Children's arithmetic skills do not transfer between applied and academic math
10 comments
·February 7, 2025brnaftr361
Anecdotally, this is true even as an adult. As a non-trad student the application side of things as they are taught are fairly effete, we learn how to translate graphs in algebra, quadratics, polynomials... I don't recall much in the way of meaningful application in either trig or algebra and what was there was remembered solely in the context of future examination.
In one hand I would argue there is virtually no incentive for play, or discovery, or superfluous activity with the math due to grading, and in fact it's disincentivized as it is one factor of a multivariate optimization problem. On the other hand I would argue that it's taught too fast as an effect of the former condition - as someone who isn't in a highly mathematical branch of STEM the use of mathematics is comparably infrequent when considering the TEM, as such atrophy sets rapidly after examination. And this could be said more generally with the S as well, though there is some degree of reinforcement there.
As things are, I feel that the timeline is askew, the won't if these institutions to produce biologists along the same timeline as they did a few decades ago is a little ridiculous considering the ballooning of quantitative discovery that has occured since, for instance, it wasn't so long ago that DNA was a conceptual exercise.
Moreover, the failure of education to keep with the times and adapt a realistic curricula for the modern era is also inhibitory. Indeed I would argue that the current academic zeitgeist is working against itself. At once being a trade program and while also trying to facilitate the development of "academia" itself are forces acting against one another. The number of premed students running the gauntlet in my program far outweigh the number of people with [let's say] legitimate interest in learning about the concepts in the program, which are also made to compete with the premeds in the limited slots available for lab internships. In my experience this leads to a chilling effect. Fortuitously, once in a lab things tend to be a little more facorable in terms of rapport.
delichon
I'm afraid that this is because academic math is often taught and tested in a way that rewards memorization rather than understanding. Here's Richard Feynman's take on the problem:
derbOac
I had a similar reaction. I had a lot of reactions, and found the paper interesting.
First, it reminded me of something a stats professor said in grad school: "there are two kinds of mathematicians, those who are good at arithmetic, and those who are not." He was speaking as someone who identified with the latter.
I can't tell if this is something related to this domain of math in particular or something broader. My guess is it's something broader.
I have colleagues (speaking as a professor) who have complained about admitted students who come in with very high grades and test scores, but who can't actually reason independently very well and despair when they are not "told exactly how to respond" on tests and whatnot. You have to be careful because sometimes these complaints hide bad teaching, but I think this is a common sentiment, and I've seen articles written about similar sentiments at other places.
The paper touches on a lot of issues, like applied versus abstract concepts, generalizability of learning, "being a good student" versus actual cognitive ability, learning how to take tests versus learning concepts, the difficulty of measuring cognitive and academic ability, and the fallibility of measuring complex human attributes in general.
1970-01-01
Feynman was correct for science in school, however arithmetic is fundamental and maybe one level above the root of all mathematics. Children should be able to do most of it via mental lookup tables and apply that knowledge on paper. For some reason, they can't.
almostgotcaught
i hate when people quote random celebrities as authoritative on any topic, let alone as a counterpoint to actual authorities (google the authors of this study).
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greentxt
"ask whether, in the urban Indian context, the arithmetic skills that are used in market transactions transfer to the more abstract maths skills taught in school."
I have a hard time with this notion of 2 different maths. I wonder if it is specific to the "urban Indian context" as the authors seem to suggest in their literature review -- I didn't pursue their references. Intuitive math that is not associated with memorization sounds like g.
peterprescott
This is really interesting, but I don't agree with this conclusion: "These findings highlight the importance of educational curricula that bridge the gap between intuitive and formal maths." (My own opinion is that educational curricula are generally not very important at all; that people are learning machines that learn what they need to in the contexts they find themselves; and that people -- as shown by this study -- struggle to effectively apply what they've learnt in one context into a different context.)
throwaway984393
[dead]
On the surface it's pretty obvious that classroom learning doesn't immediately translate to real world experience, but the paper's finding seems to be more about the extreme degree of discrepancy between the two cohorts. It almost feels like a comment on social class distinctions - there are children who get classroom educations that don't have to use it, while others have to use the skills but don't get the related education.