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Comment by andreyf | Hacker News Reader

It's not a teachers job to teach "smart".

Yes it is, by definition. Once people are "smart", in the Feynman sense, there's no need for anyone to teach them a subject - they're self-motivated learners that will seek them out on their own.

You learn the basic facts (or processes), you learn to apply them in simple situations, and you learn to apply them creatively.

Although somehow intuitive, I don't think that's a good model. What are "basic facts"? What is a "simple situation"? What does it mean to "apply facts creatively"? All of these are vaguely intuitive but not well defined, with no epistemological basis. There is a much better definition of learning - the ability to create models of our experiences, test, and refine them. I know of no reason a cheap test can't be devised to test such learning, nor of any attempts to create one.

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We seem to be at loggerheads on two points.

1 - I'm focusing on basic proficiency (a bottom up approach - you learn the basics then the hard stuff is easy), you are focusing on learning through break-through discoveries (the top-down approach). (I may be creating a false hierarchy, but I'm going to run with it).

2 - I am focusing on teachers directly teaching students, while you focus on teaching students to be self-motivated learners.

Now, I can't think of any way to teach self-motivated break-through learning. The closest thing I can think of is to make subjects interesting (getting teachers who are enthusiastic about the subject, and providing interesting text books (yeah-right)), and give the students free time to pursue their own interests (which is why I half-jokingly suggested outlawing homework). The other model I've seen (don't teach properly so students have to learn) seems a little perverse to me.

(oh, the basic facts -> simple application -> creative use? Fact - past tense. Simple application - what did Spot do? Creative (or complex) use - Why did Spot do it?)

Look up Montessori.

You're right about #1: reading, writing, and counting. But I think it stops there.

Addition and multiplication can easily be self-discovered, and, if they are, expanded to exponentiation, tetration, and Knuth's up-arrow notation [1]. The recursive relationship between x+...+x, x...x, x^...^x, etc isn't beyond most kid's minds.

Regarding #2, again, let's not be vague. Let's define teaching as creating motivation to learn - through grades, or social rewards, or whatever. Let's define "learning" as the acquisition of models. Using this model, the role of a "great teacher" becomes obvious - it isn't transplanting a models from one mind to another, but motivating the creation and evaluation of one's own models.

I'm glad you brought up "past tense" as an example of a "fact". I'll agree that we have a common experience of time (and hence, "the past"), but will note that communicating about past events is innate (no need to learn it). However modeling verbs as "past tense" or "future tense" is a trivial linguistic model - a intuitively comfortable model, but without much evidence - incapable of describing reality - in this case, our innate abilities for language.

1. http://en.wikipedia.org/wiki/Knuths_up-arrow_notation

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