Teaching Mathematics in Secondary and Middle School : An Interactive Approach

by Cangelosi, James S.

• ISBN13: 9780134392332
• ISBN10: 0134392337
• Edition: 3rd
• Format: Paperback
• Copyright: 2003-01-01
• Publisher: Prentice Hall

Summary

For senior-level and graduate courses in Methods of Teaching Mathematics for Secondary and Middle School Teachers. Focused on all the complex aspects of teaching mathematics in today's classroom and the most current NCTM recommendations and standards this text shows students how to creatively incorporate the Standards into their teaching along with inquiry instructional strategies (for leading pupils to do meaningful mathematics) and direct strategies (for developing mathematical skills). Interactive in approach, it includes an abundance of illustrative examples, numerous cases, one expansive case study that follows a mathematics teacher through his first year in the profession, cooperative learning activities, field-based activities, and transitional activities.

Table of Contents

(NOTE: Each chapter begins with Goals and Objectives and concludes with Transitional Activities.)
1. Ti(S) = L: A Set of Messy Functions.

A tidy set of functions (fi. Messy functions. Teaching as a set of functions (Ti). Students as an independent variable (Domain of Ti). Student learning as a dependent variable (Range of Ti). The mystification of mathematics. Demystifying mathematics. Monitoring your own attitudes.

2. Developing Mathematics Curricula.

A Curriculum. Two views. Real-life problems. The National Council of Teachers of Mathematics' (NCTM) Standards. Mathematics curricula outcomes. Mathematics courses. Teaching units. Designing, organizing, and conducting courses and teaching units.

3. Designing Mathematics Courses and Teaching Units.

Requisites for learning to apply mathematics to real-life problem-solving. Approaches to designing courses. Planning teaching units. Lesson planning and daily planning.

4. Leading Students to Construct Concepts and Discover Relationships.

Concept. Inductive reasoning. Construct-a-concept objectives. Lessons for construct-a-concept objectives. Indicators of achievement of construct-a-concept objectives. Discoverable relationships. Discover-a-relationship objectives. Lessons for discover-a-relationship objectives. Indicators of achievement of discover-a-relationship objectives.

5. Leading Students to Develop Knowledge, Comprehension, and Algorithmic Skills.

Mathematical information to be remembered. The acquisition and retention of information. Simple-knowledge objectives. Lessons for simple-knowledge objectives. Indicators of achievement of simple-knowledge objectives. The language of mathematics. Comprehension objectives. Lessons for comprehension objectives. Indicators of achievement of comprehension objectives. Algorithms. Algorithmic-skill objectives. Lessons for algorithmic-skill objectives. Indicators of achievement of algorithmic-skill objectives.

6. Leading Students to Solve Problems, Be Creative with Mathematics, and Willingly Do Mathematics.

Deductive reasoning for problem solving. Application objectives. Lessons for application objectives. Indicators of achievement of application objectives. Doing mathematics creatively. Creativity objectives. Lessons for creativity objectives. Indicators of achievement of creativity objectives. Influencing students' attitudes about mathematics. Indicators of achievement of affective objectives.

7. Resources and Technology for Teaching Mathematics.

Selection and use of textbooks. Sources of ideas on mathematics and teaching mathematics. Hands-on manipulatives and concrete models. Calculators. Computer technology. Video and audio equipment. Measuring instruments. The classroom arrangement. Extending the classroom beyond the walls of the school.

8. Gaining Students' Cooperation in an Environment Conducive to Doing Mathematics.

A well-designed lesson gone awry. A teacher's most perplexing problem. Allocated and transition times. Student behaviors. Teaching students to be on-task. Establishing a favorable climate for learning mathematics. Communicating effectively. Establishing rules of conduct and classroom procedures. Dealing with off-task behaviors. Conducting engaging learning activities.

9. Engaging Students in Learning Activities.

Ideas for giving directions. Variety of learning activities. Ideas for large-group presentations. Responding to students' questions. Asking students questions. Ideas for cooperative learning sessions. Ideas for independent work sessions. Ideas for homework assignments.

10. Monitoring Student Progress and Evaluating Achievement.

Difficult decisions. Common malpractice. Research-based practice. Measurements. Evaluations. Measurement validity. Measurement usability. Types of tests. Designing teacher-produced tests. Designing items. Using test results. Alternative and authentic assessments. Individualized student portfolios.

11. Theory into Practice: Casey Rudd, First-Year Mathematics Teacher.

Casey Rudd and his first teaching position. Organizing for the year. The beginning of an eventful school year. Sample Algebra I unit. Sample geometry unit. Sample consumer mathematics teaching unit. Sample precalculus unit. Inservice opportunities and the NCTM Conference. Winding down the school year and anticipating next year.

12. A Profession in Transition.

A mixed history. The NCTM-Standards driven reformation. Your role.

Appendix A.

Excerpt from Mathematics Core Curriculum: Grades 7-12 Relative to Teaching Elementary Algebra.

Appendix B.

Example of an Article from Mathematics Teacher: “An Application of Quadratic Equations to Baseball.”

Appendix C.

List of Standards from NCTM's Curriculum and Evaluation Standards for School Mathematics.

Appendix D.

Example of an Article from Mathematics Teaching in the Middle School, “Graphing Calculators Aren't Just for High School Students.”

Appendix E.

Example of an Article from Teaching Children Mathematics, “Telling Tales: Creating Graphs Using Multicultural Literature.”