Misunderstandings about Understanding
The issue of balance between procedural fluency and conceptual understanding in mathematics has served as a dividing line in education. Some believe that understanding of a procedure or algorithm must precede the procedure/algorithm itself—and if it doesn’t precede it, it should come about quickly or the result will be what some call “math zombies”. Others believe that procedural fluency and conceptual understanding is an iterative process where one feeds the other. This talk explores what understanding is and what it isn’t, as well as how misunderstandings about understanding affect students. It was prepared for a virtual conference sponsored by researchED in 2020.
I very much enjoyed your talk. There is currently an over-emphasis on "understanding" over procedural fluency, particularly in primary school, when even Year 1 students are expected to explain their answers to solving problems. Most students of this age don't have the language concepts to be able to explain their thinking when doing maths.