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Everyone is capable of, and can benefit from, mathematical thinking

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Re: Everyone is capable of, and can benefit from, mathematical thinking

#141

Post by yimmothathird »

thefaux wrote: post #17
benreesman wrote: post #2

I’m far from being any kind of serious mathematician, but I’ve learned more in the last couple years of taking that seriously as an ambition than in decades of relegating myself to inferiority on it. One of the highly generous mentors who dragged me kicking and screaming into the world of even making an attempt told me: “There are no bad math students. There are only bad math teachers who themselves had bad math teac…

Sadly, when I was a postdoc, an eminent mathematician I was working under once shared a story that he found amusing that one of his colleagues was once asked a question in the form: "This might be a stupid question, but..." and the response was "There are no stupid questions, only stupid people." Run into too many people like that, who I daresay are common in the field, and it's easy to see how people become dispirit…

[dead]

Re: Everyone is capable of, and can benefit from, mathematical thinking

#142

Post by benreesman »

ckw wrote: post #129
thefaux wrote: post #17

Earlier quoted context omitted.

Sadly, when I was a postdoc, an eminent mathematician I was working under once shared a story that he found amusing that one of his colleagues was once asked a question in the form: "This might be a stupid question, but..." and the response was "There are no stupid questions, only stupid people." Run into too many people like that, who I daresay are common in the field, and it's easy to see how people become dispirit…

That’s a south park quote: https://youtu.be/wWfacULP1o0?si=ddBWXFuQMoxxY-Yu

That was a belly laugh on a tough day.

Thank you Sir or Madame.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#144

Post by bmitc »

penguin_booze wrote: post #139

To my mind, the premature formalization of the math is the principal contributor to gas lighting and alienation of people from maths. The reduction of concepts to symbols and manipulation thereof, is an afterthought. It's misguided for them to be introduced to people right at the outset. People need to speak in plain English [0]. To some mathematicians' assertion that English is not precise enough, I say, take a hike…

What does premature formalization mean and when does it occur? Do you mean formal in the sense of using formulaic, rote manipulations or formal in the sense of proofs and rigor?

As someone who went on to study mathematics at the graduate level, I was bored out of my mind in high school math and most subjects. What's missing from a lot of primary and secondary school education is context, and that's what makes it boring. Math wasn't easy because I was particularly good at it. It was easy because it was just blindly following formulas and basic logic.

Something is very wrong with our educational system because almost all math at the primary and secondary levels is basic logic. So when people with this maximum level of mathematics education say they're "bad at math" or "don't get math", it means that they lack extremely basic logic and reasoning skills.

In my mind, we need to teach mathematics in a contextual way (note that I don't necessarily mean applications) in a way to enrich the reasoning and exploring of it. This should include applications, yes, but not be fully concentrated on applications. Sometimes one needs to just learn and think without being tied to some arbitrary standard of it being applied.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#145

Post by bmitc »

jajko wrote: post #78
ggm wrote: post #69

I want to say yes, but I have two counters. One is that math nerds at school insisted on intimidating for the win and I just hated it. The second is notation. I had a snob teacher who insisted on using Newton not Leibniz and at school in the 1970s this is just fucked. One term of weirdness contradicting what everyone else in the field did. Likewise failure to explain notation, it's hazing behaviour. So yes, everyone…

> One is that math nerds at school insisted on intimidating for the win and I just hated it. Only an adult can look and see what that was - immature, insecure little boys, desperately trying to show off as bigger/more mature or kick down anybody showing any weakness or mistake. Often issues from home manifesting hard. Its trivial to look back without emotions, but going through it... not so much. If my kids ever go t…

> Only an adult can look and see what that was - immature, insecure little boys, desperately trying to show off as bigger/more mature or kick down anybody showing any weakness or mistake. Often issues from home manifesting hard. Its trivial to look back without emotions, but going through it... not so much.

I'm not so sure that adults always get it or rise about this. This happens in the workplace all the time.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#146

Post by llm_trw »

penguin_booze wrote: post #139

To my mind, the premature formalization of the math is the principal contributor to gas lighting and alienation of people from maths. The reduction of concepts to symbols and manipulation thereof, is an afterthought. It's misguided for them to be introduced to people right at the outset. People need to speak in plain English [0]. To some mathematicians' assertion that English is not precise enough, I say, take a hike…

Mathematics is the conversion of a large number of object languages in to a single meta language that lets us talk about all of them.

The sin of modern mathematics is that it's meta language is so ill define that you need towers of software to manipulate it without contradiction. Rewriting all of it into s-expressions with a term rewriting system for proofs under a sequent calculus is an excellent first step to making it accessible.

We do not need to go back to the 16th century when men were men, an numbers positive. If people want to look at what math talks about instead of how it talks about let them pick up stamp collecting.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#147

Post by chipdart »

tgv wrote: post #121
gsabo wrote: post #15

I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…

I cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains. I've taught math to psychology students, and they just don't…

> cannot agree. It's just "feel-good thinking."

Not really. There's nothing inherently special about people who dedicated enough time to learn a subject.

> "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained.

What a bad comparison. So far in human history there were less than 200 people who ran 100m in less than 10s.

I think you're just reflecting an inflated sense of self worth.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#148

Post by llm_trw »

tgv wrote: post #121
gsabo wrote: post #15

I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…

I cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains. I've taught math to psychology students, and they just don't…

There's a difference between being able to memorize what a square root is and being able to do math - which to mathematicians means being able to organize a proof.

I've found that the people who most believe in math being a genetic ability are the ones who do not work in the symbolic world of modern math, but in the semantic world of whatever the field the math describes is.

The two are rather different.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#149

Post by llm_trw »

khafra wrote: post #54
gsabo wrote: post #15

I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…

> If it's easy, then it means you already know this material, and you're wasting your time. One thing I'm anticipating from LLM-based tutoring is an adaptive test that locates someone's frontier of knowledge, and plots an efficient route toward any capability goal through the required intermediate skills. Trying to find the places where math starts getting difficult by skimming through textbooks takes too long; espec…

>and plots an efficient route toward any capability goal through the required intermediate skills.

LLMs currently can't find efficient paths longer than 5 hops when given a simple itinerary. Expecting them to do anything but a tactical explanation of issues they have seen in training is extremely naive with something as high dimensional as math.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#150

Post by LoganDark »

sethammons wrote: post #120
LoganDark wrote: post #105

Earlier quoted context omitted.

Natural selection doesn't care about cost or advantage, only reproduction.

It is the sum of costs and advantages that lead to reproductive success. The trait is still here and still prevalent meaning people are still getting laid and starting families and presumably leading fulfilling lives. I'm not sure what you are trying to say.

> I'm not sure what you are trying to say.

I'm saying, if it doesn't ruin lives to the point of preventing reproduction, then it stays in the gene pool.

Basically, I'm saying this:

> The trait is still here and still prevalent meaning people are still getting laid and starting families and presumably leading fulfilling lives.

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