🧵 Math education: rigorous vs intuitive approach, and their arguments
Anonymous at Tue, 8 Oct 2024 22:36:08 UTC No. 16416471
I'd like to read up on the discourse surrounding whether to teach students Mathematics through a (semi-)rigorous approach or through an intuitive approach. Arguments should be both general, and also consider the distinction between those who wish to study Mathematics or any of the hard sciences later on, and those who have no interest in the subject at all (or their education for that matter). Sources don't have to be formal papers or essays--though the latter are probably best with regards to having a convincing argument be properly developed, instead of it being presented as matter of fact--they can just be excerpts from the prefaces of books or their introduction. I've seen a few of these arguments discussed briefly in some regard in a few textbooks, but it's only to justify the the level of rigor with which the topic is to be discussed.
Apart from just discourse, I'm also interested in reading any formal papers or studies examining the success or failures of either approach or their implementations, anything that provides statistics and empirical data.
I'm mainly looking at Maths education in the states and the West, but anything discussing how the Soviets approached teaching Maths and Science back in the day is welcome too.
I don't know where Common Core lies in this, but arguments in favor or against it are welcome as well.
Anonymous at Tue, 8 Oct 2024 22:43:57 UTC No. 16416500
>>16416471
Source?
Anonymous at Tue, 8 Oct 2024 22:51:35 UTC No. 16416522
>>16416500
https://inciclopedia.org/wiki/Profe
Anonymous at Tue, 8 Oct 2024 22:52:07 UTC No. 16416523
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Anonymous at Tue, 8 Oct 2024 22:52:31 UTC No. 16416528
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Anonymous at Tue, 8 Oct 2024 22:52:34 UTC No. 16416529
>testing 0.88 testing
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Anonymous at Tue, 8 Oct 2024 22:54:00 UTC No. 16416531
>>16416522
Gracias mi pequeño amigo penalizado.
Anonymous at Tue, 8 Oct 2024 23:03:09 UTC No. 16416541
>>16416471
when will you people learn that "intuition" is not fucking real? the only thing that exists is the formal definition and the formal proof. everything else is fantasy.
Anonymous at Tue, 8 Oct 2024 23:56:55 UTC No. 16416593
>>16416541
https://terrytao.wordpress.com/care
wrong.
Anonymous at Wed, 9 Oct 2024 00:52:57 UTC No. 16416643
>>16416541
Intuition's the only thing that matters. If you don't have an intuitive understanding of something then you don't understand it. No one really cares if you can prove something. All that matters is that your proofs are short. If all your proofs are short you can prove a lot of things very quickly. Having a good intuition is just having an exact understanding of every correspondence so that you can quickly build whatever proofs you need.
Anonymous at Wed, 9 Oct 2024 01:51:33 UTC No. 16416712
>>16416541
https://warosu.org/lit/thread/23884
Shame that thread on /lit/ got nuked. Comparing the two threads, it's clear that there would've been a better discussion there. I wasn't particularly interested in starting a discussion about it; I just wanted sources to read from, but I still would've liked to see people's own arguments.
Anonymous at Wed, 9 Oct 2024 18:42:27 UTC No. 16417942
Going through stages is necessary. If you try to start with semi-formal proofs, most of the students will not really understand what you're doing, and even fewer will care.
Van Hiele had some stuff to say about this as applied to geometry (PDF and link related); I don't know much about the research that's been done related to his model except that it exists, but his stages seem to match the sort of levels of understanding I've seen in students, and he makes some good points in the essay I've attached as a PDF.
https://en.wikipedia.org/wiki/Van_H