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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)

#11

Post by elementalest »

thomasahle wrote: post #2

> Anecdote: I asked a certain 6-year-old child “how much is 15 and 15”and she quickly answered, “I think it’s 30.” I asked how she figured that out so fast and she replied, “Well, everyone knows that 16 and 16 is 32, so then I subtracted the extra two 1’s.” Wait, is this girl some kind of base-2 native?

This is how i often work with things. I break them down into things that i know how to work with. I search my knowledge for elements that most closely represents the problems and then combine them.

For example, rather than remembering 12 * 6 = 72, i recall that 10 * 6 = 60 and 2 * 6 = 12, hence 60 + 12 = 72. I don't need to remember as many things and for me i can do that much faster than trying to recall it.

My memory has never been very good, so perhaps this is why i take such an approach, as i find it overall easier.

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

#13

Post by adrianN »

libeclipse wrote: post #8

He makes a really good point about traditional teaching methods. What's the point with the obsession over 'the correct method'? If the answer is correct, and the method in question can reliably reach the correct answer, in my opinion, the correct method is that one, and it differs from person to person.

The correct method might be the method that scales better. Counting on your fingers for example is a pretty decent method to add until you reach bigger numbers. If you don't use the more complicated methods, you'll never improved past some point.

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

#14

Post by Retric »

elementalest wrote: post #11
thomasahle wrote: post #2

> Anecdote: I asked a certain 6-year-old child “how much is 15 and 15”and she quickly answered, “I think it’s 30.” I asked how she figured that out so fast and she replied, “Well, everyone knows that 16 and 16 is 32, so then I subtracted the extra two 1’s.” Wait, is this girl some kind of base-2 native?

This is how i often work with things. I break them down into things that i know how to work with. I search my knowledge for elements that most closely represents the problems and then combine them. For example, rather than remembering 12 * 6 = 72, i recall that 10 * 6 = 60 and 2 * 6 = 12, hence 60 + 12 = 72. I don't need to remember as many things and for me i can do that much faster than trying to recall it. My memo…

* is a special character on HN you want to have spaces between 12 * 6 or it can look like: 126 106.

Note: it works in pairs so the final 2*6 shows up.

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

#15

Post by agumonkey »

elementalest wrote: post #11
thomasahle wrote: post #2

> Anecdote: I asked a certain 6-year-old child “how much is 15 and 15”and she quickly answered, “I think it’s 30.” I asked how she figured that out so fast and she replied, “Well, everyone knows that 16 and 16 is 32, so then I subtracted the extra two 1’s.” Wait, is this girl some kind of base-2 native?

This is how i often work with things. I break them down into things that i know how to work with. I search my knowledge for elements that most closely represents the problems and then combine them. For example, rather than remembering 12 * 6 = 72, i recall that 10 * 6 = 60 and 2 * 6 = 12, hence 60 + 12 = 72. I don't need to remember as many things and for me i can do that much faster than trying to recall it. My memo…

That's how I felt about math for a long time. The so-called good laziness. You don't bother doing the hard way, you search for tricks. Symmetries, difference from simple cases as the girl did.

Instead of memorizing algorithms, kids should be shown this. It's free gamification and, after some years, I believe it's a core idea of what is, and why math can be pleasing.

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

#16

Post by gambiting »

" This child imagined ‘Math’ to be a continuous string of mechanical tasks—an unending prospect of practice and drill. It was hard to convince him that there would not be any more tables in subsequent years"

Well, I enjoy maths, but for me my entire mathematical education was always about memorizing tables. It was made worse by the fact that during Polish exams you cannot use advanced calculators(only ones that can do addition/multiplication) so for the final exams at the age of 19 I had to remember loads of different formulas, trigonometric values for common angles etc etc.

I'm not saying he was wrong, but in a lot of educational systems maths is 90% about remembering stuff.

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

#17

Post by graycat »

Solution: For the students, answer "Why should I learn this?" and, then, give good intuitive explanations for basically how it all works from algebra, geometry, trigonometry, and calculus to probability, statistics, functional analysis, and more. For the intuition, do include pictures.

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

#19

Post by elementalest »

Retric wrote: post #14
elementalest wrote: post #11

Earlier quoted context omitted.

This is how i often work with things. I break them down into things that i know how to work with. I search my knowledge for elements that most closely represents the problems and then combine them. For example, rather than remembering 12 * 6 = 72, i recall that 10 * 6 = 60 and 2 * 6 = 12, hence 60 + 12 = 72. I don't need to remember as many things and for me i can do that much faster than trying to recall it. My memo…

* is a special character on HN you want to have spaces between 12 * 6 or it can look like: 12 6 10 6. Note: it works in pairs so the final 2*6 shows up.

Ah, thanks :D

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

#20

Post by 746F7475 »

qb45 wrote: post #6
746F7475 wrote: post #4

Earlier quoted context omitted.

It might "just" (not to be little it) be shortcut she has learned, I also used tons of my own shortcuts for answers when I was smaller (read: used to not use calculator). I could do smaller calculations like that fast and when my parents asked how I came up with them and when I answered they didn't believe me.

I think parent wondered how it's possible that she remembered 16+16=32. Children raised on positional decimal arithmetic are "supposed" to figure that 10+10=20 or 20+20=40 and then add/subtract 5+5. Of course it's easier to associate 15 with 16 than with 10 or 20, but the fact that she immediately knew 2·16 and was able to proceed further says something about either her experience with binary arithmetic or some tende…

I don't know, I always remembered things like 6+7 = 13 and if numbers I was adding were close to 6 and 7 I knew instantly how to proceed. Of course there's other tricks like, subtracting the 1 out of 6 to get 5 and then adding it to 7 making 8 then removing the 5 to get 10 with the other 5 and you are left with 10 and 3 which is easy, I guess.

At least for me it was just silly shortcuts that stuck with me like 6+7=13 or 7*7=49. Maybe why I'm little fixated to 7 is that 5 and below is easy, but with 6 and up things get little more "math-y", so with some quick shortcuts like these it's easy to adjust to 7. Or most likely I'm just full of shit, that is usually the case.

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