PRISM Magazine On-Line  - November 1999
teaching toolbox
A Problematic Subject

by Phillip Wankat and Frank Oreovicz

Teaching students how to solve problems can keep frustration to a minimum

Despite educators' efforts to ensure that students become good at problem solving, many of them just don't get it. That in itself is a problem, because engineers' primary stock in trade is their ability to develop answers to both simple and complex questions.

  There are basically two types of problems: exercises (or routines) and novel problems. Exercises are solved by using a known algorithm; once the algorithm is recognized, finishing the solution is straightforward, although perhaps tedious. With novel problems the known algorithms do not work, and problem solving becomes what you do when you don't know what to do.

Students initially find almost every task to be novel, while we would hope that graduating seniors will consider most of the curriculum to be exercises. In fact, curriculums are essentially defined by the set of tasks we expect graduates to be able to solve as exercises, and to a large extent, engineering education consists of understanding novel problems and converting them into routines. Any student can tell you this is not easy.

Laboratory and design courses typically ask students to solve novel problems on unfamiliar subjects, giving them some practice in learning how to learn. Professor Don Woods of McMaster University and his co-workers note that the best way to teach problem solving is in a separate workshop loosely connected to an engineering course that requires extensive problem solving. The workshop focuses explicitly on problem solving, while drawing on the disciplinary knowledge in the engineering course.

To teach problem solving, try following a structured strategy, which helps students see where they are stuck. One such strategy is: 1) "I can" (motivation). 2) Define the problem. 3) Explore possibilities. 4) Plan the steps. 5) Do the calculations. 6) Check the results. 7) Generalize the procedure. The steps should be solved in a looping fashion with considerable feedback between the steps.

Teach students to follow expert procedures such as spending extra time on the early parts of the strategy, drawing sketches, and checking answers. Remind them to monitor their problem-solving behavior verbally as they proceed. If stuck, show them how to use heuristics such as solving for limiting cases, solving the parts you can, using analogies, and solving for ratios.

When you demonstrate successful approaches to a problem, avoid showing only well-manicured solutions, which do not accurately convey the inherent messiness of problem solving. Even experts do not strictly follow a strategy for novel problems. The process is much more chaotic—involving sketching, trying things and checking them, rechecking the problem statement, guessing, screaming, taking breaks, and persisting until a solution is obtained.

After demonstrating some techniques, arrange the students into groups to solve problems. Depth works better than breadth, so give students a group problem in class, then assign a series of "what if?" questions that build on the basic solution. Reduce the math and increase the thinking and understanding required. Encourage reflection on their process of obtaining a solution, using the strategy as a guide.

Struggling is part of the process, but too much is discouraging. If a group is stumped, encourage them to verbalize what they are doing by asking: What are you doing? Why? How will it help solve the problem? This will often help get them unstuck. Provide students with both positive and negative feedback. Finally, since you're asking them to persist at the effort, you should, too, by making problem solving a regular activity, not an occasional diversion.

Once on the job, new engineers will earn their stripes only by effectively addressing the difficult, open-ended problems that companies need solved. By teaching the relevant skills and methods, educators can help them begin to earn their reputations as problem solvers.

 

The authors' book, Teaching Engineering, is now published
on the Web at
www.asee.org/pubs/teaching.htm.

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