One quick note: Mark Hammond recently wrote about intentionally showing (and having students create) mistakes. Some ideas are his, and others he attributes to other people (particularly Jim Doherty), but I am going to give him sole credit for the purposes of this post. He talked about showing two problems side-by-side—one with an error, and one without. The students must figure out which one is correct and where the error is.
This reminds me of the exercise I got from Assessment FOR Learning, described here. I recently repeated this exercise (with the question: “Why is the area of a right triangle ?”). Again, I had one example that actually answered this question (by combining two right triangles into a rectangle), and two examples that just explained what to do with the formula. The response from the students was intriguing: the first class was evenly split among the three as to which actually answered the question, whereas the second class picked the correct one (by a vote of 18 to 2 to 2).
Still, this is a difficult question for the students. I am having the students write short papers explaining why different algorithms give the correct answer (these algorithms are: standard multiplication algorithm, long division, “multiplying across” for fraction multiplication, “common denominators” for fraction addition and subtraction, “invert and multiply” for measurement fraction division, and “invert and multiply” for partitive fraction division). The students can submit drafts, and I will comment but not grade them. The final draft will be due at the end of the semester.
So far, students are still mostly struggling with answering the question that was given, although some progress is being made.
Okay, if it seems like the whole “physics blog” topic was just a cover for me to talk more about Assessment FOR Learning, that’s because it was. Sorry about that, physicists of the world.