Occasionally, students ask me questions about why math works the way it does. This doesn’t happen enough, in my opinion, but it does happen. The latest is why, when we perform synthetic substitution, do we use the number as it is, but in synthetic division, there’s some sign trickery. I have an answer for this. It’s not super complicated either, but whenever I’ve given the explanation in the past it’s been frustrating and incomprehensible to students. So, I don’t know if it is worth the time it takes to do that, and that kind of understanding is not necessary for skill performance. But then, what am I doing? If we don’t care about understanding or make that kind of tradeoff of “well, they don’t really need to know this” that feels like the opposite of mathematics education. I’m pretty good at explaining things like this, so I don’t think it’s me. There is such a thing as developmental readiness and that’s what’s happening here. I think.
What do you do when explanations are over the students’ heads? Is that just a normal thing that resolves itself with further mathematics study and we shouldn’t worry about it? I find “that’s just how it works” a completely unacceptable response.