Discussion, Writing, and Problem Solving

Davida  Fischman, California State University San Bernardino

ABSTRACT: A major problem for many of our students is their difficulty in translating a problem stated in paragraph form to a specific computational task. It is particularly important to address this difficulty for students who are about to become teachers, of course, and so this issue is a crucial component in our Liberal Studies curriculum, in problem solving classes. A number of methods to help students learn to analyze a problem, to understand it, and to communicate this understanding clearly are discussed here: 1. Structured group discussions: A necessary preliminary to clear writing is clear thinking, so we have students communicate pieces of the problem to one another orally only, and then reformulate and rewrite the problem before attempting to solve it. 2. Peer reading and critique of work: The goal is for one student to understand another's solution completely from the write-up without additional comments from the student's write-up. This helps avoid the expectation that the teacher be a mind reader. 3. Presentations to the class: A larger project that brings together the components of problem solving, oral and written communication, and clear, creative presentation, that include self-evaluation and a written, structured summary of the presentation.

A major problem for many of our students is their difficulty in translating a problem stated in paragraph form to a specific computational task. It is particularly important to address this difficulty for students who are about to become teachers, of course, and so this issue is a crucial component in our Liberal Studies curriculum, in problem solving classes.

We employ a number of methods to help students learn to analyze a problem, understand it, and to communicate this understanding clearly. A necessary preliminary to clear writing is clear thinking, and often people find it helpful to have a stimulus to clarify their thoughts. A useful stimulus is questions from other students – so classroom discussions in small groups are a fixed part of every class in problem solving. These should be structured at least some of the time, in order to make them more useful to the students. One way to structure a preliminary discussion of a mathematical problem: Give each student only one piece of the problem, and have the students communicate their pieces to the group only orally. Then have the group rewrite the problem together, as a group. Ask them to show how their rewritten problem gives more insight on the problem. Only then ask them to begin thinking about a solution.

When the instructor tells a student that his written solution is unclear, the student often answers “But you know what I mean.” An activity we use to raise awareness of the need for clarity is an exchange of written solutions among students. A particular problem is chosen for students to prepare written solutions. Each student then reads some one else’s work, and tries to understand it without discussion. The questions that arise here are very helpful to the students in analyzing their work and improving it.

A larger project that brings together the components of problem solving, oral and written communication, and clear, creative presentation is one in which each students prepares a problem for presentation in class. These presentations must be correct mathematically, clear, concise, and creative. They are followed by a write-up that includes an honest and useful evaluation.

Samples of student work will be presented to demonstrate these activities and student’s progress in analyzing and communicating mathematics.