Instructor: Phyllis Eilenfeldt
CourseTitle: Introduction to Problem Solving
Subject Area: Mathematics

Textbook: Problem Solving Strategies: Crossing the River with Dogs, Key Curriculum Press, Berkeley, California, 1994.


The focus of this course is to engage students working individually and in small groups in a variety of problem solving strategies such as those outlined in the textbook. Among those presented will be working backwards to solve problems, eliminating possible solutions, making charts and diagrams, and finally developing more sophisticated algebraic responses to given situations. Students will be asked to work cooperatively on many projects, and to present solutions to their classmates. A journal of reflections and solutions to problems will be kept by each student in order to document the development of language skills necessary to the comprehension and explanation of mathematics used in class.

Skills developed during the semester will include:

1. Translation of work statements into algebraic statements.

2. Using diagrams and charts to develop solutions to the Diaphantine word problems and other word problems.

3. Using Cuisenaire rods to develop visual and spatial relationships involved in area and perimeter.

4. Using pattern blocks in order to establish geometric problem solving strategies which are then related to elementary equations.

5. Developing a sense of pattern recognition in numerical sequences.

6. Constructing the patterns shown in Fibonacci numbers by studying leaves, pinecones and other natural phenomena in order to develop numerical sequences, the Golden ratio, and properties of number patterns.

How will your math grade be determined?

Students in Phyllis' Geometry and Problem Solving classes will be graded on the following system:

1. Class participation/cooperation: 40% This part of the grade includes regular attendance, behaving appropriately in class, and taking an interest in learning through all classroom activities. Students who raise questions and help in group presentations effectively will benefit from expressing their thoughts and ideas.

2. Test, quizzes, homework 30% Students need to complete homework on time. Homework which is one day late will receive half credit. After that, only partial credit will be given for homework. We will sometimes have quizzes on problem solving covering material presented in class.

3. Presentations 30% Students will be expected to present solutions to problems either as part of a group or individually. While this may be a new skill for some, we are willing to help students practice standing before a group to talk about math and particular problems. This is not used to embarrass students in any way, but is part of a new trend in passing the Regents in New York State.