I am teaching a content course for elementary education majors this semester, and I had them do presentations yesterday. Their task: “explain why an unusual multiplication or division algorithm (e.g. “Lattice Multiplication”) gives the correct answer to a multiplication/division problem.” The idea, of course, is to show how the algorithm is really just doing a definition of multiplication (usually “repeated addition”) or division (either partitive or measurement).
Several presentations were good, and one was dazzling. However, most of the presentations missed the question entirely, and simply demonstrated how to do the algorithm (and assuming that it is an algorithm worth doing). This has been an on-going challenge this semester (and every other semester I have taught this course). I have had some successes, but they are usually short-lived for most of the class.
I am also giving the students feedback on drafts of papers that explain why some algorithm gives the correct answer (according to the definition). We will see how much this helps.
Does anyone have any suggestions on how I could communicate the question (or that a question even exists)? The students are very focused on the arithmetic, but ignore the mathematics.
Tags: Math 121