Teaching Secondary and Middle School

Teaching Secondary and Middle School Mathematics combines up-to-date technology and research with a vibrant writing style to help preservice teachers grasp curriculum, teaching, and assessment issues as they relate to 6-12 mathematics.

Daniel Brahier is Associate Professor of Mathematics Education at Bowling Green State University in Ohio.

Preface

xiii

UNIT I WHAT DOES IT MEAN TO ``DO,'' ``TEACH,'' AND ``LEARN'' MATHEMATICS?

1

(60)

Mathematics as a Process

3

(26)

National and International Assessment Data

6

(5)

The Need for Reform

11

(1)

``Doing'' Mathematics

12

(12)

Problem Solving

12

(4)

Reasoning and Proof

16

(3)

Communication

19

(1)

Connections

20

(3)

Representation

23

(1)

Conclusion

24

(1)

Glossary

25

(1)

Discussion Questions and Activities

26

(1)

Bibliographic References and Resources

26

(3)

Learning Theories and Psychology in Mathematics Education

29

(32)

Research in Mathematics Education

30

(5)

Quantitative and Qualitative Methods

31

(2)

Experimental and Descriptive Research

33

(2)

Learning Theories in Mathematics

35

(19)

Bruner's Stages of Representation

36

(4)

The van Hiele Model

40

(3)

The Inquiry Approach and Constructivist Model

43

(4)

Inductive versus Deductive Teaching

47

(4)

Motivation

51

(3)

Conclusion

54

(1)

Glossary

55

(3)

Discussion Questions and Activities

58

(1)

Bibliographic References and Resources

58

(3)

UNIT II THE MATHEMATICS CURRICULUM

61

(60)

Curricular Models

63

(25)

NCTM Curriculum Standards

64

(3)

State Models

67

(1)

The Core Curriculum

68

(7)

Traditional versus Integrated Sequences

75

(8)

Conclusion

83

(1)

Glossary

84

(1)

Discussion Questions and Activities

84

(1)

Bibliographic References and Resources

85

(3)

Implementing a Course of Study

88

(33)

The Course of Study

89

(6)

Writing Goals and Objectives

95

(9)

Classifying Objectives

97

(1)

Affective Objectives

97

(1)

Cognitive Objectives

97

(7)

Selection and Organization of Resources

104

(9)

Textbooks

104

(5)

Print Resources

109

(1)

The Internet

110

(2)

Organizing a Resource File

112

(1)

Conclusion

113

(1)

Glossary

114

(1)

Discussion Questions and Activities

115

(1)

Bibliographic References and Resources

116

(1)

Sample Recommended Resource Books

117

(1)

Comap ``Hi-Map'' (High School Mathematics) Teaching Modules

117

(1)

NCTM Navigations Series

118

(1)

NCTM Addenda Series Resource Books

118

(1)

NSF-Funded Curricular Materials

119

(2)

UNIT III TEACHING MATHEMATICS

121

(120)

Planning for Instruction

123

(33)

Unit Planning

124

(6)

Lesson Planning

130

(18)

General Considerations

133

(1)

Goals and Objectives

133

(1)

Materials and Resources

134

(1)

Motivation

134

(1)

Lesson Procedure

135

(2)

Closure

137

(1)

Extension

137

(1)

Assessment

137

(1)

Sample Lesson Plans

138

(10)

Lesson Imaging versus Lesson Planning

148

(2)

Reflecting on a Lesson

150

(1)

Conclusion

151

(1)

Glossary

152

(1)

Discussion Questions and Activities

153

(1)

Bibliographic References and Resources

153

(3)

Activities---Selected Lesson Plan Ideas from The Mathematics Teacher

154

(2)

Teaching Tools and Strategies

156

(38)

Teaching Standards and Principles

158

(2)

The NCTM Professional Teaching Standards

158

(2)

The Teaching and Learning Principles

160

(1)

Selecting Activities and Problems

160

(4)

Classroom Tools

164

(10)

Hands-On Manipulative Materials

164

(5)

Use of Technology

169

(3)

Diagrams, Graphs, and Other Discussion Starters

172

(2)

Classroom Discourse

174

(8)

