Tom Lombardo, Ed.D.
Professor of Engineering
Note: This article first appeared in the March-April 2012 issue of the ATLE Newsletter.
A few weeks ago a colleague told me of his frustration with students who mindlessly plug numbers into an equation and then are surprised to discover that their answers are incorrect. “But I used a formula,” they would insist. His response: “Plugging numbers into a formula is the easy part. The challenge is knowing which formula to use for a given situation.” I find myself having similar conversations with my programming students. Some will reach into a bag of programming concepts, grab a handful of instructions at random, and throw them at the computer. I refer to this as the Jackson Pollock Design Method (JPDM). I’ll leave it to the art faculty to debate the merits of Pollock’s techniques on canvas, but as a professional engineer I can say unequivocally that the JPDM is not an acceptable problem solving methodology.
Problem solving is a higher order thinking skill that’s used in analysis and design. Many of our students seem incapable of this level of thinking. Actually they are capable of it; they simply haven’t been taught how to do it. If we want our students to be successful in our classes, we must teach higher-order thinking skills. This may seem like an extra burden for those of us teaching “content-heavy” courses (by the way, is anyone teaching a “content-light” course?) but we can teach higher order thinking skills within the context of our course material. In fact, thinking skills and content knowledge are both enhanced when we teach thinking skills in context. Cognitive scientists have developed methods to help teach problem-solving. These techniques have been tested and verified in classrooms; I’ve used many of them myself. Keep in mind that most students will be unfamiliar—and therefore uncomfortable—with some of these activities. It helps if you explain the reason for the technique when you use it.
- When presenting new material, provide students with an advance organizer that shows how the material relates to what the students already know. This can be a hierarchy/organization chart, a concept map, or a diagram that shows the concept in action. Seeing the relationship between concepts helps the students to know which concept addresses a certain problem. Use concrete examples rather than abstractions.
- Have students create their own analogies that describe the concept. This forces the students to think carefully about the concept and to incorporate it into their own existing knowledge.
- Be an example of a problem solver. When showing examples, think out loud as you work through the problem solving steps. Describe your thoughts as you go. Stop at various points and suggest that students take notes about both the steps and the rationale.
- Classify problems and describe solution methods for various problem categories. List the distinguishing characteristics of each problem and match it with a solution method. Explain why this solution fits this problem. Give students a variety of problems. Ask them to identify the distinguishing characteristics of the problem and match the problem with appropriate solution method. Don’t make them solve the problem during this activity. Just focus on identification and classification.
- After they solve a problem, have the students explain their solution step-by-step in writing. Even if they practice fewer problems (because they’re taking time to explain), the act of self-reflection causes them to learn more deeply. The students should explain their steps and the rationale for each step. A variation of this might be a pair-share activity where students explain their solution to a classmate.
These techniques fall into the category of “metacognition” – thinking about how we think. By actively dissecting our thought processes, we develop better cognitive abilities. The most important skills that we can teach our students are metacognitive skills. If you teach a man to fish you’ve fed him for a lifetime. If you teach him how to think, the possibilities are endless!
RVC Faculty can continue this conversation in the private RVC Faculty Group here: https://rvceagle.instructure.com/courses/168/discussion_topics/5610
Mayer, R. & Wittrock, M. (2006). Problem Solving. In Alexander, Patricia, and Philip Winne, eds. Handbook of Educational Psychology. 2nd ed. Mahwah, NJ: Erlbaum.
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