MA 351 Course Description

MA351 MODELS AND PROBLEM SOLVING FOR THE ELEMENTARY SCHOOL TEACHER (4 Cr.)

COURSE DESCRIPTION

Prerequisite: MA250 AND MA231 with a "C" or better.

Offered: Winter

NOTE: May not be applied toward a non-teaching major or minor in mathematics.

Introduction
This course focuses on problem solving from these perspectives: an analysis of problem solving approaches, problem solving in the k-12 curriculum, and the teaching/learning of problem solving skills and strategies. The problems involve content and skills from all areas of the mathematics curriculum, and they include applications in daily living, the business world, the sciences, logic and recreational mathematics.

Goals/Purpose
MA351 is designed to analyze the problem solving process, to strengthen the mathematics background of elementary mathematics majors and minors, and to further develop their ability to model and solve problems.

Objectives

The students will:

  1. Identify the components of the problem solving process (ala Polya).
  2. Use a variety of strategies and models to solve mathematical problems.
  3. Verbalize to their peers and instructor the struggles and the eventual solution of a problem.
  4. Write a coherent explanation of their solution of a problem.
  5. Hypothesize and generalize through an inductive process.
  6. Use deductive reasoning to solve problems and to create proofs of hypotheses
  7. Work as a member of a team to solve problems.
  8. Analyze the teaching and learning of problem solving skills.
  9. Investigate sources and problems appropriate for middle and elementary school students.
  10. Identify ways to promote the development of problem solving skills in the classroom.

Course Content

  1. Analyzing the Problem Solving Process
    1. Understanding the problem
    2. Developing a plan and selecting a strategy
    3. Carrying out the plan
    4. Looking back at solution and method
  2. Strategies, with examples
    1. Guess and check
    2. Create a table
    3. Look for a pattern
    4. Working backwards
    5. Draw a picture
    6. Write an equation
    7. Model it concretely; simulations
  3. Categories of problems
    1. Arithmetic and number theory
    2. Rational numbers: fractions, decimals, percent, direct and inverse variation
    3. Algebra and analytic geometry
    4. Geometry and measurement
    5. Trigonometry
    6. Recreational puzzles and challenges
    7. Logic and deductive reasoning
  4. Sources and resources
    1. NCTM STANDARDS 2000
    2. MICHIGAN FRAMEWORK and MI-CLIMB
    3. Commercial materials
    4. Professional journals
    5. Educational web sites