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Pair Problem Solving

Ruth Freeman

Description

Pair Problem Solving, advocated and described most clearly by Arthur Whimbey & Jack Lochhead (1982), is a form of active learning which attempts to improve problem solving ability. Its goal is to get inside the mind of a problem solver, to learn the process of problem solving by understanding each step. Its main premise is to have a set of two participants, a problem solver and a listener, work through a problem together. The problem solver solves the problem step by step and out loud, while the listener follows along, documenting the process. After the pair completes the problem, they reverse roles so the problem solver now becomes the listener, and vice versa.

Role of the Problem Solver

The problem solver solves the problem (or attempts to solve the problem), all the while vocalizing exactly the steps and thought processes going through his/her head. It is important that the problem solver not leave out any steps, even the most trivial. Verbal mention of all the steps involved is crucial to the understanding of the process.

Role of the Listener

The listener verifies the steps of the problem solver, ensures that the problem solver mentions ALL the steps, and asks for clarification of any steps that were not understood. The listener must not solve the problem on his/her own, but must instead follow the problem solver's process. If the listener notes any errors, he/she should remain silent at first, to see if the problem solver catches the error and corrects it. If the problem solver does not notice or realize the error, the listener must point it out, but must allow the problem solver to correct the error alone.

Application

This strategy is particularly useful in a mathematics or scientific environment, but can be used in any course which requires step by step solutions to problems. It is especially useful in solving math word problems, because generally more problem solving techniques are required (Whimbey, 1982). However, its value in solving difficult calculations or equations is also recognized for those students who have not yet become proficient in a particular concept.

To introduce this strategy in a classroom environment, the instructor could be the first "problem solver", and the class as a whole would be the "listener". In this way the instructor could model for the class the procedure (Hartman, 2007), until the class becomes comfortable with the process on its own.

Major Concepts

Many active learning strategies may seem childish to adult learners. This strategy will be effective with adult students because it is a non-childish way to incorporate active learning in the classroom. The older student is more likely to be able to verbalize the thought processes going through his/her mind than a child would be. This strategy involves active participation by the student which directs the classroom time away from pure lecture. It keeps students engaged in the learning process in a relatively painless way.

Relationship to Teaching Perspective

This strategy could be used when teaching from either the Apprenticeship or Developmental Perspectives as developed by Pratt & Associates (1998/2005).

From the Apprenticeship Perspective, the Teacher would be the problem solver, and the Learner would be the listener. The Teacher would, in extreme detail, relate the steps of whatever task was at hand, while the Learner would carefully note the steps, ask questions about any step which was unclear, and ensure the Instructor did not leave out any steps.

Certainly, though, a more appropriate perspective would be Developmental, with its emphasis on good learning as opposed to good teaching (Pratt, 1998/2005). Teachers from the developmental perspective seek to enhance the learners' thinking skills, which is also the main focus of pair problem solving.

Benefits

The main intent of this strategy is to allow the listener to learn problem solving by seeing the process in action. The strategy also benefits the problem solver by forcing him/her to slow down, and truly analyze why he/she would take that next step. As both listener and problem solver investigate more deeply the reasons for the steps they take, they come to a better understanding of the problem solving process and how to apply it in the future.

Drawbacks and Cautions

As with any new process, students may be reluctant at first to try this strategy. Students, especially many adults, are used to and comfortable with the "old" ways of learning - lectures and note taking. They may fight any attempts at active learning (Perry, 1970, as described in Lochhead, 1985).

Students who are not competent at problem solving may fight the idea for they feel they are being forced to display their lack of abilities to their peers.

Final Thoughts

Unfortunately, I have not yet had a chance to try out this strategy in my own Developmental Mathematics classes. I plan to test its effectiveness soon. My personal concerns with implementing the strategy are: What is the best way to pair up the students? Should the most advanced be placed with the least advanced or should they be paired somewhat closer in their abilities? Do I have enough students who can successfully problem solve in order to display their talents for others?

In math classes, solving word problems always seems to be the most dreaded task of struggling students. There is an ingrained fear of failure. I hope to utilize this pair problem solving strategy to show my students that word problems (and all math concepts at this level) are solvable, if a student knows where to begin.

References

Pratt, D., & Associates. (1998/2005). Five perspectives on teaching in adult and higher education. Malabar, FL: Krieger Publishing Company.

Hartman, H. Improving students' problem solving skills, Retrieved February 20, 2007, from http://www.ccny.cuny.edu/ctl/handbook/hartman.html

Lochhead, J. (1985). Teaching analytic reasoning skills through pair problem solving. In J. Segal, S. Chipman, & R. Glaser (Eds.), Thinking and learning skills: Relating instruction to research, (Volume 1, pp. 109-131). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Whimbey, A. & Lochhead, J. (1984). Beyond problem-solving and comprehension. Philadelphia, Pennsylvania: Franklin Institute Press.

Whimbey, A. & Lochhead, J. (1982). Problem-solving and comprehension. [Electronic version] Philadelphia, Pennsylvania: Franklin Institute Press.