In a given classroom, you are likely to see one of two mentalities toward the educational process. The first, which is most prevalent, focuses on the process. Popularized in math classrooms to make sure students understand how they got to the correct answer, this view believes that while answers are important, it’s more important that there is a structured, reliable way to get to the answers.
The second mentality is an emphasis on results. These practitioners believe that it doesn’t particularly matter how you accomplish your goal, as long as you produce results. This viewpoint is not particularly popular in education since, taught in isolation from morality (etc) it can yield a crop of lying, stealing, cheating students who don’t actually know or understand anything apart from… the way the world works.
But what if these two weren’t at odds? What would happen if the learning process was designed in such a way that students could indeed develop their own processes, tweaking and correcting until they produced verifiable results? This, of course, means designing activities in which there is no single right answer and, as such, is probably not recommended for differential equations. As my students are learning to build budgets/spending plans in Excel, I have tried to give them minimal instruction. I don’t want cookie-cutter spreadsheets that aren’t useful to the student. Instead, I want them to create, edit, revise, recreate, and publish spreadsheets that not only make sense to them, but demonstrate a clear understanding of both the process and the finished product.
Not either/or. Both/and. Process AND results.
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Greg Garner 