I wish Oliver Steele had been my algebra teacher. He has wonderful illustrations that he calls grounded proofs . For example, multiplication is commutative:
Oliver’s lovely illustrations make these abstract mathematical concepts concrete and simple.
I didn’t really get math until geometry. Word problems were the worst. They never seemed to make pictures for me. They didn’t seem to have anything to do with reality, although in retrospect I imagine that they were trying to accomplish exactly that.
Wow, I’ve never seen this kind of thing shown anywhere. I was lucky enough to have an algebra teacher growing up who used stuff like this, and I think it really influenced my teaching style. I tutor a lot of people in math from middle school students to non-traditional students who have went back to school after working for a decade or two, and no matter the topic, I always try to come up with visuals like this that help to build on a student’s existing intuition. Thanks for showing me this, now I have more ideas to bounce around. :)