Teaching Mathematics for the 21st Century: Methods and Activities for Grades 6-12, Second Edition

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9780130488336: Teaching Mathematics for the 21st Century: Methods and Activities for Grades 6-12, Second Edition

Effective teachers need to know not only “what” to teach but also “how” to teach. To that end, this practical book is geared to deepening prospective teachers' personal knowledge base while enhancing their ability to design and deliver mathematics instruction that is in line with current standards of the National Council of Teachers of Mathematics (NCTM). Extensive background in the history and evolution of mathematics education sets the stage for activities, lesson plans, investigations, and assessment tools that are thoroughly grounded in the latest research. Includes numerous articles from The Mathematics Teacher and Teaching Middle School Mathematics; as well as classroom-tested problems, investigations, and instructional sequences proven effective in diverse classrooms and a variety of school situations. For future mathematics teachers.

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From the Back Cover:

This is the first middle and secondary math methods book to focus on reform and the national standards. It prepares teachers for the challenge of assisting all students in reaching the highest level of mathematics according to their interest and realistic ambitions. It also provides contemporary methods of teaching mathematics—which facilitate successful instruction—with a strong understanding of the philosophy and psychology behind sound practices. Coverage includes methodology, curriculum materials, and use of technology, accompanied by many practical suggestions for implementation. Presents instructional sequences to help students see the development of concepts over a period of time. Includes the salient points of the NCTM Standards. For educators and school administrators.

Excerpt. © Reprinted by permission. All rights reserved.:

"It's time to let the secret out: Mathematics is not primarily a matter of plugging numbers into formulas and performing rote computations. It is a way of thinking and questioning that may be unfamiliar to many of us, but is available to almost all of us." So states John Allen Paulos in A Mathematician Reads the Newspaper (New York: Anchor Books, 1996).

This second edition of Teaching Mathematics for the 21st Century is intended to help you let the secret out—to open up to your students the wonderful discoveries and challenges of the pattern-making and problem-solving aspects of a subject you may already find fascinating. If you think back to those mathematics teachers who surely inspired you to want to emulate their enthusiasm, clarity, and reasoning ability, we believe you can see that they, too, opened doors to your understanding of content beyond the procedures. The beauty and elegance of mathematics, as well as the need to apply mathematics to become an informed citizen of our democracy, must be imparted to today's students. This can be a big challenge when these students bring into your classroom a mind-set with a more limited (and to them, boring) perspective of mathematics.

This book came out of our experiences in middle-and high-school classrooms, as well as our extensive work with pre- and in-service teachers. Not only have we provided mathematics teachers with many forms of professional development but we have also visited the classrooms of hundreds of teachers in many different types of communities and been inspired by observing situations where mathematical understanding is clearly a goal that is being realized. We call the kind of teaching that goes on in these classrooms "Standards-based," referring to the Standards documents produced by the National Council of Teachers of Mathematics (NCTM), the most recent of which is the Principles and Standards for School Mathematics (PSSM, 2000). All mathematics teachers can implement Standards based instruction in their classrooms, and all students can benefit from this experience.

We trust that the assistance provided through this book and through your pre-service and in-service classes will help you enjoy a career that is person ally and professionally satisfying. And we hope that mathematical thinking will become a common part of your students' lives.

ORGANIZATION OF THE TEXT

Teaching Mathematics for the 21st Century contains twelve chapters organized into three overall parts. The first five chapters provide both theoretical and practical suggestions concerning what you should know and consider before you "step on the stage" of your first classroom. Chapters 6 through 10 discuss the ongoing realities of the classroom—planning and fine-tuning daily lessons, managing classrooms where discourse is valued, assessing and evaluating students, and dealing with issues of equity as they affect the classroom. The final two chapters look to your future as a member of a professional community, both in how you relate to constituents outside of education and how you avail yourself of ongoing professional growth activities as a lifelong learner. Within each part, the chapters are independent and can be studied in any order.

Part I: Prior to Entering the Classroom

Chapter 1, "History and Introduction to Mathematics Education Reform," provides extensive background about the history and development of the significant concepts leading to the current reform. The chapter details methods of teaching mathematics throughout the last half of the 20th century. We discuss research in cooperative learning and offer practical suggestions for implementing cooperative learning, one of the common activities in contemporary teaching practice. The mathematical focus of the activities in this chapter is logic.

