This title is out of print.
At the end of each section are “Problems and Exercises” . These problems and exercises are different from those in a typical textbook in that they are specifically designed to help you learn how children learn mathematics. Many of these questions are from the National Assessment of Educational Progress (NAEP) and the Third International Mathematics and Science Study (TIMSS).
“Children’s Solutions and Discussion of Problems and Exercises” present both children’s solutions and errors or a discussion for some of the “Problems and Exercises”. With the NAEP and TIMSS questions, the authors provide the percentage of children who had the correct solution. With some NAEP questions they also give children’s actual solutions. All the data presented may not be indicative of how a particular child or class will perform on the problem. The data is intended to provide a general idea on how many children perform on similar problems.
To help you reflect on the connections and understandings that will occur through doing the problems and exercises, each section also has “Questions for Discussion”. These are general questions for you to discuss, write about, or reflect upon.
Chapter 1 Problem Solving
1.1 An Introduction to Problem Solving
1.3 Mathematical Reasoning
Chapter 2 Sets
2.1 Set Theory
2.2 Venn Diagrams
Chapter 3 Whole Numbers
3.1 Numeration Systems
3.2 Addition and Subtraction
3.3 Multiplication and Division
3.4 Properties of Whole Number Operations
3.6 Mental Math & Estimation
Chapter 4 Number Theory
4.1 Factors and Multiples
4.2 Divisibility Tests
4.3 Prime and Composite Numbers
4.4 Greatest Common Factor & Least Common Multiple
Chapter 5 Integers
5.1 Children’s Understanding of Negative Numbers
5.2 Addition and Subtraction of Integers
5.3 Multiplication and Division of Integers
Chapter 6 Rational Numbers - Fractions
6.2 Addition and Subtraction of Fractions
6.3 Multiplication and Division of Fractions
6.4 Properties of Rational Numbers
Chapter 7 Decimals, Percents, and Real Numbers
7.1 Place Value
7.3 Decimal Computation
7.4 Ratio and Proportion
7.6 Rational, Irrational, and Real Numbers
Chapter 8 &
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David Feikes earned a Bachelor's degree from Ball State University, a Master's degree from Purdue University North Central, and a Doctorate in Mathematics Education from Purdue University. At Purdue University North Central, he teaches mathematics content courses, mathematics methods courses, and graduate mathematics education courses for elementary teachers. His research interests are on how children learn mathematics and how teachers, preservice teachers, and parents can use this knowledge to help children learn mathematics. In his spare time he coaches youth soccer and builds houses.
Keith Schwingendorf earned a B.S. degree in mathematics with honors, and M.S. and Ph.D. degrees in mathematics from Purdue University. He taught mathematics at Purdue University West Lafayette, 1971-1992. He moved on to the Purdue University North Central campus to teach mathematics as an Associate Professor of Mathematics in 1992. He was promoted to Professor of Mathematics in 1996. Dr. Schwingendorf has collaborated on four National Science Foundation (NSF) Calculus Reform grants totaling $994,000, 1988-1997, which resulted in the publication of two calculus texts, a pre-calculus text, numerous research papers, and many other publications. He earned three outstanding teaching awards: one at Purdue West Lafayette, where was also named a top ten teacher in the School of Science three times; and two awards at Purdue North Central. He Chaired the Mathematics, Statistics, and Physics Department, January 2002 - June 2006. He has been Dean of the College of Science since July 1, 2006. He and Dr. David Feikes collaborated on two NSF grants, totaling $375,000, 2002-2007, to research how children learn and understand mathematics concepts in order to help pre-service elementary education majors enhance their teaching of and understanding of children’s learning of mathematics. The most significant result of their teamwork is their book Connecting Mathematics for Elementary Teachers (CMET) published in July 2008 by Pearson Education. Dr. Schwingendorf enjoys golf, walking, swimming, traveling and spending time with his family, and he is an enthusiastic Purdue sports fan.
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