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Marvin Minsky: What makes mathematics hard to learn? (2008)

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Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#51

Post by chriscappuccio »

sergiosgc wrote: post #28
aout wrote: post #27

There is something quite interesting about the form of the article. While Mr Minsky talks about teaching using the "deck of cards method" and why it might not be the best approach if the child wants to advance to more complex subjects he also wants us to learn about his experiments (which are quite good!). Having read the article I find it well written but WHAT THE HELL?! Why doesn't he use pictures? simple diagrams?…

He doesn't use pictures because neither his target audience nor the subject matter require pictures. His target audience is composed of people who are interested in mathematics teaching (parents, teachers and such). He expects (correctly in my opinion) that these have handled and can handle long texts. The subject matter is an opinion piece without much underlying data, so graphical representation is not required. Th…

Amen.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#52

Post by toddan »

Not everyone can learn math. I my self had brilliant and great math tutors that my parents hired for me. I event went to special private math classes with brilliant math teachers and i tried to the best of my abilities to get good at it and pass the advanced math courses in highschool. Still i suck greatly at math and i always will.

I am very grateful for all the help my parents provided for me without it i would not pass even the first math classes in highschool.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#54

Post by qb45 »

fmap wrote: post #50

This is a wonderful series of articles and I find myself nodding along with most of it. However, these lines really made me cringe: A child was sent to me for tutoring because of failing a geometry class, and gave this excuse: " I must have been absent on the day when they explained how to prove a theorem." No wonder this child was confused—and seemed both amazed and relieved when I explained that there was no standa…

> I think interactive theorem provers would go a long way towards making children understand symbolic reasoning.

I can agree with that, but symbolic reasoning isn't everything. As shown by Gödel, you can't have symbolic system capable of proving every true fact about natural arithmetic without also proving some false "facts" about natural arithmetic.

The ultimate game doesn't have rules. On some level, math is just few pieces of meat speculating about abstract notions originating from and tied to their physical experience. Or something like that :)

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#55

Post by j2kun »

vdnkh wrote: post #44

"Why do some children find Math hard to learn? I suspect that this is often caused by starting with the practice and drill of a bunch of skills called Arithmetic—and instead of promoting inventiveness, we focus on preventing mistakes. I suspect that this negative emphasis leads many children not only to dislike Arithmetic, but also later to become averse to everything else that smells of technology. It might even lea…

To the contrary, don't most interview problems overemphasize inventiveness?

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#56

Post by j2kun »

crispyambulance wrote: post #42
kazinator wrote: post #38

While kids may find arithmetic to be boring and demotivating, they're able to do it. It's when math gets symbolic that you get the permanent attrition. For instance, most people never get to calculus. When you progress from arithmetic to abstract, it hardly gets easier . Moreover, memorizing. You go from memorizing multiplication tables to other kinds of tables, like tables of equations giving various identities, row…

Disagree. Kids disengage from math for many different reasons. There is no single pattern to it. If it were that simple, it would not have remained an issue since schools were commonplace. Minsky solidly makes the point that when math is taught as nothing more than an endless series of tedious drills with no purpose in sight, of course it demotivates kids. No one likes pointless Sisyphean tasks. Many students, howeve…

> Many students, however, "rediscover" math when they get to their first class that involves theorems and proofs (often in high-school geometry)

High school geometry (at least in the US, and in my experience) is the worst of them all! Two-column proofs should be banned.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#57

Post by j2kun »

toddan wrote: post #52

Not everyone can learn math. I my self had brilliant and great math tutors that my parents hired for me. I event went to special private math classes with brilliant math teachers and i tried to the best of my abilities to get good at it and pass the advanced math courses in highschool. Still i suck greatly at math and i always will. I am very grateful for all the help my parents provided for me without it i would not…

Barring an extremely small number of cases, this is not true by any means. The cognitive skills required to learn math are the same as the cognitive skills required to learn language. If you're interested in learning more about this, check out Keith Devlin's "The Math Gene" [1]

[1]: http://www.amazon.com/The-Math-Gene-Mathematical-Thinking/dp...

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#59

Post by kyled »

It's simple. If you're not passionate for a topic you're not going to care for it.

I hated math when I wasn't passionate about it. In school a lot of math classes were about route memorization, not going through or writing beautiful proofs.

Why don't they teach more abstract math in school? I love studying number theory and category theory.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#60

Post by nothis »

That old topic. Ironically, I find people who work with math (chosen to work with math, that is) to probably be quite unqualified to truly understand the problem. He opens by saying that learning avoiding mistakes before any bigger concepts is a major root of this but then again, people do make mistakes in math (even math professors) and it's a field where any mistake can completely invalidate the work. Also most people learn math for practical uses rather than as a science or field of research which also gives a different perspective (for most people, it's more important in life to not drop a zero when calculating a bill than it is to understand, say, a Homomorphism).

Math simply is hard. It goes against all our good-enough, subconscious brain functions we use every day to make basic "bigger or smaller" decisions. The problems mathematicians call "interesting" are counter-intuitive pretty much by definition and now imagine someone thinking like that writing a math book for children. The language used is vast and was built over literally millennia of mathematicians appending their own little modifiers above, below, and all around other mathematical symbols, resulting in monstrosities like the function for the Fourier Transformation which can actually be described quite intuitively geometrically.

Mathematicians want "simplicity" and "beauty" but their definition of either is absurdly different from any that would take into account basic human intuition. That's the problem. And there barely are any mathematicians that would admit that this could ever be a bad thing.

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