Long/DeTemple/Millman's Mathematical Reasoning for Elementary Teachers presents the mathematical content needed for teaching within the context of the elementary classroom, giving future teachers the motivation they need while also showing them the bigger picture of when they will use and teach the concepts. The program also endeavors to answer the frequently-asked "Why are we learning this?" by going beyond skill explanations and showing the ways that these concepts are implemented in the future classroom and what types of questions children may ask. Now updated to include the Common Core State Standards for Mathematics, the text imparts mathematical reasoning skills, a deep conceptual understanding, and a positive attitude to those who aspire to be elementary or middle school teachers.
Teaching and Learning Experience
This program will provide a better teaching and learning experience-for you and your students. Here's how:
Personalized learning with MyMathLab: MyMathLab delivers proven results in helping students succeed and provides engaging experiences that personalize learning.
Features for the future classroom demonstrate the relevance of the concepts students are learning, the ways in which the mathematical concepts will be employed in the classroom, provide perspective on the importance of learning the material, and engage students to learn by doing.
Strong pedagogical tools help students to understand and retain the essential principals.
1. Thinking Critically 1.1 An Introduction to Problem Solving 1.2 Polya's Problem-Solving Principles and the Standards for Mathematical Practice of the Common Core State Standards for Mathematics 1.3 More Problem-Solving Strategies 1.4 Algebra as a 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 Algorithms for Addition and Subtraction of Whole Numbers 3.3 Algorithms for Multiplication and Division of Whole Numbers 3.4 Mental Arithmetic and Estimation 3.5 Nondecimal Positional Systems 4. Number Theory 4.1 Divisibility of Natural Numbers 4.2 Tests for Divisibility 4.3 Greatest Common Divisors and Least Common Multiples 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 The Rational Number System 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, Graphing, and Connections with Geometry 8.1 Variables, Algebraic Expressions, and Functions 8.2 Graphing Points, Lines, and Elementary Functions 8.3 Connections between Algebra and Geometry 9. Geometric Figures 9.1 Figures in the Plane 9.2 Curves and Polygons in the Plane 10. Measurement: Length, Area, and Volume 10.1 The Measurement Process 10.2 Area and Perimeter 10.3 The Pythagorean Theorem 10.4 Volume 10.5 Surface Area 11. Transformations, Symmetries, and Tilings 11.1 Rigid Motions and Similarity Transformations 11.2 Patterns and Symmetries 11.3 Tilings and Escher-like Designs 12. Congruence, Constructions, and Similarity 12.1 Congruent Triangles 12.2 Constructing Geometric Figures 12.3 Similar Triangles 13. Statistics: The Interpretation of Data 13.1 Organizing and Representing Data 13.2 Measuring the Center and Variation of Data 13.3 Statistical Inference 14. Probability 14.1 The Basics of Probability 14.2 Applications of Counting Principles to Probability 14.3 Permutations and Combinations 14.4 Odds, Expected Values, Geometric Probability, and Simulations Appendices-Online A. Manipulatives in the Mathematics Classroom B. Getting the Most out of Your Calculator C. A Brief Guide to The Geometer's Sketchpad D. Resources