Teaching secondary and middle school mathematics / Daniel J. Brahier.

Format:

Book

Author/Creator:

Brahier, Daniel J.

Language:

English

Subjects (All):

Mathematics--Study and teaching (Middle school).

Mathematics.

Mathematics--Study and teaching (Secondary).

Physical Description:

xvi, 394 pages : illustrations ; 24 cm

Edition:

Second edition.

Place of Publication:

Boston, MA : Pearson/Allyn and Bacon, [2005]

Contents:

Unit I What Does It Mean to "Do," "Teach," and "Learn" Mathematics? 1

Chapter 1 Mathematics as a Process 3

National and International Assessment Data 6

The Need for Reform 11

"Doing" Mathematics 12

Problem Solving 12

Reasoning and Proof 16

Communication 19

Connections 20

Representation 23

Chapter 2 Learning Theories and Psychology in Mathematics Education 29

Research in Mathematics Education 30

Quantitative and Qualitative Methods 31

Experimental and Descriptive Research 33

Learning Theories in Mathematics 35

Bruner's Stages of Representation 36

The van Hiele Model 40

The Inquiry Approach and Constructivist Model 43

Inductive versus Deductive Teaching 47

Motivation 51

Unit II The Mathematics Curriculum 61

Chapter 3 Curricular Models 63

NCTM Curriculum Standards 64

State Models 67

The Core Curriculum 68

Traditional versus Integrated Sequences 75

Chapter 4 Implementing a Course of Study 88

The Course of Study 89

Writing Goals and Objectives 95

Classifying Objectives 97

Affective Objectives 97

Cognitive Objectives 97

Selection and Organization of Resources 104

Textbooks 104

Print Resources 109

The Internet 110

Organizing a Resource File 112

Sample Recommended Resource Books 117

COMAP "Hi-Map" (High School Mathematics) Teaching Modules 117

NCTM Navigations Series 118

NCTM Addenda Series Resource Books 118

NSF-Funded Curricular Materials 119

Unit III Teaching Mathematics 121

Chapter 5 Planning for Instruction 123

Unit Planning 124

Lesson Planning 130

General Considerations 133

Goals and Objectives 133

Materials and Resources 134

Motivation 134

Lesson Procedure 135

Closure 137

Extension 137

Assessment 137

Sample Lesson Plans 138

Lesson Imaging versus Lesson Planning 148

Reflecting on a Lesson 150

Chapter 6 Teaching Tools and Strategies 156

Teaching Standards and Principles 158

The NCTM Professional Teaching Standards 158

The Teaching and Learning Principles 160

Selecting Activities and Problems 160

Classroom Tools 164

Hands-On Manipulative Materials 164

Use of Technology 169

Diagrams, Graphs, and Other Discussion Starters 172

Classroom Discourse 174

Student and Teacher Roles 174

Questioning Skills 175

Cooperative Learning 178

Learning Environment 182

Reflective Practices 188

Chapter 7 Teaching Specific Mathematics Content 194

The Teaching of Algebra 196

The Teaching of Geometry 205

The Teaching of Data Analysis and Probability 214

The Teaching of Discrete Mathematics 226

Unit IV Assessment in Mathematics 241

Chapter 8 The Role of Assessment 243

Purposes for Assessment 245

Test Construction 248

Preparing Items 248

Ensuring Validity and Reliability 251

Scoring Student Work 252

Including Review Items 253

Limitations to Written Tests 253

Alternate Strategies for Assessing Student Progress 255

Journals 255

Open-Ended Questions and Rubrics 258

Individual and Team Projects 261

Observations and Checklists 265

Interviews 268

Portfolios 270

Chapter 9 Principles of Assessment Practices 278

NCTM Recommendations on Assessment 279

The Assessment Standards 279

The Assessment Principle 284

Equity and Assessment 284

Homework Assignments 286

Homework Amount and Frequency 287

Checking Homework Assignments 291

Using Homework Assignments in Assessment 293

Evaluation: Determining Final Grades 296

Unit V Meeting Individual Student and Teacher Needs 305

Chapter 10 Meeting the Needs of All Students 307

Defining and Achieving Equity 309

Students with Special Needs 310

Gender 315

Ethnic and Cultural Issues 320

General Suggestions for Meeting Diverse Student Needs 325

Chapter 11 The Teacher of Mathematics in the School Community 333

Working with Parents 334

The Supervision and Evaluation of Teachers 341

Functioning in a Department 347

Ongoing Professional Development 348

Making the Case for Long-Term Development 348

Opportunities for Professional Development 351

The Professional Development Plan 354

Professional Organizations 359

Curriculum Projects 359

Activities and Lesson Plan Ideas 360

General Mathematics Education Sites 361

Appendix B Cases 362

Case 1 The Marble Line (algebra) 363

Case 2 Chances Are (probability) 375.

Notes:

Includes bibliographical references and index.

ISBN:

0205412637

OCLC:

54822662