A student said she had trouble memorizing the unit circle — a difficulty for many, many students. As I told her, part of the problem is that she is not taught patterns that help one memorize it all and not taught (or reminded of) some context (geometry) that also helps.
I also said:
Oh, but I think it’s not math that is the problem; the problem is that you did not have sufficient memorization of language when you were younger. Very few people memorize things over the past few decades as they did over 50 years ago. Has long-term consequences for our brain’s functioning and our ability to understand and appreciate language and symbols.
People have known this for centuries. We can learn more about what is going on in our brains and minds by studying neuroscience and brain plasticity. These studies add to what we know, but don’t contradict it or allow us to know this for the first time. Knowledge closer to the perceptual level has priority over the later. Knowledge we need to know to draw a more advanced conclusion does not cease to be knowledge when we use it to draw a conclusion or inductive generalization.