Teaching and Learning High School Mathematics

A perfect resource for high school mathematics teachers, this book helps them develop or refine their own teaching philosophy. They’ll learn how to create a supportive classroom environment in which their students think together, take intellectual risks, and debate ideas. They’ll gain a better understanding about the importance of cooperative learning strategies through immersion. And they’ll engage in logic and reasoning. Puzzles and activities are presented to bring the material to life as well. All of this will help high school mathematics bring the excitement of the subject into the classroom.

Table of Contents:
Course Introduction                         Mathematics Education: Where Do I Stand?       Unit One. Encouraging Communication in Mathematics Classrooms       (Mathematics Strand: Logic and Reasoning) Unit One Team-Builder: Carpet Square Maze      Preparing to Observe Mathematics Classrooms: Focus on Equity               Listening to Students Reason About Mathematics   1.1    Developing Questioning Strategies: Conjecturing and Reasoning                                 1.2   Exploring Mathematical Concepts Cooperatively: Reasoning with Conditional Statements                                                                                                 1.3   Using Representations to Investigate Mathematics: Reasoning with Conjunctions, Disjunctions, and Negations                                                                   1.4    Learning from Students: Valid and Invalid Arguments                                                1.5    Summarizing Classroom Observations and Listening to Students: Focus on Equity                                                                                                             Synthesizing Unit One                                                                                                            Unit One Investigation: Carpet Square Mazes   Unit Two. High School Students and How They Learn                                                    (Mathematics Strands: Geometry and Measurement) Unit Two Team-Builder: Transformed Snowflakes                                                               Preparing to Observe Mathematics Classrooms: Focus on Learning                                      Listening to Students Reason About Geometry                                                                     Understanding Geometry Learning: Coordinate Geometry                                                   2.2  Building Conceptual Understanding: Congruence and Similarity                                 2.3    Learning Mathematics through Multiple Perspectives: Quadrilaterals and Constructions        2.4    Using Physical Tools and Technology: Circles                                                              2.5    Tasks with High Cognitive Demand: Measurement in the Plane and in Space                                       2.6    Doing Mathematics: Axiomatic Systems                                                                      2.7    Summarizing Classroom Observations and Listening to Students                                Synthesizing Unit Two                       Unit Two Investigation: Transformations                                                                               Unit Three. Planning for Instruction (Mathematics Strands: Algebra and Functions) Unit Three Team-Builder: Find Your Function Family Preparing to Observe Mathematics Classrooms: Focus on Curriculum and Technology                                                                                                                                Listening to Students Reason about Functions                                                                      3.1    Building on Students' Knowledge and Experiences: Understanding Variables and Linear Functions                                                                                     3.2    Thinking about Learning Outcomes: Exponential Functions                                        3.3    Active Learning: Modeling Data Through Experiments                                               3.4    Teaching with Technology: Geometry of Functions                                                     3.5    Increasing Challenge or Accessibility of Problems: Polynomial Functions                   3.6    Accommodating Different Learning Styles: Rational Functions                                  3.7   Summarizing Observations and Listening to Students                                                  Synthesizing Unit  Three                                                                                                         Unit Three Investigation: Families of Functions Unit Four. Lesson Planning                                                                                                 (Mathematics Strands: Data Analysis and Probability) Unit Four Team-Builder: A Dream Team in Hockey                                                             Preparing to Observe Mathematics Classrooms: Focus on Teaching                                      Listening to Students Reason about Data Analysis and Probability                                      4.1    Planning a Lesson Launch and Explore: Data Analysis                                                  4.2   Planning a Lesson Share and Summarize: Probability                                                   4.3    Blending Direct Instruction into a Lesson: Variability and Distributions                     4.4    Planning for Alternative Schedules: Statistical Decision Making                                 4.5    Summarizing Observations and Listening to Students                                                  Synthesizing Unit Four                                                                                                           Unit Four Investigation: Build Your Own Dream Team                                                                      Unit Five. Assessment of Students' Learning                                                                     (Mathematics Strand: Precalculus) Unit Five Team-Builder:  Conic Conundrums                                                                     Preparing to Observe Mathematics Classrooms: Focus on Assessment                                 Listening to Students Reason about Precalculus                                                                      5.1   Daily Assessments: Limits                                                                                             5.2    Rubrics: Rates of Change                                                                                              5.3    Designing and Aligning Tests with Instruction                                                             5.4    Alternative Assessments: Accumulations                                                                      5.5    Summarizing Observations and Listening to Students                                                  Synthesizing Unit Five                                                                                                           Unit Five Investigation: Conic Sections Unit Six. Collaborating with Educational Partners                                                           Listening to Educational Partners about Issues in Mathematics Education                           6.1    Evaluating Curriculum Materials                                                                                     6.2   Coordinating Curricula Beyond the Classroom                                                             6.3    Continued Professional Development                                                                           6.4    Summarizing Interviews on Educational Issues                                                                          Synthesizing Unit Six

About the Author :
Dr. Charlene Beckmann is a professor of Mathematics at Grand Valley State University. Her research interests include: assessment, cooperative learning, real life uses of mathematics, functions, games, literature and mathematics, technology, how conceptual understanding builds their ability to understand and write proofs.