The Mathematics That Every Secondary School Math Teacher Needs to Know (Studies in Mathematical Thinking and Learning Series)

What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the deep mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT": M Multiple Approaches/Representations A Applications to Real Life T Technology H History N Nature of Mathematics: Reasoning and Proof S Solving Problems I Interlinking Concepts: Connections G Grade Levels H Honing of Mathematical Skills T Typical Errors This text is aligned with the recently released Common Core State Standards, and is ideally suited for a capstone mathematics course in a secondary mathematics certification program. It is also appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers. "What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. Features of this title include: Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great 'MATH-N-SIGHT' - M: Multiple Approaches/Representations, A: Applications to Real Life, T: Technology, H: History, N: Nature of Mathematics - Reasoning and Proof, S: Solving Problems, I: Interlinking Concepts - Connections, G: Grade Levels, H: Honing of Mathematical Skills, and T: Typical Errors"--Provided by publisher BOOK COVER......Page 1 TITLE......Page 6 COPYRIGHT......Page 7 BRIEF CONTENTS......Page 8 CONTENTS......Page 10 PREFACE/INTRODUCTION......Page 18 NOTES TO THE READER/PROFESSOR......Page 22 ACKNOWLEDGEMENTS......Page 28 CHAPTER 1 INTUITION AND PROOF......Page 30 CHAPTER 2 BASICS OF NUMBER THEORY......Page 46 CHAPTER 3 THEORY OF EQUATIONS......Page 98 CHAPTER 4 MEASUREMENT: AREA AND VOLUME......Page 142 CHAPTER 5 THE TRIANGLE: ITS STUDY AND CONSEQUENCES......Page 188 CHAPTER 6 BUILDING THE REAL NUMBER SYSTEM......Page 244 CHAPTER 7 BUILDING THE COMPLEX NUMBERS......Page 336 CHAPTER 8 INDUCTION, RECURSION, AND FRACTAL DIMENSION......Page 386 CHAPTER 9 FUNCTIONS AND MODELING......Page 426 CHAPTER 10 GEOMETRIC TRANSFORMATIONS......Page 480 CHAPTER 11 TRIGONOMETRY......Page 542 CHAPTER 12 DATA ANALYSIS AND PROBABILITY......Page 628 CHAPTER 13 INTRODUCTION TO NON-EUCLIDEAN GEOMETRY......Page 706 CHAPTER 14 THREE PROBLEMS OF ANTIQUITY......Page 734 BIBLIOGRAPHY......Page 750 APPENDIX......Page 752 INDEX......Page 758 This clear, interactive, learner-centered text and resource will help pre-service and in-service secondary mathematics teachers gain the deep mathematical insight they need to teach their students in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining Bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. This title helps pre-service and in-service teachers gain the mathematical insight they need to engage their students in learning mathematics in a multifaceted way.