Well I have a different approach. Sometimes I write and hack it to solve a particular problem. The code might be elegant or not, but if you understand the problem you can probably grok the code.
Next I generalize it a bit. Specific variables configurable parameters. Something that happened implicitly or with a single line of code gets handled by its own function. Now it’s general but makes much less sense at first because it’s no longer tied to one problem, but a whole set of problems. It’s a lot less teachable and certainly not self-evident any more.
The problem with math education is that we think the solution approach would be inherently superior to the first, and would make a better textbook—because it’s more generic. But that is not how real people learn—they would all “do” math the first way. By taking away the ability of the student to do the generalization themselves we are depriving them of the real pleasure of programming (or math).
Maybe back when paper was scarce this approach made sense but not any more.
Ideally I would love to present a million specific solutions and let them generalize themselves. That is exactly how we would train a ANN. Not be regurgitating the canned solution but by giving it all sorts of data and letting it generalize for itself. So why don’t we do this for human students? When it comes to education I think people have a blind spot towards how learning is actually done.
Well I have a different approach. Sometimes I write and hack it to solve a particular problem. The code might be elegant or not, but if you understand the problem you can probably grok the code.
Next I generalize it a bit. Specific variables configurable parameters. Something that happened implicitly or with a single line of code gets handled by its own function. Now it’s general but makes much less sense at first because it’s no longer tied to one problem, but a whole set of problems. It’s a lot less teachable and certainly not self-evident any more.
The problem with math education is that we think the solution approach would be inherently superior to the first, and would make a better textbook—because it’s more generic. But that is not how real people learn—they would all “do” math the first way. By taking away the ability of the student to do the generalization themselves we are depriving them of the real pleasure of programming (or math).
Maybe back when paper was scarce this approach made sense but not any more.
Ideally I would love to present a million specific solutions and let them generalize themselves. That is exactly how we would train a ANN. Not be regurgitating the canned solution but by giving it all sorts of data and letting it generalize for itself. So why don’t we do this for human students? When it comes to education I think people have a blind spot towards how learning is actually done.
Education != learning.