XIV. How To Use Pair Problem Solving
In this book, we have used pair problem solving to develop the basic analytical reasoning skills essential for success on standardized tests and throughout school. In a sequel, Beyond Problem Solving and Comprehension (Whimbey & Lochhead, 1984), we provide a thorough preparation for the quantitative sections of the SAT, as well as for the GRE and the professional examinations. But pair problem solving has a much wider array of applications. In this chapter we consider how teachers, students, parents, and managers can use pair problem solving in many of their normal activities.
Teachers
Pair problem solving can be a lively alternative to modes of teaching you normally employ. Only in rare circumstances is it appropriate as the primary method of instruction, but it is extremely useful whenever there is a need to reach a deeper understanding of some form of analysis. A good time for pair problem solving is whenever students are having more difficulty than you think they should. It might be when you first introduce word problems involving percentage calculations or when you assign the first Russian novel in a literature class. Not only will pair problem solving encourage students to think carefully about what they are doing, it will also provide you with an opportunity to listen in and possibly discover the cause of the most serious problems.
All you need to conduct a pair problem-solving class is a few short problems and a brief statement of the rules. The first time your class is introduced to pair problem solving it is best to keep the problems easy. This allows students to concentrate on the talking-listening process and not get too caught up in the issues of reaching a correct solution. We recommend that you use problems from an appropriate section of Problem Solving and Comprehension. These problems have been proven effective starters with groups ranging from elementary school children to college professors. Once your class is comfortable with pair problem solving you can use it in a wide variety of situations, and you may find it useful to modify the rules to encourage many different kinds of group work. We consider a few of the options in the sections here.
Many different group structures can be built out of the practice and experience gained in pair problem solving. One of the most commonly used approaches is the triad in which the third member of the group acts as an observer-recorder or, alternatively, a referee. This person’s function is to watch the other two and comment on how well they are staying in their roles. Teachers who use pair problem solving at the elementary level often find that the third member is essential in order to keep the problem solver and listener aware of their own actions. For some children, it is only through the experience of watching other listeners that they can learn to control their own listening behavior. (Problems appropriate for elementary school can be found in Thinking Through. Math Word Problems by Whimbey, Lochhead, & Potter, 1990.) There is no limit to the number of different group combinations and roles that can be generated. The design that is best for you and your students is something you must find for yourself. As long as students are involved with their work and learning new ways of thinking the goals of pair problem solving are being met.
Mathematics and Science
Problems form a natural part of most math and science courses. Pair problem solving works best with problems involving more than straight calculation, such as word problems presenting situations that must be analyzed and reformulated before beginning calculations. Pure calculation, whether arithmetic or algebraic, rarely provide room for discussion. This is because most students perform calculations on automatic; they are largely unaware of the choices made in deciding what step to do next.
Classic end-of-chapter word problems are not the only option. If students are having difficulty reading their text, ask the problem solver to paraphrase a sentence or paragraph while the listener probes to find out how the translation is being made. The problem solver could be asked to take a position on some controversial application of science and to defend it (e.g., should rabbits be used in research?). Problems from old SAT or Regents exams might be used if improved performance on these tests is a goal of your course. With multiple choice tests it is sometimes possible to find which distractor items are most commonly selected by the students you teach. If you have such information you might ask the problem solver to explain a line of reasoning that could produce the most popular incorrect answers. Alternatively the problem-solving pair could take turns defining a line of reasoning for each possible answer in sequence and then decide which of all the given answers represents the best choice and why.
English teachers are sometimes at a loss for short problems. Texts such as Analyze, Organize, Write (Whimbey & Jenkins, 1987), Analytical Writing and Thinking (Linden & Whimbey, 1990a), and Analytical Reading and Reasoning (Whimbey, 1989), provide a wealth of short problems. Other appropriate tasks include:
Sentence ordering: Students are given a set of jumbled sentences and asked to order them to form a coherent paragraph.
Text interpretation: The problem solver is asked to give the meaning of a sentence, paragraph, or stanza.
Error correction: The problem solver is given a text that has some number of errors that must be found.
Additional suggestions may be found in Why Johnny Can’t Write (Linden & Whimbey, 1990b).
