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Teaching and Learning High School Mathematics

Teaching and Learning High School Mathematics

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

ISBN: 978-0-470-45450-3

Nov 2009

560 pages

In Stock



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.


Related Resources

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

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