Teaching and Learning High School Mathematics

Too many high school students, faced with mathematics in courses at the level of algebra and beyond, find themselves struggling with abstract concepts and unwilling to pursue further study of mathematics. When students curtail their course taking in mathematics, they may be impacting their college and career options. Thus, high school mathematics teachers have the responsibility to help students recognize the value and importance of mathematics while also designing instruction that makes mathematics accessible to all students. Ball and Bass (2000), as well as other mathematics educators, have recognized that mathematics teachers not only need to know mathematics content and mathematics pedagogy (i.e., teaching strategies) but they also need to know how these ideas are integrated. This mathematical knowledge for teaching is the knowledge that teachers of mathematics need and it differs from the knowledge that research or applied mathematicians must know. This text is designed to provide teachers with insights into this mathematical knowledge for teaching. Teaching and Learning High School Mathematics is likely different from many other texts that you have used. It integrates both content and pedagogy to help you develop and build your own understanding of teaching. The text is designed to help you develop “deep conceptual understanding of fundamental mathematics” (Ma 1999) so that you are able to approach mathematics from multiple perspectives with many tools. Such flexibility in teaching is essential if teachers are to help all students become mathematically proficient. Throughout this book, you are encouraged to work in cooperative teams. This strategy is designed to help you develop a mathematics learning community and build a professional network that will be a valuable resource during your professional career. Hopefully, you will experience the benefits of engaging in rich mathematical discussions with peers and consider how to encourage such learning environments in your own classrooms. Lesson planning is another element pervasive throughout this text. To help teachers plan for effective student-centered lessons, the Question Response Support (QRS) Guide is introduced in Lesson 1.1 and used throughout the remainder of the lessons. The QRS Guide is a tool on which teachers may record tasks or questions (Q) for students, expected and observed student responses (R), and teacher support (S) in the form of additional “just enough” questions to support students in their progress on the task. In each unit, teachers expand their repertoire of teaching and learning elements and strategies and incorporate these elements as they plan additional lesson segments. In Unit 4 lesson planning is formally introduced as teachers put together elements from previous units into complete, cohesive lesson plans.  

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 Conundrum 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.