Teaching and Learning High School Mathematics

by Beckmann, Charlene E.; Thompson, Denisse R.; Rubenstein , Rheta N.

• ISBN13: 9780470454503
• ISBN10: 0470454504
• Edition: 1st
• Format: Paperback
• Copyright: 2009-11-02
• Publisher: Wiley

Summary

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.

Author Biography

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.

Table of Contents

Course Introduction

Mathematics Education: Where Do I Stand?

Encouraging Communication in Mathematics Classrooms (Mathematics Strand: Logic and Reasoning)

Unit 1 Team-Builder: Carpet Square Maze

Preparing to Observe Mathematics Classrooms: Focus on Equity

Listening to Students Reason About Mathematics

Developing Questioning Strategies: Conjecturing and Reasoning

Exploring Mathematical Concepts Cooperatively: Reasoning with

Conditional Statements

Using Representations to Investigate Mathematics: Reasoning with

Conjunctions, Disjunctions, and Negations

Learning from Students: Valid and Invalid Arguments

Summarizing Classroom Observations and Listening to Students:

Focus on Equity

Synthesizing Unit One

Unit 1 Investigation: Carpet Square Mazes

High School Students and How They Learn (Mathematics Strands: Geometry and Measurement)

Unit 2 Team-Builder: Transformed Snowflakes

Preparing to Observe Mathematics Classrooms: Focus on Learning

Listening to Students Reason About Geometry

Understanding Geometry Learning: Coordinate Geometry

Building Conceptual Understanding: Congruence and Similarity

Learning Mathematics through Multiple Perspectives: Quadrilaterals and Constructions

Using Physical Tools and Technology: Circles

Tasks with High Cognitive Demand: Measurement in the Plane and in Space

Doing Mathematics: Axiomatic Systems

Summarizing Classroom Observations and Listening to Students

Synthesizing Unit Two

Unit 2 Investigation: Transformations

Planning for Instruction (Mathematics Strands: Algebra and Functions)

Unit 3 Team-Builder: Find Your Function Family

Preparing to Observe Mathematics Classrooms: Focus on Curriculum and Technology

Listening to Students Reason about Functions

Building on Students' Knowledge and Experiences: Understanding

Variables and Linear Functions

Thinking about Learning Outcomes: Exponential Functions

Active Learning: Modeling Data Through Experiments

Teaching with Technology: Geometry of Functions

Increasing Challenge or Accessibility of Problems: Polynomial Functions

Accommodating Different Learning Styles: Rational Functions

Summarizing Observations and Listening to Students

Synthesizing Unit Three

Unit 3 Investigation: Families of Functions

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

Planning a Lesson Launch and Explore: Data Analysis

Planning a Lesson Share and Summarize: Probability

Blending Direct Instruction into a Lesson: Variability and Distributions

Planning for Alternative Schedules: Statistical Decision Making

Summarizing Observations and Listening to Students

Synthesizing Unit Four

Unit 4 Investigation: Build Your Own Dream Team

Assessment of Students' Learning (Mathematics Strand: Precalculus)

Unit 5 Team-Builder: Conic Conundrums

Preparing to Observe Mathematics Classrooms:

Focus on Assessment

Listening to Students Reason about Precalculus

Daily Assessments: Limits

Rubrics: Rates of Change

Designing and Aligning Tests with Instruction

Alternative Assessments: Accumulations

Summarizing Observations and Listening to Students

Synthesizing Unit Five

Unit 5 Investigation: Conic Sections

Collaborating with Educational Partners

Listening to Educational Partners about Issues in Mathematics Education

Evaluating Curriculum Materials

Coordinating Curricula Beyond the Classroom

Continued Professional Development

Summarizing Interviews on Educational Issues

Synthesizing Unit Six

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