This book demonstrates how some of the fundamental ideas of algebra can be introduced, developed, and extended. It focuses on repeating and growing patterns, introduces the concepts of variable and equality, and examines relations and functions. Its activities are designed to capture the interest of small children as they investigate growing patterns, use pictures of dogs with varying numbers of spots to solve for missing addends, and use spinners to identify and explore functions. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.
Navigating through Algebra in Prekindergarten-Grade 2 is the first of four grade-band books that demonstrate how some of the fundamental ideas of algebra can be introduced, developed, and extended. The introduction to this book is an overview of the development of algebraic reasoning from prekindergarten through grade 12. Each of the three chapters that follow the introduction focuses on a basic idea of algebra. Chapter 1 deals with repeating and growing patterns, chapter 2 introduces the concepts of variable and equality, and chapter 3 introduces relations and functions.
Each chapter begins with a discussion of the foundational ideas and the expectations for students' accomplishments by the end of grade 2. This discussion is followed by student activities that introduce and promote familiarity with the basic ideas. At the beginning of each activity, the recommended grades are identified in the margin and a summary of the activity is presented. The goals to be achieved, the prerequisite skills and knowledge, and the materials necessary for conducting the activities are presented. Some of the activities have blackline masters, which are signaled by an icon and identified in the materials list and can be found in the appendix. They can also be printed from the CD-ROM that accompanies the book. The CD, also signaled by an icon, contains two applets for students to manipulate and resources for professional development.
All the activities have the same format. Each consists of three sections: "Engage," "Explore," and "Extend." The "Engage" section presents tasks designed to capture students' interest. "Explore" presents the core investigation that all students should be able to do. "Extend" offers additional activities for students who demonstrate continued interest and want to do some challenging mathematics. Throughout the activities, questions are posed to stimulate students to think more deeply about the mathematical ideas. After some questions, possible responses are shown in parentheses. Margin notes include teaching tips, anticipated student responses to some of the questions or activities, students' work, copies of blackline masters and solutions to problems on them, and quotations from Principles and Standards for School Mathematics (National Council of Teachers of Mathematics 2000). The discussion for each activity identifies connections with other content strands in the curriculum and to process strands, offers insights about students' performance, and suggests ways to modify the activities for students who are experiencing difficulty or who are in need of enrichment. Although grade levels are recommended, most of the activities can be modified for use by students at other levels in the pre-K-2 grade band. In order to make modifications that will most enhance students' learning, teachers are urged to observe students' performance by taking note of the appropriateness of their mathematical vocabulary, the clarity of their explanations, the robustness of the rationale for their solutions, and the complexity of their creations.
