Solving Principles. 1.3 More Problem-Solving Strategies. 1.4 Algebra as Problem-Solving Strategy 1.5 Additional Problem-Solving Strategies 1.6 Reasoning Mathematically
2. Sets and Whole Numbers 2.1 Sets and Operations on Sets. 2.2 Sets, Counting, and the Whole Numbers. 2.3 Addition and Subtraction of Whole Numbers. 2.4 Multiplication and Division of Whole Numbers.
3. Numeration and Computation 3.1 Numeration Systems Past and Present. 3.2 Nondecimal Positional Systems. 3.3 Algorithms for Adding and Subtracting Whole Numbers. 3.4 Algorithms for Multiplication and Division of Whole Numbers. 3.5 Mental Arithmetic and Estimation. 3.6 Getting the Most Out of Your Calculator.
4. Number Theory 4.1 Divisibility of Natural Numbers. 4.2 Tests for Divisibility. 4.3 Greatest Common Divisors and Least Common Multiples. 4.4 Codes and Credit Card Numbers: Connections to Number Theory.
5. Integers 5.1 Representations of Integers. 5.2 Addition and Subtraction of Integers. 5.3 Multiplication and Division of Integers.
6. Fractions and Rational Numbers 6.1 The Basic Concepts of Fractions and Rational Numbers. 6.2 Addition and Subtraction of Fractions 6.3 Multiplication and Division of Fractions 6.4 Properties and Applications of Rational Numbers
7. Decimals, Real Numbers, and Proportional Reasoning 7.1 Decimals and Real Numbers 7.2 Computations with Decimals. 7.3 Proportional Reasoning 7.4 Percent.
8. Algebraic Reasoning 8.1 Expressions, Functions, and Equations 8.2 Graphing Functions in the Cartesian Plane
9. Statistics: The Interpretation of Data 9.1 Graphical Representation of Data. 9.2 Measures of Central Tendency and Variability. 9.3 Statistical Inference and Sampling
10. Probability 10.1 Empirical Probability. 10.2 Principles of Counting. 10.3 Permutations and Combinations 10.4 Theoretical Probability
11. Geometric Figures 11.1 Figures in the Plane. 11.2 Curves and Polygons in the Plane. 11.3 Figures in Space. 11.4 Networks.
12. Measurement 12.1 The Measurement Process. 12.2 Area and Perimeter. 12.3 The Pythagorean Theorem. 12.4 Surface Area and Volume.
13. Transformations, Symmetries, and Tilings 13.1 Rigid Motions and Similarity Transformations. 13.2 Patterns and Symmetries. 13.3 Tilings and Escher-like Design.
14. Congruence, Constructions, and Similarities 14.1 Congruent Triangles. 14.2 Constructing Geometric Figures. 14.3 Similar Triangles.