Marvin Minsky: What makes Mathematics hard to learn?(wiki.laptop.org)
wiki.laptop.org
Marvin Minsky: What makes Mathematics hard to learn?
http://wiki.laptop.org/go/Marvin_Minsky#What_makes_Mathematics_hard_to_learn.3F
10 comments
Looking at the systemic failures of the US education system leaves me unable to see a viable route to a high functioning system[1]. This leaves me wondering, when I have children, how to deal with educating them when even the very best private OR public schools have to conform to a very broken system, and when home schooling might even be illegal.
The only solid answer I can come up with is to move, though I am not sure where to. I live in Tokyo right now, but the school system there is even worse.
On a different note, I was surprised that Minsky makes the mistake of suggesting that it is a positive thing that subjects other than math are taught by bombarding students with tons of new words to remember (names, dates, etc), saying "[in other areas] each pupil learns hundreds of new words in every term. You learn the names of many countries and organizations, the names of leaders and battles and wars"
The students by and large "learn" these useless data points one week, regurgitate them for the test, and then forget them when the testing is over. We would do far better to teach people to think for themselves, to analyze information as it comes at them, and to focus, in as much as we really want them to remember history, on the relation of people and events as a narrative story, rather than obsessing on meaningless dates.
[1] world-leading in meaningful terms, not just learned-knowledge tests.
The only solid answer I can come up with is to move, though I am not sure where to. I live in Tokyo right now, but the school system there is even worse.
On a different note, I was surprised that Minsky makes the mistake of suggesting that it is a positive thing that subjects other than math are taught by bombarding students with tons of new words to remember (names, dates, etc), saying "[in other areas] each pupil learns hundreds of new words in every term. You learn the names of many countries and organizations, the names of leaders and battles and wars"
The students by and large "learn" these useless data points one week, regurgitate them for the test, and then forget them when the testing is over. We would do far better to teach people to think for themselves, to analyze information as it comes at them, and to focus, in as much as we really want them to remember history, on the relation of people and events as a narrative story, rather than obsessing on meaningless dates.
[1] world-leading in meaningful terms, not just learned-knowledge tests.
"...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)
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)
Seconded. I recently read 'The Undercover Economist'. I kept thinking that everyone in every field needs some grasp of basic economics.
That was the third book that I was trying to remember but it became "etc". Thanks! I also highly recommend it.
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).
"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).
Because it takes a genius to explain it in the simplest, clearest way possible.
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.
Math is hard? Since when? ;-)
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.