I really enjoyed this post. It was fun to read and really drove home the point about starting with examples. I also thought it was helpful that it didn’t just saying, “teach by example”. I feel that simplistic idea is all too common and often leads to bad teaching where example after example is given with no clear definitions or high level explanations. However, this article emphasized how one needs to build on the example to connect it with abstract ideas. This creates a bridge between what we already understand and what we are learning.
As I was thinking about this to write this review, I was trying to think of examples where it makes more sense to explain the abstract thing first and then give examples. I had great difficulty coming up with any examples where abstract first makes sense. The few possible examples I could think of came from pure math, and even there I wonder if it wouldn’t still help to start with examples.
The most abstract subject I’ve ever studied is category theory. Recently I was learning about adjoint functors, and here indeed the abstract definition make sense entirely independent of any examples. However, having learned the definition one can’t really do anything with adjoint functors until one has seen it in some examples. So this might be an example where the abstraction-example-abstraction order or explanation makes sense. On the other hand, once I learned about the free-forgetfull adjunction, I thought that would have been a good example to start with to build intuition before introducing the abstract definition. I realized that my favorite teachers of the subject still use a lot of examples. Like Bartosz Milewski, who comes at category theory from the perspective of a programmer.
Learning to program is also a good example where in advance one might think it would make sense to learn a bunch of abstractions first. However, in practice, one learns to code by example, then after having mastered some examples, learning the principles behind them.
I really enjoyed this post. It was fun to read and really drove home the point about starting with examples. I also thought it was helpful that it didn’t just saying, “teach by example”. I feel that simplistic idea is all too common and often leads to bad teaching where example after example is given with no clear definitions or high level explanations. However, this article emphasized how one needs to build on the example to connect it with abstract ideas. This creates a bridge between what we already understand and what we are learning.
As I was thinking about this to write this review, I was trying to think of examples where it makes more sense to explain the abstract thing first and then give examples. I had great difficulty coming up with any examples where abstract first makes sense. The few possible examples I could think of came from pure math, and even there I wonder if it wouldn’t still help to start with examples.
The most abstract subject I’ve ever studied is category theory. Recently I was learning about adjoint functors, and here indeed the abstract definition make sense entirely independent of any examples. However, having learned the definition one can’t really do anything with adjoint functors until one has seen it in some examples. So this might be an example where the abstraction-example-abstraction order or explanation makes sense. On the other hand, once I learned about the free-forgetfull adjunction, I thought that would have been a good example to start with to build intuition before introducing the abstract definition. I realized that my favorite teachers of the subject still use a lot of examples. Like Bartosz Milewski, who comes at category theory from the perspective of a programmer.
Learning to program is also a good example where in advance one might think it would make sense to learn a bunch of abstractions first. However, in practice, one learns to code by example, then after having mastered some examples, learning the principles behind them.