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> Abstraction makes the mechanics of solving a problem orthogonal to the specifics. Not sure what you mean. Providing context does not change underlying math o
by adam_arthur 6y ago
> Abstraction makes the mechanics of solving a problem orthogonal to the specifics.
Not sure what you mean. Providing context does not change underlying math or mechanics of solving the problem at all. Just the same as if you asked somebody to solve FizzBuzz or BeepBoop.
What it does is make the rote exercise of solving more meaningful and relatable. Things that are relatable tend to be more easily internalized.
Talking about early childhood apples etc is missing the point. I'm talking about generic methodology to learn a new concept in a timeboxed way, not a multi-year development. Though thinking behind the two is the same.
- username90 6y agoIt changes the problem in the minds of the student. If you call variables X and Y they wont assume that X and Y are special for this case. If instead you call them kilograms and kilometers people will assume that you teach them something that has to do with kilograms and kilometers and not some general purpose math equation.
- adam_arthur 6y agoIt's easy. You say here's a general purpose math equation. Now here's an example of computing something useful with it, using real world concepts.
- username90 6y agoBut often those real world applications are way harder to understand than the initial abstract problem they had. Involving other subjects only works if the students are already well versed in those subjects. And before you say "just learn those subjects first then?", often it is easier to first learn the abstract math and then learn those concepts than the other way around, since making sense of those equations is hard even when you do know the math and close to impossible when you don't.