Social Studies
Many of the techniques described in the two previous sections can be used in the social disciplines: paraphrasing paragraphs, taking and defending a position, chronologically or logically connecting a series of events. Standardized tests and distractor items can also be analyzed. Discussion and debate are critical aspects of the social sciences. Pair problem solving is an excellent preparation for participation in larger group discussions; it increases the precision of the speakers and the attention and critical astuteness of the listeners.
Languages
The techniques described for English also apply to foreign language instruction. In addition, the following extension may prove useful. Pair 1 translates a sentence from English to French and gives the translation to Pair 2. The second pair translates the French back to English. Finally all four students get together to compare the original English with the derived English; if the meaning of these two sentences is incompatible, the group then must decide where the mistranslation occurred.
Adjusting to the Pace
Most teachers find their first experiences with pair problem solving a little disquieting. The students are busy; the room is noisy but you the teacher may not be sure what to do. You can sit with a group and listen in, but often this results in the pair looking to you for guidance rather than getting on with their task. If you keep quiet and out of the way you may feel that you are not doing your job, or to put it another way you may feel ignored and unimportant. Pair problem solving does require that you look on your job as a teacher in a new light. It is the students who are the workers; you are a manager and as long as the students are working effectively you are doing your job. Often there will be more than enough questions to keep you busy but when there aren’t, enjoy the break, you deserve it. For more insight into this view of teaching read Control Theory in the Classroom (Glasser, 1986).
Students
Pair problem solving is an excellent study tool. Learning is more effective and homework more enjoyable when you do it with other students. Yet when two or more students get together to study they often find other things to do and may not know how to work well as a team. Pair problem solving is a good way to develop meaningful cooperation. Once you have learned to be a good listener and to ask tough questions you can always make sure that the problem solver does not get away with a solution that may sound good but that does not really make sense. Study groups of up to five students can operate with one student solving a problem while all of the others ask questions. If the problem solver gets stuck another student may be able to take over.
Pair problem solving can also be useful when you must study alone. We know of one physicist who used to study for exams by writing out a detailed solution to a problem (acting the role of problem solver) and then attacking the solution (acting out the role of listener). The listener role can also be useful when you read. Ask the author how he/she comes to his conclusions or what evidence he/she has for her views. Of course the authors cannot answer back so you will have to give them some help yourself.
Parents
Instead of telling your children how to do their algebra, try working with them as a listener. That way you can help even when you do not understand the material yourself (and if you are a good listener your kids may never find out that you are in over your head!). Pair problem solving can do a great deal more than improve learning; it can advance interpersonal understanding. Once, in the end-of-the-year evaluations of a math course that used pair problem solving, a student reported that the course had taught him to get along better with his mother. What he probably meant by this was that he had learned to listen to people who had different ideas from his own and that he now could appreciate their reasoning. Standard tutoring or lecturing is a one way process. It is usually pretty frustrating to all concerned and tends to drive people apart. Pair problem solving helps people understand each other and brings them closer together.
Pair Problem Solving in the Workplace
Today cooperation is replacing competition in more and more work situations. Yet few of us have any training in cooperative thinking or group problem solving. Pair problem solving is an excellent system for building skills for team thinking, creativity, trouble shooting, and design. Often when a group of people meet to discuss an issue, each individual strives to show off his or her own competence or cut down other people’s ideas. To counter these tendencies a technique known as brainstorming forbids criticism. But this does not really solve the problem, because criticism is essential to building an effective solution. Pair problem solving encourages constant criticism without degenerating into personal bickering.
Most people, including highly talented people, have very little conscious awareness of how they produce creative new ideas or how they reach decisions. When you have little understanding of how you think yourself, the conclusions reached by others can be completely baffling. In the highly charged, competitive environment of the corporate rat race it is easy to see other people’s ideas in a bad light. Pair problem solving develops both an understanding of your own reasoning processes and an appreciation of those of other people. Furthermore it shows you how, working with other people, you can refine ideas and problem solutions so that the end result is better than any single contribution. This experience and the experiences of sharing your thought processes create a feeling of intimacy and trust. It establishes the base for a group to move from bickering to brilliance.