Read this article by David Ginsburg in Education Week: “You Must Always May Show Your Work.” He wrote about whether or not students should be required to show their work when completing math problems.
This is interesting because I just had this discussion in my class this morning. My students asked when it is necessary to show their work. I gave them examples of when it is necessary (open-ended exam problems) and when it is not (when it is a concept not being taught in the course: a concept they should have already learned).
Depending upon the topic/concept I am teaching, it is more beneficial for my students to show their work so they can truly understand why procedures work. One example is dividing fractions. If the topic is new, students should get used to working through the procedure (showing work). When dividing fractions is a concept embedded within another concept (like simplifying complex fractions), then it is not necessary to show the work involved in dividing fractions. This is just one of many examples.
While I understand both arguments (requiring work and allowing just the answers), there’s a time for both. In many cases, students can answer questions conceptually, but have difficulty expressing solutions mathematically. In other cases students are able to memorize answer sets and can recall those answers easily, but do not understand the concepts. As an instructor, I must use my judgment to make sure my students are prepared for the next course, a certification exam, teaching, or whatever the course is designed to accomplish.
What are thoughts about students showing their work? Do you require that they show their work or allow just answers?