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Memorizing things like SOHCAHTOA and FOIL may not be a vital life skill for everyone, but everyone can benefit from the base logical thinking required to identi

Memorizing things like SOHCAHTOA and FOIL may not be a vital life skill for everyone, but everyone can benefit from the base logical thinking required to identify a variable, break a problem down into steps, plan and execute a solution. At a bare minimum, the basics of algebra (and to a lesser extent precalc, such as understanding limits and differentials) foster a type of abstract thinking and skills that pretty much anyone can benefit from.

theGnuMe 4y ago
Except that the traditional way of teaching the subject does not reason from first principles which is what you are advocating. The new math stuff does... I think parents hate it cause we don't understand it and it screws up the college pipeline. To illustrate my point of the uselessness of our conventional mathematical training. ChatGPT gets a 700 out of 800 on the SAT Math section, but ask ChatGPT a reasoning question that requires math... it can't do it. That shows you just how useless the SAT actually is except for training kids to pattern match.
- ekidd 4y ago
  ChatGPT 4's math abilities are really hit or miss. I asked it to act as a "Socratic tutor" for the de-biasing terms in exponential moving averages. And it walked me through the problem, and it actually pointed out errors in my derivation (even though I was using a half-baked mix of Unicode and LaTeX). That was honestly pretty impressive. On the other hand, GPT 3.5 is painfully bad at basic arithmetic. Apparently it can add long numbers, but you actually need to explain the addition algorithm and give it some examples. Then it can walk through the process step by step, just like an elementary school student. In a lot of cases, I suspect ChatGPT 4 is pulling from a tiny corner of the training distribution. It has seen most of the web, and it doesn't need to see things often to talk about them. I've seen it successfully summarize the contents of obscure personal blogs, or of a very minor news story that was current for a week in 2009. So it wouldn't surprise me if GPT 4 performs well on tasks that are mentioned on a half dozen obscure web pages, or something like that.
brnaftr361 4y ago
Can you define what you mean by abstract thinking skills? Everything else you've listed can be acquired as a dishwasher or a line cook. Anyways, the classes always seemed to me to tend more towards shut up and calculate than they did building a robust understanding and perhaps most important of it all: a mathematical intuition. I always found it profoundly stupid that there were never any essay questions in math, I expect those who elect to teach the subject are often wont to expediency (which would explain the number of coaches in the department) rather than an inclination towards the subject itself.
- yellowcake0 4y ago
  During graduate school I interacted with academics working in math education who felt similarly, that math should be taught through essay questions, e.g. "explain the concept of a limit", and the like. I've always felt it was a deeply misguided pedagogy and I hope it does not become popular. Solving well crafted exercises requires a deep understanding of the material, it's unnecessary to check understanding in some other way.
  - brnaftr361 4y ago
    Well for one it's prompting you to make a meaningful linguistic exercise of the matter, which is at once a creative task and secondly it enforces a more dynamic approach to whatever problem is presented. I wonder if you could get a professor to do anything more than plug and chug, and that's a skill we've long ago delegated to glass. Not only do I want to explain these things in my mother tongue, I expect to know why some variable is in some such place, and how a cube of some other variable is related to the problem at hand. Calculation is banal.
- zdragnar 4y ago
  I grew up in the midwest US, and what we called "word problems" were a pretty common component to learning (classes), practicing (homework) and verification (testing). The one that stuck with me is the explanation of how speedometers and police radars actually calculate speed using derivatives in pre/entry calculus. We also learned to write very basic proofs. I would consider both of these to be the essay equivalent of mathematics. Students who didn't show an interest in higher maths courses either took slower versions of the earlier courses where they could get more time with the material, or more business oriented maths such as basic statistics and accounting. AP Calculus was the closest I experienced to "shut up and calculate", if only because our teacher somehow managed to get behind the lesson plan in our first week and we ended up doing homework for lessons the night before the class where she would actually explain it. That was the second most brutal experience of my academic career, only after the semester in college where I was taking a macro economics course taught by a Polish grad student and a micro econ course taught by a Greek grad student; neither of them pronounced things (especially, and perhaps obviously, the greek letters in equations) the same way, and it turned into a nightmare keeping things straight.

