A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

Book Preface

The twelfth edition of A Problem Solving Approach to Mathematics for Elementary School Teachers is designed  to prepare outstanding future elementary and middle school teachers. This edition continues to be heavily concept- and skill-based, with an emphasis on active and collaborative learning. The content has been revised and updated to better prepare students to become teachers in their own classrooms. National Standards for Mathematics
• Common Core State Standards for Mathematics The National Governors Association spearheaded the effort to develop the Common Core Standards (2010); they have been adopted by many states and are used in this text to highlight concepts. The complete text of the Common Core Standards is found at www.corestandards.org.
• Principles and Standards The National Council of Teachers of Mathematics (NCTM) publication, Principles and Standards of School Mathematics (2000) continues to be a guide for the course. The complete text of the NCTM Principles and Standards can be found online at www.nctm.org.
Our Goals
• To present appropriate mathematics in an intellectually honest and mathematically correct manner.
• To use problem solving as an integral part of mathematics.
• To approach mathematics in a sequence that instills confidence and challenges students.
• To provide opportunities for alternate forms of teaching and learning.
• To provide communication and technology problems to develop writing skills that allow students to practice reasoning and explanation through mathematical exposition.
• To provide core mathematics for prospective elementary and middle school teachers in a way that challenges them to determine why mathematics is done as it is.
• To provide core mathematics that allows instructors to use methods integrated with content.
• To assist prospective teachers with connecting mathematics, its ideas, and its applications.
• To assist future teachers in becoming familiar with the content and philosophy of the national standards listed above.
The twelfth edition gives instructors a variety of approaches to teaching, encourages discussion and collaboration among future teachers and with their instructors, and aids the integration of projects into the curriculum. Most importantly, it promotes discovery and active learning.

New to This Edition
• At reviewers’ suggestions, we moved topics related to logic from Chapter 1 to Chapter 2, where sets and the operations of union and intersection are covered.
• Learning Objectives are listed at the beginning of every section to focus student attention on the key ideas.
• This text has always reflected the content and processes set forth in today’s new state mathematics standards and the Common Core State Standards (CCSS). In the twelfth edition, we have further tightened the connections to the standards and made them more explicit in the narrative and exercises:

• CCSS are cited within sections to focus student attention and provide a springboard for discussion of their content.
• More exercises that address the CCSS have been added, particularly in the Mathematical Connections portion of the exercise sets.
• The treatment of many topics has been enhanced to reflect a tighter connection to the CCSS. Examples include:
• Chapter 1: Expanded the Four-Step Polya Problem solving process with input from Standards for Mathematical Practice. The process is referred to in examples throughout the chapter.
• Chapter 2: Moved the logic section from Chapter 1 to emphasize the connections to sets and language. Logical reasoning is now an integral part of Chapter 2.
• Chapter 5: Now includes a definition of addition for integers that uses absolute value—included because it is one of the techniques used in operations on integers in CCSS.

• Chapter 6: The section on ratio and proportion now uses the types of diagrams to set up the proportions that are mentioned in CCSS.
• Chapter 8: Algebraic Thinking is extended to real numbers with greater emphasis on multistep word problems, as described in CCSS.
• Chapter 13: Following CCSS emphasis on transformations and symmetry, these topics are expanded in exposition and in problem sets. New engaging problems were added.
• Chapter 14: All measurement topics are now together in this chapter. Linear measure had been separated out, but because of measurement being highlighted in CCSS, all of the topics are in the same chapter.
• The text has been streamlined to help students focus on what’s really needed. We made judicious cuts with the student in mind.
• Some of the chapter opener scenarios and exercises have been revised to make them more relevant and engaging.
• The chapter summary charts have been revised to make them more comprehensive resources for students as they prepare for tests.