Teaching Mathematics for the 21st Century: Methods and Activities for Grades 6-12 / Edition 3

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Overview

This third edition of T eaching Mathematics for the 21st Century continues to help teachers let the secret out–to open up to their students the wonderful discoveries and challenges of the pattern-making and problem-solving aspects of a fascinating subject: mathematics. The rationale remains the same–to enable prospective and current teachers to access and use tools and strategies to effectively teach mathematics to contemporary students. Changing demographics, knowledge of how people learn, and technology all impact the way we educate our young people. This edition incorporates lessons and strategies from programs that have proven success in many types of classrooms. Many of these examples help students connect mathematics to real life situations and communicate their understanding of the underlying concepts. Although technology is constantly being upgraded, ways to increase student motivation through its application remains a goal. For example--since applets can enhance a lesson whether the teacher uses a computer projector, a “smart” board, or has students work individually on computers--we have identified several sources of mathematics applets that can be correlated to various lessons. Research citations and summaries have been updated to reflect current information on teaching and learning. For future teachers.

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Editorial Reviews

Booknews
For potential math teachers, shows how to open the world of mathematics to students, giving both theoretical and practical suggestions on things to consider before going into the classroom as well as coverage of the ongoing reality of the classroom, with advice on planning, managing classrooms where discourse is valued, and dealing with issues of equity. Many problems, investigations, and instructional sequences for use in the classroom are provided. Coverage also includes professional issues. Huetinck teaches at California State University-Northridge; Munshin is affiliated with the Los Angeles Unified School District. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780132281423
  • Publisher: Pearson
  • Publication date: 7/26/2007
  • Series: Pearson Custom Education Series
  • Edition description: New Edition
  • Edition number: 3
  • Pages: 576
  • Product dimensions: 8.20 (w) x 10.80 (h) x 1.20 (d)

Table of Contents

PART I-Prior to Entering the Classroom

CHAPTER 1-History and Introduction to Mathematics Education Reform

CHAPTER 2-Learning, Motivation, and Basic Management Skills

CHAPTER 3-Concrete to Abstract With Tools, Manipulatives, Computer Programs, and Calculators

CHAPTER 4-Based Curricula With Sample Lessons

CHAPTER 5-Geometry and Algebra Redefined

PART II -Teaching and Learning in the Classroom

CHAPTER 6-Planning Instruction

CHAPTER 7-Promoting Communication in the Classroom

CHAPTER 8-Monitoring and Evaluating Individual Student Performance

CHAPTER 9-Student Equity

CHAPTER 10-Focus on Performance Assessment

PART III-Ongoing Development

CHAPTER 11-Communicating With Parents and Community

CHAPTER 12-Professional Growth

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Introduction

"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 kindof 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.

Chapter 12, "Professional Growth," encourages students to be lifelong learners of the profession of teaching. This chapter discusses the topic of evaluation by supervisors, which is of paramount concern to the beginning teacher. Certification through the National Board for Professional Teaching Standards is described as a goal of exemplary teachers. The mathematical focus of lessons written and shared by experienced teacher leaders is on postcore topics in discrete mathematics, trigonometry, and pre-calculus.

FEATURES INCLUDED IN THE TEXT

This book is suitable for both undergraduate and graduate courses for teachers of mathematics, as well as for in-service enrichment courses. It may also be used for classes for supplementary credential programs and for retraining persons from other careers who are becoming teachers. We selected mathematical material and pedagogy of great richness, anticipating that this text not only will be useful to undergraduate and graduate methods students and professors, but also will continue to be a resource to teachers throughout their career.

To support those objectives, Teaching Mathematics for the 21st Century includes a variety of features:

  • Many chapters contain vignettes taken from actual classroom experiences.
  • Exemplary teachers have contributed their philosophies on different issues and materials that work in their classrooms.
  • The problems, investigations, and instructional sequences in every chapter have been classroom tested with secondary-level students. They demonstrate the wide range of activities to be found in today's mathematics curricula.
  • Additional activities at the end of each chapter provide mathematics exercises to use along with or in place of those integrated in the chapters.
  • In the back of the book, "Activity Notes to the Teacher for Selected Problems" helps teachers implement the content and methods found in the activities, sample lessons, and instructional sequences of each chapter.
  • An annotated list of recommended resources is given at the end of each chapter.
  • An extensive list of references combined for all the chapters appears at the end of the book.

NEW TO THIS EDITION

This second edition has been extensively reworked to update materials and make the format of the activities more accessible. A number of these enhancements merit special notice:

  • Throughout the text, we apply the NCTM's Principles and Standards of School Mathematics. Chapters quote the core principles and main ideas of the PSSM where appropriate. Each of the activities, sample lessons, and instructional sequences indicates the relevant standard, so both pre-service and in-service teachers can see how they might apply these standards in the classroom.
  • Activities, lessons, and instructional sequences are interactive. An improved format allows greater ease of use with secondary-level students. These significant elements of the text encourage involvement in Standards-based quality mathematics in every chapter. In each chapter's introduction, an "About the Activities for This Chapter'" section describes how the mathematical lessons work with the discussion material of the text and with each other to build power in mathematical thinking. The integration of activities and discussion topics helps teachers apply educational theory to actual mathematics lessons.
  • For additional interactive opportunities, a Companion Website includes links to other helpful resources on the Internet. When you see the Website icon, additional information about this topic can be accessed on our Website.
  • A variety of Instructional Resources have been added to the end of each chapter. Many of these are recent books and articles in The Mathematics Teacher and Teaching Middle School Mathematics published since the first edition of this text.
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