Student and Teacher Roles

174

(1)

Questioning Skills

175

(3)

Cooperative Learning

178

(4)

Learning Environment

182

(6)

Reflective Practices

188

(1)

Conclusion

189

(1)

Glossary

190

(1)

Discussion Questions and Activities

191

(1)

Bibliographic References and Resources

192

(2)

Teaching Specific Mathematics Content

194

(47)

The Teaching of Algebra

196

(9)

Algebra---Sample Lesson Plan

198

(2)

Algebra---Activities Sampler

200

(5)

The Teaching of Geometry

205

(9)

Geometry---Sample Lesson Plan

207

(3)

Geometry---Activities Sampler

210

(4)

The Teaching of Data Analysis and Probability

214

(12)

Data Analysis and Probability---Sample Lesson Plan

217

(2)

Data Analysis and Probability---Activities Sampler

219

(7)

The Teaching of Discrete Mathematics

226

(10)

Discrete Mathematics---Sample Lesson Plan

228

(3)

Discrete Mathematics---Activities Sampler

231

(5)

Conclusion

236

(1)

Glossary

237

(1)

Discussion Questions and Activities

237

(1)

Bibliographic References and Resources

238

(3)

UNIT IV ASSESSMENT IN MATHEMATICS

241

(64)

The Role of Assessment

243

(35)

What Is Assessment?

244

(1)

Purposes for Assessment

245

(3)

Test Construction

248

(7)

Preparing Items

248

(3)

Ensuring Validity and Reliability

251

(1)

Scoring Student Work

252

(1)

Including Review Items

253

(1)

Limitations to Written Tests

253

(2)

Alternate Strategies for Assessing Student Progress

255

(17)

Journals

255

(3)

Open-Ended Questions and Rubrics

258

(3)

Individual and Team Projects

261

(4)

Observations and Checklists

265

(3)

Interviews

268

(2)

Portfolios

270

(2)

Conclusion

272

(2)

Glossary

274

(1)

Discussion Questions and Activities

275

(1)

Bibliographic References and Resources

276

(2)

Principles of Assessment Practices

278

(27)

NCTM Recommendations on Assessment

279

(5)

The Assessment Standards

279

(5)

The Assessment Principle

284

(1)

Equity and Assessment

284

(2)

Homework Assignments

286

(10)

Homework Amount and Frequency

287

(4)

Checking Homework Assignments

291

(2)

Using Homework Assignments in Assessment

293

(3)

Evaluation: Determining Final Grades

296

(5)

Conclusion

301

(1)

Glossary

302

(1)

Discussion Questions and Activities

302

(1)

Bibliographic References and Resources

303

(2)

UNIT V MEETING INDIVIDUAL STUDENT AND TEACHER NEEDS

305

(54)

Meeting the Needs of All Students

307

(26)

Defining and Achieving Equity

309

(16)

Students with Special Needs

310

(5)

Gender

315

(5)

Ethnic and Cultural Issues

320

(5)

General Suggestions for Meeting Diverse Student Needs

325

(3)

Conclusion

328

(1)

Glossary

328

(1)

Discussion Questions and Activities

329

(1)

Bibliographic References and Resources

330

(3)

The Teacher of Mathematics in the School Community

333

(26)

Working with Parents

334

(7)

The Supervision and Evaluation of Teachers

341

(6)

Functioning in a Department

347

(1)

Ongoing Professional Development

348

(7)

Making the Case for Long-Term Development

348

(3)

Opportunities for Professional Development

351

(3)

The Professional Development Plan

354

(1)

Conclusion

355

(1)

Discussion Questions and Activities

355

(1)

Bibliographic References and Resources

356

(3)

Appendix A Recommended Web Sites

359

(3)

Professional Organizations

359

(1)

Curriculum Projects

359

(1)

Activities and Lesson Plan Ideas

360

(1)

General Mathematics Education Sites

361

(1)

Appendix B Cases

362

(21)

Case 1: The Marble Line (algebra)

363

(12)

Case 2: Chances Are (probability)

375

(8)

Index

383

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Teaching Secondary and Middle School Mathematics

Summary

Author Biography

Table of Contents

Supplemental Materials