In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.
Often I’ll cover a topic in class that students really should have learned in a previous class but just didn’t. For example, in my experience, a significant fraction of my senior math majors have significant gaps in their backgrounds from Precalculus:
- About a third have no memory of ever learning the Rational Root Test.
- About a third have no memory of ever learning synthetic division.
- About half have no memory of ever learning Descartes’ Rule of Signs.
- Almost none have learned the Conjugate Root Theorem.
Often, these students will feel somewhat crestfallen about these gaps in their background knowledge… they’re about to graduate from college with a degree in mathematics and are now discovering that they’re missing some pretty basic things that they really should have learned in high school. And I don’t want them to feel crestfallen. Certainly, these gaps need to be addressed, but I don’t want them to feel discouraged.
Hence one of my favorite motivational one-liners:
It’s not your fault if you don’t know what you’ve never been taught.
I think this strikes the appropriate balance between acknowledging that there’s a gap that needs to be addressed and assuring the students that I don’t think they’re stupid for having this gap.