Teaching and Learning High School Mathematics

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.

• 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 MazePreparing to Observe Mathematics Classrooms: Focus on EquityListening to Students Reason About Mathematics1.1 Developing Questioning Strategies: Conjecturing and Reasoning1.2 Exploring Mathematical Concepts Cooperatively: Reasoning with Conditional Statements1.3 Using Representations to Investigate Mathematics: Reasoning with Conjunctions, Disjunctions, and Negations1.4 Learning from Students: Valid and Invalid Arguments1.5  Summarizing Classroom Observations and Listening to Students: Focus on Equity Synthesizing Unit One Unit One Investigation: Carpet Square MazesUnit 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 Similarity2.3 Learning Mathematics through Multiple Perspectives: Quadrilaterals and Constructions2.4 Using Physical Tools and Technology: Circles2.5 Tasks with High Cognitive Demand: Measurement in the Plane and in Space2.6 Doing Mathematics: Axiomatic Systems2.7 Summarizing Classroom Observations and Listening to Students Synthesizing Unit TwoUnit Two Investigation: TransformationsUnit Three. Planning for Instruction(Mathematics Strands: Algebra and Functions)Unit Three Team-Builder: Find Your Function FamilyPreparing to Observe Mathematics Classrooms: Focus on Curriculum and Technology          Listening to Students Reason about Functions3.1 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 Functions3.5 Increasing Challenge or Accessibility of Problems: Polynomial Functions3.6 Accommodating Different Learning Styles: Rational Functions3.7 Summarizing Observations and Listening to Students                          Synthesizing Unit  Three                                                                                Unit Three Investigation: Families of FunctionsUnit Four. Lesson Planning(Mathematics Strands: Data Analysis and Probability)Unit Four Team-Builder: A Dream Team in HockeyPreparing to Observe Mathematics Classrooms: Focus on TeachingListening to Students Reason about Data Analysis and Probability4.1 Planning a Lesson Launch and Explore: Data Analysis4.2 Planning a Lesson Share and Summarize: Probability4.3 Blending Direct Instruction into a Lesson: Variability and Distributions4.4 Planning for Alternative Schedules: Statistical Decision Making4.5 Summarizing Observations and Listening to Students               Synthesizing Unit Four                 Unit Four Investigation: Build Your Own Dream TeamUnit Five. Assessment of Students' Learning  (Mathematics Strand: Precalculus)Unit Five Team-Builder: Conic ConundrumPreparing to Observe Mathematics Classrooms:Focus on Assessment          Listening to Students Reason about Precalculus5.1 Daily Assessments: Limits                                                     5.2 Rubrics: Rates of Change5.3 Designing and Aligning Tests with Instruction5.4 Alternative Assessments: Accumulations5.5 Summarizing Observations and Listening to Students Synthesizing Unit FiveUnit Five Investigation: Conic SectionsUnit Six. Collaborating with Educational PartnersListening to Educational Partners about Issues in Mathematics Education6.1 Evaluating Curriculum Materials6.2 Coordinating Curricula Beyond the Classroom6.3 Continued Professional Development        6.4 Summarizing Interviews on Educational IssuesSynthesizing Unit Six