A problem solving approach to mathematics for elementary school teachers
著者
書誌事項
A problem solving approach to mathematics for elementary school teachers
Pearson, Addison-Wesley, c2004
8th ed.
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This best-selling text emphasizes solid mathematics content, problem-solving skills, and analytical techniques. The eighth edition focuses on the National Council of Teachers of Mathematics (NCTM) Principles and Standards 2000. The text allows for a variety of approaches to teaching, encourages discussion and collaboration among students and with their instructors, allows for the integration of projects into the curriculum, and promotes discovery and active learning. Students using this text will receive solid preparation in mathematics, develop confidence in their math skills and benefit from teaching and learning techniques that really work.
目次
1. An Introduction to Problem Solving.
Explorations with Patterns.
Mathematics and Problem Solving.
Algebraic Thinking.
*Logic: An Introduction.
2. Sets, Whole Numbers, and Functions.
Describing Sets.
Other Set Operations and Their Properties.
Addition and Subtraction of Whole-Numbers.
Multiplication and Division of Whole-Numbers.
Functions.
3. Numeration Systems and Whole Number Computation.
Numeration Systems.
Algorithms for Whole-Number Addition and Subtraction.
Algorithms for Whole-Number Multiplication and Division.
Mental Mathematics and Estimation for Whole-Number Operations.
4. Integers and Number Theory.
Integers and the Operations of Addition and Subtraction.
Multiplication and Division of Integers.
Divisibility.
Prime and Composite Numbers.
Greatest Common Divisor and Least Common Multiple.
*Clock and Modular Arithmetic.
5. Rational Numbers as Fractions.
The Set of Rational Numbers.
Addition and Subtraction of Rational Numbers.
Multiplication and Division of Rational Numbers.
Proportional Reasoning.
6. Decimals, Percents, and Real Numbers.
Introduction to Decimals.
Operations on Decimals.
Nonterminating Decimals.
Percents.
*Computing Interest.
Real Numbers.
7. Probability.
How Probabilities Are Determined.
Multistage Experiments with Tree Diagrams and Geometric Probabilities.
Using Simulations in Probability.
Odds, Conditional Probability, and Expected Value.
Using Permutations and Combinations in Probability.
8. Data Analysis/Statistics: An Introduction.
Statistical Graphs.
Measures of Central Tendency and Variation.
Abuses of Statistics.
9. Introductory Geometry.
Basic Notions.
Polygons.
More About Angles.
Geometry in Three Dimensions.
*Networks.
10. Constructions, Congruence, and Similarity.
Congruence Through Constructions.
Other Congruence Properties.
Other Constructions.
Similar Triangles and Similar Figures.
Trigonometry Rations via Similarity
Lines in a Cartesian Coordinate System.
11. Concepts of Measurement.
Linear Measure.
Areas of Polygons and Circles.
The Pythagorean Theorem.
Surface Areas.
Volume, Mass, and Temperature.
12. Motion Geometry and Tessellations.
Translations and Rotations.
Reflections and Glide Reflections.
Size Transformations.
Symmetries.
*Tessellations of the Plane.
Appendix I. Using a Spreadsheet.
Appendix II. Graphing Calculators.
Appendix III. Using a Geometry Drawing Utility.
Answers to Selected Problems.
Index.
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