Why are some things perceived as a “waste of time”?
I visited a high school math class today where the ‘Foundations of Mathematics and Pre-calculus’ students were beginning a unit on measurement, including conversions between imperial and metric systems. The teacher spent quite a bit of time facilitating a discussion with the students about the concept of measuring: the various aspects of things that we measure, how we might measure things in “difficult” situations (e.g., finding the surface area of an irregularly shaped puddle), and when in life we use particular imperial units of measurement.
It was a great discussion, with the students putting forth many ideas, some wonderfully “out of the box”. As it got to the point that the teacher was setting the students to work doing some of the questions from the text book, he came over to me and made the comment, “I think the kids think this discussion was a waste of time. I know that when I was in school, I would have felt a discussion like today’s was a waste of time.”
I have no doubt that both statements are true – that the teacher remembered feeling discussions about the “big ideas” were a waste of time, and that his students, although they found it interesting, also felt it was a waste of time. The question, however, is why are such discussions perceived as such?
Personally, I think it comes down to the fact discussions about conceptual understanding are not given any honour, any value. Students look at how marks are derived and figure out pretty quickly that those things which are important are what show up on tests, quizzes, and such. If nothing about the big ideas, about the conceptual understanding, about the meaning behind the mathematics is asked when it “counts”, then it seems clear that those things are not valued. They are not important.
We, as teachers, have to decide what is really important in mathematics, and if that includes conceptual understanding, then we must include questions and/or tasks that get to the heart of that conceptual understanding in our assessments. It is not always easy to do – such items will likely not fit into a multiple-choice kind of test to be marked quickly on a Scantron. But again, we must ask ourselves what we value, what we believe is important.
Our assessments will reflect our true beliefs.