Teaching mathematics in secondary and middle school : an interactive approach / James S. Cangelosi.

Format:

Book

Author/Creator:

Cangelosi, James S.

Language:

English

Subjects (All):

Mathematics--Study and teaching (Secondary).

Mathematics.

Mathematics--Study and teaching (Middle school).

Physical Description:

xii, 436 pages : illustrations ; 28 cm

Edition:

Third edition.

Place of Publication:

Upper Saddle River, N.J. : Merrill, [2003]

Contents:

Chapter 1 Beginning a Career as a Professional Mathematics Teacher 1

Preservice Preparation and Professional Portfolios 2

Selecting a Teaching Position 3

Teaching Loads and Other Responsibilities 14

Organizing for the Year 18

The Beginning of an Eventful School Year 30

Learning From Experiences 41

Chapter 2 Gaining Students' Cooperation in an Environment Conducive to Doing Mathematics 50

Well-Planned Lessons Gone Awry 50

Allocated and Transition Times 53

Student Behaviors 56

Establishing a Favorable Climate for Learning Mathematics 62

Communicating and Interacting With Students 63

Communicating With Students' Parents 70

Establishing Standards for Conduct and Routine Classroom Procedures 72

Working With Students as Individuals 75

Systematically Dealing With Off-Task Behaviors 84

Chapter 3 Motivating Students to Engage in Mathematical Learning Activities 88

Motivating Students to Do Mathematics 88

Directing Students Into Learning Activities 90

Variety of Learning Activities 97

Engaging Students in Large-Group Presentations 97

Responding to Students' Questions 108

Asking Students Questions 113

Engaging Students in Cooperative-Learning Sessions 118

Engaging Students in Independent-Work Sessions 121

Motivating Students to Complete Homework Assignments 123

Chapter 4 Developing Mathematics Curricula 130

A Curriculum 130

The Gap Between Research-Based Mathematics Curricula and Typical Practice 133

PSSM's Equity Principle 143

PSSM's Curriculum Principle 144

PSSM's Teaching Principle 145

PSSM's Learning Principle 146

PSSM's Assessment Principle 147

PSSM's Technology Principle 147

PSSM's Content Standards and Expectations 148

PSSM's Process Standards 149

Designing Mathematics Courses 164

Teaching Units 164

Daily Planning 169

Chapter 5 Leading Students to Construct Concepts and Discover Relationships 172

Mathematical Concepts 173

Inductive Reasoning 177

Construct-a-Concept Objectives 178

Lessons for Construct-a-Concept Objectives 178

Miniexperiments Relevant to Students' Achievement of Construct-a-Concept Objectives 189

Discoverable Mathematical Relationships 192

Discover-a-Relationship Objectives 194

Lessons for Discover-a-Relationship Objectives 194

Miniexperiments Relevant to Students' Achievement of Discover-a-Relationship Objectives 202

Chapter 6 Leading Students to Develop Knowledge and Algorithmic Skills 207

Mathematical Information to Be Remembered 207

The Acquisition and Retention of Information 209

Simple-Knowledge Objectives 211

Lessons for Simple-Knowledge Objectives 211

Miniexperiments Relevant to Students' Achievement of Simple-Knowledge Objectives 214

Algorithms 216

Algorithmic-Skill Objectives 217

Lessons for Algorithmic-Skill Objectives 217

Miniexperiments Relevant to Students' Achievement of Algorithmic-Skill Objectives 223

Chapter 7 Leading Students to Communicate With Mathematics 229

The Power of Mathematical Language 229

What Is the Question? 233

Negotiating the Language of Mathematics 235

Comprehension-and-Communication Objectives 239

Lessons for Comprehension-and-Communication Objectives 239

Speaking, Listening to, and Writing Mathematics 245

Miniexperiments Relevant to Students' Achievement of Comprehension-and-Communication Objectives 250

Chapter 8 Leading Students to Creatively Use Mathematics 254

Deductive Reasoning for Problem Solving 255

Application Objectives 256

Lessons for Application Objectives 256

A Four-Stage Lesson for an Application Objective 258

Miniexperiments Relevant to Students' Achievement of Application Objectives 260

Doing Mathematics Creatively 263

Creative-Thinking Objectives 264

Lessons for Creative-Thinking Objectives 265

Incorporating Synectics Into Creative-Thinking Lessons 265

Miniexperiments Relevant to Students' Achievement of Creative-Thinking Objectives 266

Influencing Students' Attitudes About Mathematics 269

Miniexperiments Relevant to Students' Achievement of Affective Objectives 273

Chapter 9 Assessing and Reporting Students' Progress With Mathematics 277

Complex Decisions 278

Measurement Usefulness 301

Common Malpractice 308

Designing Measurements of Students' Achievement of Unit Goals 309

Using Test Results for Formative Feedback 315

Assigning Grades to Measurement Scores 315

Portfolios for Communicating Summative Evaluations of Student Achievement 318

Tests You Did Not Design 320

High-Stakes Tests 325

Chapter 10 Technology and Resources for Teaching and Learning Mathematics 332

Selection and Use of Textbooks 332

Sources of Ideas for Teaching Mathematics 334

Hands-On Manipulatives and Concrete Models 336

Computer-Assisted Mathematics Teaching 346

Calculator-Assisted Mathematics Teaching 357

Technology for Presentations 361

Extending Your Mathematics Classroom Beyond the Walls of the School 364

Chapter 11 Analyzing Examples of Mathematics Curricula and Instructional Practice 366

Building From Experiences 366

A Sixth-Grade Mathematics Course 367

A Prealgebra Course 372

An Algebra I Course 375

A Geometry Course 401

Algebra II, Trigonometry, and Precalculus 406

A Life-Skills Mathematics Course 412

AP and Concurrent-Enrollment Mathematics Courses 416.

Notes:

Includes bibliographical references (pages 423-429) and index.

ISBN:

0130950181

OCLC:

48163325