One of the biggest differences I’ve experienced in my Fundamentals of Electrical and Computer Engineering class [ECE 110L] since incorporating more group-based problem discussion and solving activities into lectures is a shift in the students’ questions from “How?” to “Why?”
A few times during each class meeting I ask the students to work with their neighbors to discuss strategies for approaching a problem. While the students are discussing the problem, TAs and I roam the room to answer questions, provide pointers, ask related open-ended questions, and generally offer support. I specifically ask the students to focus on approaches and strategies for the given problem, and not become bogged down in the algebra or arithmetic associated with arriving at a specific numerical answer.
You may have noticed I said, “approaches and strategies,” plural. For a fair number of students, this is one of the first times they are asked to think about quantitative problems that have a single correct numerical answer but for which there is not a single solution, or a best approach, to arrive at that answer. There often are many approaches to solving a problem, all of which are equally valid and effective. For a given problem, some solution methods may be more efficient than others, resulting in a more concise solution. For a given student, some solution methods may feel more natural and intuitive, and therefore be preferred over others by that student.
When the students engage in discussing problem solving strategies with their peers, they experience first-hand the potential ambiguity in selecting a problem solving approach and see that uncertainty in how to approach a problem is a natural part of the problem solving process. From this, they gain confidence in their abilities to solve problems even when they don’t immediately see the path from beginning to end.
The small group conversations spark debate about which approach is “better” and this is where questions shift from “How?” to “Why?” because the discussion shifts from how to compute the answer to why an alternate strategy is also a valid approach to solving the problem.
Getting from “How?” to “Why?” is beneficial for students in two ways. First, it helps them understand concepts beyond a superficial level of figuring out which numbers to plug into which equations. Second, and perhaps more importantly, it also helps them develop the ability to generalize concepts from an isolated idea to a comprehensive, universally applicable, construct. Strengthening their problem-solving skills by deepening their understanding of concepts and improving their ability to generalize these concepts fosters the development of their analytic maturity – the ability to apply fundamental concepts to solve new problems, particularly problems that are unlike those they have seen before.
I ask students to self-evaluate their active participation in class three times during the semester: a few weeks into the semester, about halfway through the semester, and shortly before the end of the semester. In the final self-evaluation, I also ask the students what elements of their active participation this semester do they expect to carry forward into other classes in future semesters. One student’s response to this question exemplifies the benefits students see when their perspective shifts from “How?” to “Why?”…
I hope to carry forward a love for understanding the “why” rather than just the “how”: I’ve found that the “how” easily follows when I have a genuine understanding of the theory behind a procedure.