Succeeding at Teaching Secondary Mathematics: Your First Year »

Dr. Julie Sliva Spitzer brings to this topic a rich background in mathematics, technology, and special education. As an associate professor of mathematics education at San Jose State University, she teaches methods of mathematics instruction to aspiring educators and supervises their field experiences. Julie continues to enjoy inservice work with teachers grades K–12. Julie’s research interests include studying teacher and student attitudes toward teaching and learning mathematics, and best practices for teaching mathematics to special needs learners. She is a frequent presenter at the National Council of Teachers of Mathematics Annual Meetings, the California Mathematics Annual Conference, and the International Group for the Psychology of Mathematics Education, North American Chapter. Dr. Spitzer can be reached at sliva@math.sjsu.edu.

Cheryl D. Roddick is an associate professor in the Department of Mathematics at San José State University. She currently teaches mathematics and mathematics methods courses to students in K-12 education. She also supervises field experiences for student teachers at the secondary level.
Dr. Roddick’s research interests include the conceptual understanding of fractions and teacher change relative to teaching mathematics. She has presented her research in local as well as national mathematics education conferences. She also facilitates K-12 inservice activities with teachers in local school districts. Dr. Roddick may be reached at roddick@math.sjsu.edu.

This practical resource helps beginning secondary mathematics teachers design a curriculum that is meaningful, differentiate instruction, engage students, meet standards, assess student understanding, and more.

Acknowledgments vii

About the Authors ix

Introduction 1

1 A Glimpse at Mathematics Instruction 3

Two Illustrations 4

Vignette 1: Algebra I—Shake Across America 4

Discussion 7

Adaptations and Extensions 10

Vignette 2: Seventh Grade—Surface Area With Polydron Shapes 10

Discussion 14

Adaptations and Extensions 15

Success in Teaching Mathematics 16

Summary 16

2 Standards-Based Teaching 17

Why Do We Need Standards for Teaching Mathematics? 18

The National Council of Teachers of Mathematics (NCTM) Principles and Standards 18

State and District Standards for Teaching Mathematics 24

The Relationship Between Standards and Standards Based Mathematics Textbooks 25

Aligning Algebraic Reasoning With the Process Standards 26

Summary 31

3 Engaging Students in Learning Mathematics 33

What Is Engagement? 34

Engaging Learners in the Affective Domain 34

Vignette 1: Math Clubs 35

Vignette 2: Seventh Grade&Math Jeopardy 35

Glasser's Five Basic Needs 36

Vignette 3: Increasing a Student's Confidence in Mathematics 38

A Fresh Look at Math Clubs and Math Jeopardy 39

Affective Issues Related to Teaching and Learning Mathematics 42

Students Engaged in Learning Probability 44

Engaging Learners in the Behavioral Domain 51

Engaging Learners in the Cognitive Domain 53

Summary 56

4 Engagement Strategies for Special Populations 57

Vignette 1 Disparate Learners in Algebra I 57

The Special Needs Learner 59

The Gifted Learner 65

The English Language Learner 70

Example of Engaging Learners in a Mathematics Classroom 74

Vignette 2 Permutations, Counting, and Ice Cream Cones 74

Discussion 78

Summary 79

5 Assessment 81

Types of Assessment 82

Rubrics 88

Developing Assessments: The Use of Backward Design 89

Grading and Assessment Schemes 91

Practical Ways of Assessing Throughout the Instructional Process 92

Tailoring Assessments for Special Populations 92

Data Driven Instructional Practices 97

A Word About Standardized Tests 98

Summary 98

6 Putting It All Together 99

The Year at a Glance: Designing Your Curriculum 99

Making Connections Within Mathematics 100

Mathematical Connections Across the Grades 102

More Connections Across the Grades 105

Making Connections Across the Curriculum 106

Succeeding at Teaching Mathematics—and Loving It! 107

Appendix A Solutions to Shake Across America 109

Appendix B Solution to the Following Problem From the Polydron Vignette 111

Appendix C The Dart Board Game Solution 113

Appendix D Generalization for Original Pizza Problem 115

References 117

Index 121