Mathematical Reasoning for Elementary Teachers, Media Update
Gebonden Engels 2018 9780134758824Samenvatting
For courses in Mathematics for Teachers or Mathematics for Future Elementary Teachers.
Fosters reasoning skills, deep conceptual understanding, and a positive attitude in aspiring elementary or middle school teachers
Mathematical Reasoning for Elementary Teachers presents the mathematical content needed for teaching within the context of the elementary classroom. The authors endeavor to answer the frequently asked question “Why are we learning this?” by going beyond skill explanations to show how these concepts are implemented in the future classroom, and what types of questions children may ask. The Common Core State Standards for Mathematics are included.
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Specificaties
Lezersrecensies
Inhoudsopgave
- 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
- 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
- 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
- Number Theory
- 4.1 Divisibility of Natural Numbers
- 4.2 Tests for Divisibility
- 4.3 Greatest Common Divisors and Least Common Multiples
- Integers
- 5.1 Representation of Integers
- 5.2 Addition and Subtraction of Integers
- 5.3 Multiplication and Division of Integers
- 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
- Decimals, Real Numbers, and Proportional Reasoning
- 7.1 Decimals and Real Numbers
- 7.2 Computations with Decimals
- 7.3 Proportional Reasoning
- 7.4 Percent
- 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
- Geometric Figures
- 9.1 Figures in the Plane
- 9.2 Curves and Polygons in the Plane
- 9.3 Figures in Space
- 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
- Transformations, Symmetries, and Tilings
- 11.1 Rigid Motions and Similarity Transformations
- 11.2 Patterns and Symmetries
- 11.3 Tilings and Escher-like Designs
- Congruence, Constructions, and Similarity
- 12.1 Congruent Triangles
- 12.2 Constructing Geometric Figures
- 12.3 Similar Triangles
- Statistics: The Interpretation of Data
- 13.1 Organizing and Representing Data
- 13.2 Measuring the Center and Variation of Data
- 13.3 Statistical Inference
- 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
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