Chapter 2, "Learning, Motivation, and Basic Management Skills," begins by discussing the main learning theories and models of intelligence that underlie the educational psychology behind reform in mathematics education. The section on motivation introduces some main concepts of the topic. Aspects of motivation are interwoven with the selection of activities and instructional design throughout the book. The second half of the chapter is devoted to decisions related to management skills teachers need before the first day of class. Examples and problems center on probability. Different approaches to probability tasks illustrate different theories of learning. Motivation and management issues also come into play with this content area, since probability tasks most often involve hands-on activities.

Chapter 3, "Concrete to Abstract With Tools, Manipulatives, Computer Programs, and Calculators," introduces a variety of methods to increase the preservice teacher's tool kit of teaching ideas. An effective way to explore this chapter is with a series of stations using the different manipulatives and calculators in a round-robin laboratory setting. Groups of students spend a given time at each station to become familiar with the available manipulative, and then they rotate to the next station. If class sets are available, lessons and activities using the MIRA, patty paper, and graphing calculators can be done more easily with the entire class working simultaneously on the same exercise in cooperative groups. Of course, the computer activities can be supplemented according to the computer software available at your site. The unifying topics for this chapter consist of the foundational concepts of arithmetic, geometry, and algebra. Secondary teachers need to understand the concept development approach to mathematics both as a preferred way of introducing new topics and as an approach to intervention.

Chapter 4, "Standards-Based Curricula With Sample Lessons," provides an opportunity to explore elements of different reform curricula, including sample materials from some programs. The chapter contrasts and compares segments of instructional sequences within some exemplary middle- and high-school programs. The emphasis is on data analysis activities incorporating methods of data collection (including the use of probeware) and ways to analyze data. What better content to link with reform materials than data analysis, since it effectively meshes the Technology Principle with the Representation and Communication Standards of the PSSM?

Chapter 5, "Geometry and Algebra Redefined?" explores the current development of these areas of mathematics and illustrates effective ways to integrate them. Algebra and geometry activities in the chapter provide the vehicle for this discussion.

Part II: Teaching and Learning in the Classroom

The second part of the text begins with Chapter 6, "Planning Instruction." This chapter starts with an overview of the teacher's community and school culture. Next, a discussion of semester, unit, and daily planning gives examples for each stage in the planning process. The chapter highlights different strategies for effective lessons based on the materials to be studied. The examples and problems in this chapter focus on matrices and their applications, as that topic lends itself to many different grade levels and applications.

Chapter 7, "Promoting Communication in the Classroom," presents a view of discipline as an integral part of instruction and classroom communication. We offer practical suggestions for promoting discourse, encouraging communication through student writing, and building a community of learners. Illustrations and problems are drawn from the discrete mathematics topics of graph theory and group theory, both of which lend themselves well to various types of classroom communication.

In Chapter 8, "Assessing Individual Student Performance," we introduce formative assessment and summative assessment (evaluation). The discussion includes basic test design and grade determination, topics of great concern to beginning teachers. Activities involving patterns in mathematics illustrate the importance of assessing students' mathematical reasoning in a Standards based classroom.

The topic of Chapter 9, "Student Equity," is complex and broad. This chapter serves only as an introduction to some of the equity issues facing teachers. The prevailing issue throughout the chapter is how to make mathematics accessible to all students. A discussion of the effects of tracking is followed by considerations of effective ways to help multicultural/multiethnic students, females, gifted/ talented students, and students with mild learning difficulties to be successful in mathematics. The mathematical emphasis of this chapter is nonstandard problems that are rich in content yet open to a variety of solution approaches.

Chapter 10, "Focus on Performance Assessment," extends the discussion of assessment in Chapter 8 by exploring the use of performance tasks and rubric scoring. In our experience, the area of assessment has grown so complex, with alternative methods unfamiliar to student teachers, that it is best to approach assessment in two different chapters with time between to absorb this broad and very important aspect of Standards based teaching. The role of externally mandated assessments also is presented. The chapter also touches on uses of the Internet by mathematics students and their families. Investigations in applied mathematics and modeling allow students to practice writing solutions that are assessed by rubrics.

Part III: Ongoing Development

The third part of this text opens with Chapter 11, "Communicating With Parents and Community." This chapter demonstrates effective ways to interact with parents, the school community, and other mathematics students. Topics include managing back-to-school nights, parent conferences, family mathematics nights, and entry into mathematics contests. The mathematical content comprises number sense, estimation, and measurement, all of which are mathematical tasks that can be connected to real-life experiences....

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