IMPROVING STUDENTS' PROBLEM SOLVING SKILLS

Introduction
There are many ways faculty can help students become better problem-solvers. Two teaching strategies are presented here, with a special emphasis on their use in mathematics and science: pair problem-solving and thinking aloud.

Pair Problem-Solving
The "pair problem-solving" method involves one person solving a problem and talking aloud constantly about all of the thoughts that are going through his or her mind as the work progresses. The thinker-talker can be either the teacher or the student. The other person in the pair is the analytical listener, who carefully tracks the problem solver's process and progress. Whimbey and Lochhead (1982) describe this technique as a thinker and listener pair working on problems and rotating roles. Pair problem-solving has become a popular way of helping students think about their own problem-solving. It is a higher-level thinking (metacognitive), self-monitoring strategy that gives students feedback on what is understood and what is still unclear. It helps students identify what parts of a problem they understand and where they get stuck. Externalizing thoughts enables them to be seen from a fresh perspective. Instructors can teach students how to solve problems, how to do "pair problem-solving", as well as how to think aloud, by first modeling these processes.

There is a real value to using the "pair problem-solving" model in a classroom setting. You can have all the students work in pairs, with one serving as the THINKER, while the other serves as the analytical LISTENER. After solving a problem, students rotate roles so that everyone serves as both the thinker/problem-solver and analytical listener. The thinker verbalizes out loud ALL the thoughts that arise in the process of completing an academic task. The listener actively attends to what the thinker says, examines the accuracy, points out errors, and keeps the thinker talking aloud. Together, the students can discover errors, misconceptions, disorganizations, and other impediments to academic performance. The teacher needs to observe each pair, monitor progress, and provide feedback on the process. This approach has been demonstrated to be an effective approach for helping students learn (Whimbey & Lochhead, 1982).

Thinking Aloud
A related technique involves one person saying out loud all the steps and all the mental work done when performing an academic task, e.g. solving a problem, answering a question, conducting an experiment, reading through lecture/textbook notes. When the thinker-talker is the subject matter expert, the process allows them to model their own thinking for students. This modeling shows the students how to approach and think about the material. It lets the students hear what goes on in an expert's head when a text is read, a homework assignment is attacked, study for a test is planned, an essay is written, an error is found, or a problem is solved. It also should include statements from the expert that externalize his or her feelings, so that students can learn how to self-regulate their own emotions.

When the student is the thinker-talker, the process is valuable even when the student is alone. The student becomes more aware of what goes on in their head when performing an academic task and frequently this provides real insight into improving performance. It tends to make students more systematic in their thought processes and helps them catch errors before they go too far in the wrong direction. Many students already use the think-aloud strategy, but are afraid to admit it. Some students may be reluctant to even try it and they may need the professor to demonstrate it and advocate its use, so that they know that it is a strategy that smart people often use when thinking about complex ideas and solving problems.

How to Think Aloud: Problem-Solver's Task

1. Translate your thoughts, e.g. ideas and images, into words and say them aloud.
2. Verbalize aloud all the steps that you go through when solving problems. Do not censor. No thought or step is too small, easy, obvious, or unimportant to verbalize.
3. Verbalize all the thinking you do before you start to solve the problem, e.g. what you are going to do, when, why, and how. Even second-guessing yourself is important to verbalize aloud, e.g. "I think I should use that long, complicated formula we were using a couple of weeks ago. What was it called, the quadratic equation? No, maybe not. Maybe I'm supposed to use the formula we used in class yesterday."
4. Verbalize all thoughts during the problem-solving, e.g. "Okay, I'm almost through with this division problem. Now that I have the answer, all I have to do is multiply to check and see if my answer is right."

1. Think along with the problem-solver. Follow every step and make sure you understand every step. If not, ask a question. Have the problem-solver identify and define important terms, variables, rules, and procedures. Make sure the problem-solver vocalizes all the steps and does all the work. If the problem-solver skips over a step without thinking aloud, ask him or her to explain the missing thought.
2. Do NOT work the problem out independently. Listen to and work along with the problem solver.
3. Never let the problem solver get ahead of you. Whenever necessary, ask the problem-solver to wait so you can check a procedure or computation and catch up. If the problem-solver is working too fast, slow them down so you can follow carefully, analytically, and accurately.
4. Check the problem-solver at every step. Don't wait for the answer. Check everything - each computation, diagram, procedure. In the back of your mind, constantly ask yourself, "Is that right? Did I check that?" To promote precise thinking, have the thinker carefully define important terms and variables.
5. If you find an error, avoid correcting it. Point it out and try to get the problem-solver to correct it. If he or she gets stuck, ask questions to guide thinking in the right direction. If necessary, give some suggestions, hints or partial answers. Give the answer only as a last resort.