The primary purpose of Mathematics for Elementary Teachers: An Activity Approach is to engage prospective elementary and middle school teachers in mathematical activities that will enhance their conceptual knowledge, introduce them to important manipulatives, and model the kind of mathematical learning experiences they will be expected to provide for their students.

The National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (“Standards 2000”) and its predecessor, Curriculum and Evaluation Standards for School Mathematics, strongly assert that students learn mathematics well only when they construct their own mathematical thinking. Information can be transmitted from one person to another but mathematical understanding and knowledge come from within the learner as that individual explores, discovers, and makes connections.

The National Council of Teachers of Mathematics’ Professional Standards for Teaching Mathematics presents a vision of mathematics teaching that “redirects mathematics instruction from a focus on presenting content through lecture and demonstration to a focus on active participation and involvement. Mathematics instructors do not simply deliver content; rather, they facilitate learners’ construction of their own knowledge of mathematics.”

This book contains activities and materials to actively engage students in mathematical explorations. It provides prospective elementary and middle school teachers the opportunity to examine and learn mathematics in a meaningful way. It provides the instructor with the resources to make students’ mathematical activity the focus of attention.

Reasons for Mathematical Activities

It is well known that effective teachers have a good understanding of the mathematics they teach and are skillful in choosing and using a variety of appropriate instructional techniques. The importance of using manipulatives in mathematics teaching and learning is well documented and amply illustrated in the pages of the Principles and Standards for School Mathematics. Interviews with teachers successfully using manipulatives in classrooms revealed the following commonalities: the teachers had all received training for using manipulatives; they designed their own lessons and worked through the lessons with manipulatives themselves; and they prepared for classroom use of the manipulatives by anticipating how the class would react to the activity.¹

Mathematics for Elementary Teachers: An Activity Approach is a collection of activities for prospective teachers that involves inductive and deductive reasoning. The activities allow students to think deeply about how manipulatives and visual models contribute to understanding mathematical concepts. Students experience mathematics directly by using models that embody concepts and promote mathematical thinking. This book represents the belief that:

• Prospective teachers who learn mathematics through appropriate use of manipulatives, models, and diagrams are more likely to develop a solid conceptual basis and a deeper understanding of the mathematics they will teach.

• Prospective teachers who learn mathematics by being actively involved in doing mathematics will be more likely to teach in the same manner.

• Prospective teachers who use manipulatives effectively in their learning will experience how manipulatives assist understanding and be more likely to use them effectively in their teaching.

• Becoming familiar with manipulatives and models in structured activities will help prepare prospective teachers to develop similar lessons for their students.

• A concrete approach diminishes the mathematical anxiety often accompanying a more abstract approach.

• Tactile and visual approaches provide mental images that, for some students, can be easily retained to provide understanding for symbolic representations.

Features

Mathematics for Elementary Teachers: An Activity Approach contains 11 chapters with 34 activity sets and accompanying materials to provide a self-contained mathematics laboratory. Here are the special features of this book.

Active Learning Each activity set uses physical materials and/or visual models to provide a context for understanding. The questions and activities in each activity set are sequentially developed to encourage discovery and to provide depth into the topic.

Cooperative Learning The activity sets can be done individually or in small groups. In particular, Activity Set 2.3, Logic Problems for Cooperative Learning Groups, is designed for small-group interaction.

Individual Reflections Throughout the activity sets, students are asked to describe patterns, discuss their thinking, and write explanations of their reasoning.

Manipulative Kit and Material Cards The Manipulative Kit contains 9 common manipulatives on color card stock together with storage envelopes. The Activity Book also has 40 additional material cards with manipulatives, models, grids, templates, game mats, and other materials to be used in the activities.

Pedagogy The activity sets demonstrate ways that manipulatives and visual models can be used in classrooms to promote conceptual understanding and mathematical thinking. There are concrete or visual models for teaching the following topics:

Just for Fun Each activity set is followed by a Just for Fun activity. These are related to the topics of the activity sets and often are recreational or artistic.

Classroom Ideas At the end of each chapter a Suggested Classroom Activity is given for students to try with children. In addition, any of the activities in the book can be adapted for use with children.

Readings for More Classroom Ideas There is a selected list of readings at the end of each chapter. Some of the articles were written by classroom teachers about activities they have successfully used. Also, there are references to articles and books that discuss reform issues for teachers. Additional sources can be found on the Online Learning Center (described below).

Puzzlers Brain teasers are interspersed throughout the text to add variety and provide practice in problem solving.

Answer Section Answers to all puzzlers and selected (*) questions from the activity sets are in the back of the Activity Book.

Supplements

Activity Book Instructor’s Manual (ISBN 0-07-282146-9) The Instructor’s Manual for Mathematics for Elementary Teachers: An Activity Approach contains answers for all activity sets, puzzlers, and Just for Fun activities. There is a set of sample test questions, with answers, for each chapter of the activity book. There are blackline masters of various grids used throughout the book.

Companion Text (ISBN 0-07-253294-7) The text, Mathematics for Elementary Teachers: A Conceptual Approach, Sixth Edition, is a companion volume to this activity book. Like the activity book, the text contains 11 chapters and 34 sections. Each of these sections corresponds to an activity in the activity book. The text also contains a one-page math activity at the beginning of each section that uses the same Manipulative Kit as the activity book.

Online Learning Center (www.mhhe.com/bennett-nelson)

This new website created for the Sixth Edition of the activity book and its companion text offers a variety of resources to both instructors and students. From this site you can:

• Use the Digital Manipulative Kit to carry out various activities using colored manipulatives online.

• Access 11 interactive mathematics applets to learn key mathematical concepts.

• Obtain Writing/Discussion questions about teaching issues and mathematics concepts.

• Download color masters for transparencies of the manipulatives and black and white masters for a variety of grids and dot paper.

• Access an extended bibliography and list of Internet links.

• Explore 14 open-ended computer investigations with the browser-based Mathematics Investigator software to generate data.

• Download instructions and exercises for Network Graphs and Logo.

Class Formats

The familiar chapter headings in Mathematics for Elementary Teachers: An Activity Approach will be convenient for those who wish to use the activities with the companion text or another mathematics textbook. Many of the activity sets are independent and may be selected out of sequence.

Mathematics for Elementary Teachers: An Activity Approach can be effectively used in a variety of class formats:

• A lab course based on the activity sets with outside readings from a reference text or journals

• A combination lab and recitation course in which the activities are used as starting points, followed by discussions or lectures based on extensions of the ideas raised in the activity sets

• A traditional lecture/recitation course with the activity sets as supplemental and used for assignments

Acknowledgments

The authors would like to thank the students and instructors who have used the previous editions of this book, along with the instructors who reviewed this book and its companion text, Mathematics for Elementary Teachers: A Conceptual Approach. The authors are sincerely grateful for the helpful suggestions and continued support.