I've worked in math education before. I've seen this sort of mentality in my students, and I always try to go back to basics wherever. This is made more difficult when students don't want to share their thought process, often out of a fear of appearing 'bad at math'.
I recently stumbled on "Examplar" where they try to teach computer science by having the students write their own examples of how a correct program _should_ work, which forces them to reveal their thought process, and helps a teacher see any misconceptions. This feels like a pretty generalizable thing, if all teachers are always thinking about mapping each student's conceptual understanding of the thing when they encounter difficulties
it really does feel like the difference between driving a car blind vs being able to actually see where you're headed. The problem is driving blind DOES seem to work "well enough" and when some students just don't get it, we shrug and say "I guess they're not good at [thing]" which breaks my heart
oh, whoops!! I didn't even bother to check the equation, I was just thinking about the concept that he was guessing and not actually plugging it in. Thank you for catching this and for leaving a comment here!!! lemme re-adjust the equations
This has me thinking about the "learn to think by probing people on twitter" thing:
- Up until TODAY, my plan for "improve my world model" was "read & make flashcards from a few chapters from an economics textbook, then an x textbook, then a y textbook, until I have a good knowledge base"
- But, this is VERY inefficient!!
- You're learning without an x, guessing at what will be useful to you, maybe, one day in the future
Vs:
- Asking "Why does this person think this"? is the same as ("x causes person to think this")
- Now you have a concrete thing to look for, and crucially, a feedback loop, as you can test if you were right or wrong
It's so easy (for me at least) to be a very passive learner. Like, putting loads of time into learning, but not learning to answer particular questions. Very silly in retrospect - hopefully I can break the habit
I've worked in math education before. I've seen this sort of mentality in my students, and I always try to go back to basics wherever. This is made more difficult when students don't want to share their thought process, often out of a fear of appearing 'bad at math'.
I recently stumbled on "Examplar" where they try to teach computer science by having the students write their own examples of how a correct program _should_ work, which forces them to reveal their thought process, and helps a teacher see any misconceptions. This feels like a pretty generalizable thing, if all teachers are always thinking about mapping each student's conceptual understanding of the thing when they encounter difficulties
it really does feel like the difference between driving a car blind vs being able to actually see where you're headed. The problem is driving blind DOES seem to work "well enough" and when some students just don't get it, we shrug and say "I guess they're not good at [thing]" which breaks my heart
https://blog.brownplt.org/2024/01/01/examplar.html
Great article!
x^2 -1 =1 means x is sqrt(2), not 1. Using ^ for power, not sure if I can mathjax in comments
This sentence confuses me 'He says “one half!” I say not quite, he says, “one!!” which is correct, but he’s clearly guessing'
'One' is not correct? What am I missing?
oh, whoops!! I didn't even bother to check the equation, I was just thinking about the concept that he was guessing and not actually plugging it in. Thank you for catching this and for leaving a comment here!!! lemme re-adjust the equations
This has me thinking about the "learn to think by probing people on twitter" thing:
- Up until TODAY, my plan for "improve my world model" was "read & make flashcards from a few chapters from an economics textbook, then an x textbook, then a y textbook, until I have a good knowledge base"
- But, this is VERY inefficient!!
- You're learning without an x, guessing at what will be useful to you, maybe, one day in the future
Vs:
- Asking "Why does this person think this"? is the same as ("x causes person to think this")
- Now you have a concrete thing to look for, and crucially, a feedback loop, as you can test if you were right or wrong
It's so easy (for me at least) to be a very passive learner. Like, putting loads of time into learning, but not learning to answer particular questions. Very silly in retrospect - hopefully I can break the habit