When I was in my doctoral program, I was amazed at some of the research coming out on kids’ understanding of math concepts. We assume that children all learn pretty much the same math at roughly the same ages, and that they learn these concepts in math class.
In fact, there’s a wide natural variation, and not necessarily a lot of correlation between the math kids are taught in school and the math they actually know.
For example, when researchers assess kids for “multiplicative thinking” (multiplication as a separate concept, not just repeated addition) they find that a few children have multiplicative thinking as early as kindergarten, long before multiplication is taught in school. And, despite several years of formal instruction, half of all fifth graders don’t yet have solid multiplicative thinking.
Math is not a natural skill. We learn math one step at a time, our brains building connections between neurons which link each new concept to what we already know. It’s a cumulative process, much like learning a foreign language.
I’ve been using Khan Academy videos with my students; much like a foreign language program, students can play lessons over as often as necessary and review until they are “fluent.”
I’m also very excited to see Khan videos now being used for actual classroom instruction in the form of Flip Teaching (the lectures are listened to at home, and the practice and projects that were typically done as homework are done in the classroom).