theGnuMe 4y ago

Except that the traditional way of teaching the subject does not reason from first principles which is what you are advocating. The new math stuff does... I think parents hate it cause we don't understand it and it screws up the college pipeline. To illustrate my point of the uselessness of our conventional mathematical training. ChatGPT gets a 700 out of 800 on the SAT Math section, but ask ChatGPT a reasoning question that requires math... it can't do it. That shows you just how useless the SAT actually is except for training kids to pattern match.

ekidd 4y ago
ChatGPT 4's math abilities are really hit or miss. I asked it to act as a "Socratic tutor" for the de-biasing terms in exponential moving averages. And it walked me through the problem, and it actually pointed out errors in my derivation (even though I was using a half-baked mix of Unicode and LaTeX). That was honestly pretty impressive. On the other hand, GPT 3.5 is painfully bad at basic arithmetic. Apparently it can add long numbers, but you actually need to explain the addition algorithm and give it some examples. Then it can walk through the process step by step, just like an elementary school student. In a lot of cases, I suspect ChatGPT 4 is pulling from a tiny corner of the training distribution. It has seen most of the web, and it doesn't need to see things often to talk about them. I've seen it successfully summarize the contents of obscure personal blogs, or of a very minor news story that was current for a week in 2009. So it wouldn't surprise me if GPT 4 performs well on tasks that are mentioned on a half dozen obscure web pages, or something like that.

brnaftr361 4y ago

Can you define what you mean by abstract thinking skills? Everything else you've listed can be acquired as a dishwasher or a line cook. Anyways, the classes always seemed to me to tend more towards shut up and calculate than they did building a robust understanding and perhaps most important of it all: a mathematical intuition. I always found it profoundly stupid that there were never any essay questions in math, I expect those who elect to teach the subject are often wont to expediency (which would explain the number of coaches in the department) rather than an inclination towards the subject itself.

yellowcake0 4y ago
During graduate school I interacted with academics working in math education who felt similarly, that math should be taught through essay questions, e.g. "explain the concept of a limit", and the like. I've always felt it was a deeply misguided pedagogy and I hope it does not become popular. Solving well crafted exercises requires a deep understanding of the material, it's unnecessary to check understanding in some other way.
- brnaftr361 4y ago
  Well for one it's prompting you to make a meaningful linguistic exercise of the matter, which is at once a creative task and secondly it enforces a more dynamic approach to whatever problem is presented. I wonder if you could get a professor to do anything more than plug and chug, and that's a skill we've long ago delegated to glass. Not only do I want to explain these things in my mother tongue, I expect to know why some variable is in some such place, and how a cube of some other variable is related to the problem at hand. Calculation is banal.
zdragnar 4y ago
I grew up in the midwest US, and what we called "word problems" were a pretty common component to learning (classes), practicing (homework) and verification (testing). The one that stuck with me is the explanation of how speedometers and police radars actually calculate speed using derivatives in pre/entry calculus. We also learned to write very basic proofs. I would consider both of these to be the essay equivalent of mathematics. Students who didn't show an interest in higher maths courses either took slower versions of the earlier courses where they could get more time with the material, or more business oriented maths such as basic statistics and accounting. AP Calculus was the closest I experienced to "shut up and calculate", if only because our teacher somehow managed to get behind the lesson plan in our first week and we ended up doing homework for lessons the night before the class where she would actually explain it. That was the second most brutal experience of my academic career, only after the semester in college where I was taking a macro economics course taught by a Polish grad student and a micro econ course taught by a Greek grad student; neither of them pronounced things (especially, and perhaps obviously, the greek letters in equations) the same way, and it turned into a nightmare keeping things straight.