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
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