sketerpot comments on Open Thread June 2010, Part 4 - Less Wrong

5 Post author: Will_Newsome 19 June 2010 04:34AM

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Comment author: sketerpot 21 June 2010 05:02:11AM *  3 points [-]

Well above average mathematical ability and cannot do calculus to the extent of understanding rates of change? For crying out loud.

People get the simple concepts mixed together with a bunch of mathy-looking symbols and equations, and it all congeals into an undifferentiated mass of confusing math. Yes, I know calculus is actually pretty straightforward, but we're probably not a representative sample. Talk with random bewildered college freshmen to combat sample bias. I did this, and what I learned is that most people have serious trouble learning calculus.

Now, if you want to be able to partially understand a bunch of physics stuff but you don't necessarily need to be able to do the math, you could probably get away with a small subset of what people learn in calculus classes. If you learned about integration and differentiation (but not how to do them symbolically), as well as vectors, vector fields, and divergence and curl, then you could probably get more benefit-per-hour-of-study than if you went and learned calculus properly. It leaves a bad taste in my mouth, though.

Comment author: wedrifid 21 June 2010 06:52:59AM 2 points [-]

what I learned is that most people have serious trouble learning calculus.

When taught well the calculus required for the sort of applications you mentioned is not something that causes significant trouble, certainly not compared to vector fields, divergence or curl. By taught well, if you will excuse my lack of seemly modesty, is how I taught it in my (extremely brief - don't let me get started on what I think of western school systems) stint teaching high school physics. The biggest problem for people learning basic calculus is that people teaching it try to convey that it is hard.

I'm only talking here about the level of stuff required for everyday physics. Definitely not for the vast majority of calculus that we try to teach them.

Comment author: Emile 21 June 2010 08:57:32AM 0 points [-]

don't let me get started on what I think of western school systems

Aw, please ? I'd be interested in hearing about the differences with other systems :)

Comment author: wedrifid 21 June 2010 10:25:32AM *  7 points [-]

It has been said that democracy is the worst form of government except all the others that have been tried. --Sir Winston Churchill

I'm not quite going to make that analogy but I will hasten to assert that there are far worse systems of education than ours. Including some that are 'like ours but magnified".

In terms of healthy psychological development and practical skill acquisition the apprenticeship systems of various cultures have been better. Right now I can refer to the school system on one of the Solomon Islands. The culture is that of a primitive coastal village but with western influences. Western teaching materials and a teacher are provided but occurs in the morning for 4 hours a day. No breaks are needed and nor is any pointless time wasting. The children then spend their time surfing. But they surf carrying spears and catch fish while they are doing it.

What appeals to me about that system is:

  • The shorter time period.
    • Most of the time kids spend at school is a blatant waste. in particular, in the youngest years a lot of what the kids are doing is 'growing older'. That is what is required for their brains to handle the next critical learning skills.
    • Much more than 4 hours a day of learning is squandered on diminishing returns. The Cambridge Handbook of Expertise and Expert Performance suggests that 4 hours per day of deliberate practice (7 days a week for 10 years) is a good approximate guide for how to gain world-class expert level performance in a field. It is remarkably stable across many domains.
  • The children's social lives are not dominated by playground politics and are not essentially limited to same age peers.
  • Not only are the extracurricular activities physically healthier than more time wasted in classes they are better for brain development too. What is the formula for increased release of and optimized attention control and cognitive performance? Aerobic exercise + activities requiring extensive coordination + a healthy diet including adequate Omega-3 intake. That's right. Spending hours swimming, surfing and catching fish with spears is just about perfect.
Comment author: SilasBarta 21 June 2010 09:03:50PM 1 point [-]

I agree, and this is a tragedy in that it makes it so students don't have marketable skill by 14 as they would in an apprentice system, and so are dependent on mommy and daddy. This "age of genuine independence from parents" is increasing all the time, and there's no excuse for it. It disenfrachises children more than any legal age restrictions on this or that.

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