Some thoughts on what it means in teaching to work with the hand you’re dealt
A month ago or so I was talking to a colleague about a course that we both have taught in the past and we got around to the issue that the students often entered the course without as complete of a background in a particular area of mathematics (the details don’t matter, but what comes next does). We had different opinions as to what one should do about this. And my colleague commented, “You have to face reality and deal with the hand you’ve been dealt.” I nodded, but then realized that what I thought that meant was completely different than what he meant.
I took it to mean that we had to work with the knowledge that our students came with, possibly avoiding or deemphasizing parts of the course that required a knowledge deeper than they could handle, or maybe we should rethink about how those elements of the course are presented. My colleague thought it meant we should take time out of the course to (re)teach the relevant material, possibly taking a good part out of the course to do so. Personally, I don’t choose to reteach prerequisite material. I am willing to remind students of this knowledge and provide resources or references for them to learn it on their own, but I don’t want to go backwards. But now I wonder if this makes me weaken the course or avoid the tougher topics. Or if I’m challenging them enough.
Another twist to the interpretation is what it means when we say a student doesn’t have the necessary background. There’s a big difference between the student actually not ever seeing the relevant material, between having seen it but not being currently that fluent in it. I tend to assume that the latter situation is true, which justifies not doing an extensive review or reteach, but also doing some short, just-in-time reminders of the relevant material in the current context. Good or bad, this approach avoids going too in depth into the background material and forces me and the students to figure out the parts that are useful for the course material.
I’m still not sure how these choices impact the course; it is good to be aware and maybe I can pay more attention to why I’m making the decisions I make.