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Comment by nitrogen | Hacker News Reader

I disagree with this traditional pedagogical approach. Learning is much easier when motivated by a complex problem to solve that requires learning and applying multiple "building block" concepts. Start big, then learn small.

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It seems counter-intuitive, but I've found that this works for me also. For example, I could never learn basic mathematical concepts until I had seem them in action as a part of a larger framework or practical problem.

For example, differentiation by itself is just pushing symbols around according to some arbitrary-seeming rules. It's not until I did physics that its purpose made sense. I studied calculus for years, and it never "clicked" for me, and I forgot most of it promptly. Then in just a semester of physics where I was applying it in the context of complicated problems, it suddenly felt like second-nature. I had to basically re-learn all of it from scratch, but with the context of my physics problems it was so easy!

I've had similar experiences teaching programming to junior staff. Anything you talk about in isolation goes in one ear and out the other. They have to encounter the problem in something larger that they are solving for the solution to make sense and motivate them to learn.

An example is string-escaping. E.g.: how do you represent the quote symbol in a quoted string? This seems trivial, but it trips up everyone when they are getting started. I mean literally everyone. So okay, I make sure to cover it in like... lesson #1 or #2 because string literals are everywhere, and escaping is common. Every single time, the people that sat through that lesson will ask me a week later to help me fix as program that has a literal like 'O'Brian' in it, and they can't figure out why it's broken. But once I show them that they should have used 'O''Brian' or 'O\'Brian', it all makes sense to them and they memorise the technique.

Yes. I always found it odd, especially in mathematical textbooks, but to some degree also other areas, when a field is explained top down from a theory that is the end result of hundreds of years of discovery, fiddling and trial and error. As if that whole theory was god given and just happened without motivation or process. Besides making it harder to understand by going abstract idea first, it also makes it harder to develop an understanding for how people come up with and improve ideas over time.

About 20 years ago I read a book on spread spectrum radio. Unlike all the others each chapter was in three parts. The first part explained the problem. The things people tried to solve it. Problems with those solutions. And then second part explained the canonical solution, how it solved issues. The third was a formal description and analysis

That book was totally great. Even if you got lost in the math reading the last formal part you understood what was going on.

Do you remember the name of the book and the author?

It makes complete sense for mathematics. Few of the mathematicians I know have any interest in applying math to much of anything besides math research. The whole business is entirely abstract.

I dont see how it is easier. Maybe it is motivating for someone, but I never found it easier to deal with complex problems first and only then moving to simple one. For me, it was easier to learn simple things first. And "do simple thing first" also seems to work much better at my kids, no matter what I am teaching them.

I find it motivating to have the story of how someone uses the skill to solve a complex real-world problem. I think you are right that it is overwhelming to start out by solving that complex large-scope problem first.

Absolutely, but that's a framing device/motivational aspect, rather than the mechanics of the actual learning.

"Here's what we're aiming for, and here's why it matters" should be the introduction, setting the scene and establishing the flow, but then you introduce the various blocks-that-will-be-built and start working up to them in the stepped fashion.

I think the missing link is going from a real world application to a practical teaching problem. A topic that motivates an audience would also depend on the audience.

Trying to think of a good example reminds me of a puzzle game; and how sometimes the contrived puzzles in such games can be obtuse or phrased poorly because they really don't want to give away the answer.

The example should start with an unsolvable problem, then simplify aspects to make it more of an estimation model; which is a useful skill as well.

That requires for the person to actually care about the complex problem, otherwise they'll ignore it and focus on the the individual building blocks in isolation.

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