The post on that reading comprehension study is good (and reminded me of some of my complaints about GPT a couple years ago, although the LLMs have gotten much better since then).
But the thing that really stood out to me is that I feel much this same way about math instruction:
i have seen this repeatedly, too - actually i was particularly taken with how similar this is to the behavior of struggling readers at much younger ages - and would summarize the hypothesis i have forged over time as: struggling readers do not expect what they read to make sense. my hypothesis for why this is the case is that their reading deficits were not attended to or remediated adequately early enough, and so, in their formative years - the early to mid elementary grades - they spent a lot of time "reading" things that did not make sense to them - in fact they spent much more time doing this than they ever did reading things that did make sense to them - and so they did not internalize a meaningful subjective sense of what it feels like to actually read things.
One of the big problems I have primarily in Calculus 1 (which is the lowest-level course I've taught) is that students just don't expect math to make sense. There's a bunch of rules to follow, which you have to memorize, and then you look at an expression and use some rule that seems like you could use it.
But that's not how competent mathematicians (and I use that word in the broadest possible sense) interact with mathematics. Mathematical formulas mean things. They have syntax, and semantics, and you can break apart a computation and talk about what individual terms mean and are doing, and what manipulation you're doing and what that corresponds to.
(Sometimes, of course, that's easier than others. Calc 2, in particular, involves a lot of "tricks" where it's hard to explain the logic in the middle of using them. But that's why I'm focusing on Calc 1 here, which is mostly not like that but does have a lot of application-y problems where this semantic understanding is important.)
But if you've never worked through a math problem and felt like everything was meaningful, you don't expect meaning in what you're doing, and you don't expect your own work to make sense. And then, well, it won't, and you'll struggle and get lost in the middle of every problem.














