> In other words, in science and math education in particular, it’s easy to slip into teaching methods that emphasize understanding and that avoid the sometimes painful repetition and practice that underlie fluency. I learned Russian not just by understanding it—understanding, after all, is facile, and can easily slip away. (What did that word понимать mean?) I learned Russian by [...]
This is a misleading use of 'understanding' being equated to remembering.
The thing that made math so much easier to learn for me was that as soon as I understood a concept or method of logic, it was effortless to internalize and recall. Things that only depend on 'facts', like the meaning of понимать is what can't be understood and must be remembered. But if that was your native (or closely related) language it could be understood by seeing its roots and construction.
The hard part is getting someone get a foothold in an unfamiliar subject so that other understandings can be built upon it. What the author seemed to have done is two things: turn an aversion into an interest and realize that they can actually learn math, not merely memorized.
> The thing that made math so much easier to learn for me was that as soon as I understood a concept or method of logic, it was effortless to internalize and recall.
Mathematics is not a spectator sport. - George Polya
Somewhat ironically, I actually read this article after it surfaced on Hacker News on some previous occasion and did not realise until I got to the point where the author mentions how she worked on Russian trawlers in the Bering sea. The brain readily remembers unusual stuff but not the mundane.
There was plenty of semi-unusual stuff before that paragraph - switching from languages to engineering, starting later in life after leaving the army etc. But it seems these were still too general to have made an imprint in my long term memory. Working a trawler in the Bering sea as a translator - that’s something I’ve not seen in any other article before or heard any other human talk about. Memory connection made.
I think this is half the reason why solving problems and memorisation is needed for a lot of people - the material is so abstract that people struggle to tether it to anything in their memory.
I've been reading papers on generative deep learning models and recently read the book "Moonwalking with Einstein".
I think there's some interesting analogies with the chunking this author describes and learning an embedding space or "latent" in some modern machine learning models. Through repetition, inputs such as math symbols or words can produce latent vectors that may be greatly reduced in dimensionality compared to their inputs.
Interestingly, human have an incredible ability to rote memorize images extremely rapidly compared to other types of data, but simply remembering images of dozens of equations is not sufficient to become a great physicist!
I think, in a sense pure practiced repetition is not the same thing as memory recall.
She uses words that don't mean what she thinks they mean.
"Rote learning for understanding"
Yeah, that's the opposite of the meaning of rote.
She says "practicing" when most people would say "working on understanding", as in her discussion of f=ma. Practicing is doing the same thing. Thinking about all the ramifications of something, changes for different conditions is not practicing.
She's doing exactly the things that people focusing understanding recommend, she's just using the wrong terminology to describe it, then calling it a disagreement.
"I rewired my brain to do <thing>" — back in my day we used to call that learning, especially after we found out that your neural pathways change constantly, strengthening and pruning inefficiencies, when learning and repeating any kind of behaviour, be it practicing a language or becoming addicted to a drug.
I guess "I finally learned and understood maths" is not as engaging a title.
This is a misleading use of 'understanding' being equated to remembering.
The thing that made math so much easier to learn for me was that as soon as I understood a concept or method of logic, it was effortless to internalize and recall. Things that only depend on 'facts', like the meaning of понимать is what can't be understood and must be remembered. But if that was your native (or closely related) language it could be understood by seeing its roots and construction.
The hard part is getting someone get a foothold in an unfamiliar subject so that other understandings can be built upon it. What the author seemed to have done is two things: turn an aversion into an interest and realize that they can actually learn math, not merely memorized.