Mathematical Reasoning for Elementary Teachers

by Long, Calvin T.; DeTemple, Duane W.

• ISBN13: 9780321286963
• ISBN10: 0321286960
• Edition: 4th
• Format: Hardcover
• Copyright: 2006-01-01
• Publisher: Addison Wesley

Summary

The fourth edition of Mathematical Reasoning has an increased focus on professional development and connecting the material from this class to the elementary and middle school classroom. The authors have provided more meaningful content and pedagogy to arm readers with all the tools that they will need to become excellent elementary or middle school teachers. Thinking Critically. Sets and Whole Numbers. Numeration and Computation. Number Theory. Integers. Fractions and Rational Numbers. Decimals and Real Numbers. Algebraic Reasoning and Representation. Statistics: The Interpretation of Data. Probability. Geometric Figures. Measurement. Transformations, Symmetries, and Tilings. Congruence, Constructions, and Similarities. For all readers interested in mathematical reasoning for elementary teachers.

Table of Contents

Thinking Critically

Some Surprising Tidbits

An Introduction to Problem Solving

Pólya's Problem-Solving Principles

More Problem-Solving Strategies

Additional Problem-Solving Strategies

Sets and Whole Numbers

Sets and Operations on Sets

Sets, Counting, and the Whole Numbers

Addition and Subtraction of Whole Numbers

Multiplication and Division of Whole Numbers

Numeration and Computation

Numeration Systems Past and Present

Nondecimal Positional Systems

Algorithms for Adding and Subtracting Whole Numbers

Algorithms for Multiplication and Division of Whole Numbers

Mental Arithmetic and Estimation

Getting the Most Out of Your Calculator

Number Theory

Divisibility of Natural Numbers

Tests for Divisibility

Greatest Common Divisors and Least Common Multiples

Codes and Credit Card Numbers: Connections to Number Theory

Integers

Representation of Integers

Addition and Subtraction of Integers

Multiplication and Division of Integers

Clock Arithmetic

Fractions and Rational Numbers

The Basic Concepts of Fractions and Rational Numbers

The Arithmetic of Rational Numbers

The Rational Number System

Decimals and Real Numbers

Decimals

Computations with Decimals

Ratio and Proportion

Percent

Algebraic Reasoning and Representation

Algebraic Expressions and Equations

Functions

Graphing Functions in the Cartesian Plane

Statistics: The Interpretation of Data

The Graphical Representation of Data

Measures of Central Tendency and Variability

Statistical Inference

Probability

Empirical Probability

Principles of Counting

Theoretical Probability

Geometric Figures

Figures in the Plane

Curves and Polygons in the Plane

Figures in Space

Networks

Measurement

The Measurement Process

Area and Perimeter

The Pythagorean Theorem

Surface Area and Volume

Transformations, Symmetries, and Tilings

Rigid Motions and Similarity Transformations

Patterns and Symmetries

Tilings and Escher-like Designs

Congruence, Constructions, and Similarities

Congruent Triangles

Constructing Geometric Figures

Similar Triangles

Appendices

Manipulatives in the Mathematics Classroom

Spreadsheets

Graphing Calculators

A Brief Guide to The Geometer's Sketchpad

Resources

Answers to Selected Problems

Acknowledgments

Mathematical Lexicon

Index and Pronunciation Guide

Table of Contents provided by Publisher. All Rights Reserved.