PROBLEM EXPLORATION

FRANK CASDEN

The topics to be included are:

The problem solving strategies of

Draw a picture/make a diagram

Make a systematic list

Eliminate possibilities

Find a pattern

Solve a simpler related problem

Guess and check

Act it out/make a physical model

Mathematical puzzles

The course focuses on two **skill areas**: the mastery of
the problem solving strategies listed, and communication of mathematical reasoning
both orally and in written form.

There are several forms to the **assessment** of students
work in this class. Students are required to do all of their work in a notebook
which is checked every day. Comments are made on the students'progress on the
"practice problems". Students are also required to make regular presentations
on the board to the whole class. A Problem of the Week is assigned as homework.
After each strategy is practiced in class, students work on a Problem Set which
is then rated on a scale from "Beginner", "Apprentice", Professional", to "Master."
There is a final exam at the end of each cycle which is rated in the same manner
as the Problem Sets. The ratings, for which a rubric exists, measures degrees
of mastery of the problem solb n ving strategies as well as the explanations
of their mathematical thinking.

**Instructional Materials**:

*Problem Solving Strategies - Crossing the River with Dogs,
*Ted Herr and Ken Johnson, Key Curriculum Press

*Vermont Mathematics Portfolio Committee*: Exemplars

*Thinking about Thinking*, Ira Ewen, New York City Bd.
of Educ.

Shell Centre for Mathematical Education

The** Instructional Strategies** used are a combination
of teacher centered instruction, Cooperative group work, and whole class discussion.
The majority of the time students will be working in small cooperative groups
to explore the problem solving strategies as well as serve as an audience to
discuss each members written explanation of their work.