

Marvin Minsky: What makes Mathematics hard to learn? - hhm
http://wiki.laptop.org/go/Marvin_Minsky#What_makes_Mathematics_hard_to_learn.3F

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Prrometheus
I enjoy this kind of thoughtful exposition on teaching methods in mathematics;
I’ve read several here over the last few days.

This kind of essay attempts to answer the question “How should math be
taught?” or at least “How can math be taught better?”. However, another
question always weighs heavier on my mind: “How should the process of teaching
be designed in order to give incentive for teachers to use the best
instruction methods available?” After all, I doubt that Minsky’s ideas will be
adopted nationwide by the NEA, for all their merit.

It would be shortsighted to lobby for a new curriculum or for a few idealistic
young folks to enter the teaching profession to implement these ideas. Long
term improvement can only be gained by addressing the incentives facing those
in control of the teaching process.

Technology gives students an additional source of instruction that they did
not have before. It may be that society uses technology to route around the
stagnant educational bureaucracy like a body routing nerve signals around a
brain lesion. Minsky is involved in this technological solution, and it may
ultimately prove to be the fastest moving and most effective method of change.
Thousands of students will read articles like Minsky’s on the internet, and
they will know that there are better things waiting for them after government
school.

Also, I am a strong supporter of school choice. For their faults, the
incentives faced by instructors in a market are an order of magnitude better
than the incentives faced by instructors in a modern school bureaucracy.I
would rather have educators competing to please their ultimate customers than
have them competing for a higher bureaucrat’s favor.

However, I rarely find smart people willing to grapple with this higher-order
problem unless they have a background in economics. Geeks need to learn that
they can’t hack society unless they understand and comprehend the structures
surrounding the problem that they wish to solve.

~~~
pchristensen
"...I rarely find smart people willing to grapple with this higher-order
problem unless they have a background in economics"

Interesting. I recently came to the same conclusion (for myself anyways) - my
thinking became a lot bigger after reading (addmittedly pop-)economics books
like Freakonomics, Hidden Order (the better of the two IMHO), etc. It's not
perfect, but I have yet to see a better explanation than the utility-
maximizing principle (I made up that name but you get the idea). The key is to
remember that all utility is not created equal, and that there are diminishing
returns. (sorry, rambling)

~~~
jsmcgd
Seconded. I recently read 'The Undercover Economist'. I kept thinking that
everyone in every field needs some grasp of basic economics.

~~~
pchristensen
That was the third book that I was trying to remember but it became "etc".
Thanks! I also highly recommend it.

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giardini
In the case of the multiplication tables, Minsky missed an opportunity to
point out to the child that the product (a x b) of any two numbers in the
multiplication table can also be obtained by _counting_ the number of items in
the multiplication table bound by the rectangle of height a and of width b.
That would have provided additional motivation and insight into solving other
problems (e.g., area).

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comatose_kid
"Out of the Labrynth: Setting mathematics free" is a great book which touches
on these issues in more detail. It is written by creators of the Math Circle
idea of teaching children math (www.themathcircle.org).

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henning
Because it takes a genius to explain it in the simplest, clearest way
possible.

~~~
hhm
I "half" agree. It doesn't take a genius, but it surely takes a lot of effort,
intention and of course, some intelligence too. Without those, there is no way
you can teach maths, or history or anything else without making them boring
and stupid.

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fgb
Math is hard? Since when? ;-)

