Teaching and Learning Middle Grades Mathematics
June 2008, ©2004
Teaching and Learning Middle Grades Mathematics is the ideal text for future teachers who are completing their pre-service instruction. Through readings, lessons, sample middle grades exercises, and more, future teachers learn to address the teaching and learning of algebraic and geometric thinking at the level appropriate for middle grades students. The lessons in this text follow a popular collaborative teaching method used in middle schools called Launch, Explore, Share and Summarize that involves very little lecturing, a lot of group work, and class discussions. Teaching and Learning Middle Grades Mathematics will serve as a life long resources to students, as each lesson is filled with student pages which are worksheets that can be modified for use in actual middle grades classrooms. The text comes packaged with a CD-ROM that will be a valuable resource, containing professional readings that correlate directly to the lessons in the text.
Preface and Acknowledgments.
Mathematics Education: Where Do I Stand?
Getting to Know Colleagues: Uniquely Us.
Unit One: A Learning Community.
Mathematics Strand: Reasoning with Patterns and Algebra.
Unit One Investigation: Figurate Numbers.
Preparing to Interview Students about Reasoning with Patterns.
1.1. Problem Solving: Careful Counting.
1.2. Reasoning and Proof: Patterns and Multiplication.
1.3. Generalizing from Patterns: The Concept of Variable.
1.4. Using Experiments: Exploring Graphs and Lines.
1.5. Learning with Materials: Integers and Equations.
1.6. Using Contexts: Functions.
1.7. Using Interviews to Understand Students' Reasoning with Patterns.
Synthesizing Unit One.
Unit Two: The Learning of Mathematics.
Mathematics Strand: Rational Numbers and their Uses.
Unit Two Investigation: Four Fours.
Preparing to Interview Students about Proportional Reasoning.
2.1. Using Multiple Representations: Rational Numbers.
2.2. Using Learning Theory: Fractions, Decimals, and Percents.
2.3. Developing Meanings of Operations: Addition and Subtraction.
2.4. Developing Meanings of Operations: Multiplication and Division.
2.5. Analyzing Student Thinking: Proportional Reasoning.
2.6. Using Interviews to Understand Students' Proportional Reasoning.
Synthesizing Unit Two.
Unit Three: Planning and Instruction.
Mathematics Strand: Geometry, Measurement, and Transformations.
Unit Three Investigation: Historical Formulas.
Preparing to Interview Students about Perimeter and Area.
3.1. Identifying Worthwhile Mathematical Tasks: Measurement Formulas.
3.2. Lesson Planning: Proportions among Measures in Similar Figures.
3.3. Guided Discovery: Quadrilaterals.
3.4. Open-Ended Exploration: Tessellations.
3.5. Integrating Direct Instruction with Guided Discovery: Transformations.
3.6. Effective Classroom Discourse: The Pythagorean Theorem.
3.7. Using Interviews to Plan Instruction on Perimeter and Area.
Synthesizing Unit Three.
Unit Four: Assessment.
Mathematics Strand: Data Analysis and Probability.
Unit Four Investigation: Pascal's Triangle.
Preparing to Interview Students about Their Views on Assessment.
4.1. Multiple Uses of Assessment: Categorical and Discrete Data.
4.2. Assessment That Highlights Students' Thinking: Continuous Data.
4.3. Managing and Grading Every Day: Introduction to Probability.
4.4. Rubrics and Their Uses: Systematic Counts for Probabilities.
4.5. Issues in Developing and Using Tests.
4.6. Using Interviews to Develop a Classroom Assessment Plan.
Synthesizing Unit Four.
Unit Five: Collaborating with Educational Partners.
Preparing to Interview Educational Partners.
5.1. Curriculum Integration.
5.2. Facilitating Educational Growth.
5.3. Evaluating Curriculum Materials.
5.4. Using Interviews to Prepare for Educational Collaboration.
Synthesizing Unit Five.
References and Permissions.
- Consists of five units that correlate to the NCTM Principles and Standards, focusing on one mathematics strand, and one principle.
Each lesson is structured around Launch, Explore, Share and Summarize, a collaborative teaching method.
Lessons end with Developing Mathematical Pedagogy and Deepening Mathematics Understanding questions that ask students to reflect on their own learning of mathematics.
Icons appear (one for portfolio and one for field work) that indicate questions that will help students start building their professional portfolio or that are appropriate for field work.
Units begin and end with interviews that are to be conducted with middle grades students or teachers.
CD-ROM with readings and all of the student pages (from the text) in Microsoft Word so that students can manipulate/alter them for their own courses. Other valuable resources appear as well including black line masters.