This MIT lecture by Sanjoy Mahajan was, I thought, well worth watching.
He talks about a range of things. Mainly how the art of problem solving is distinct from the skill of pattern matching, and how to cultivate the former.
He identifies the following types of problem solving approaches (as some):
- Reducing to already solved cases
- Look for simple/extreme cases to look for pattern
- guessing
- symmetry
- be lazy
- use good representations (e.g. drawings), and
- analogy
And in terms of teaching them he recommends the following:
- Name the types of approach (so you can recognise what you
- Diversity of examples to use the technique in (and not the same problem rephrased)
- Ask yourself Wheeler’s Question: “What one or two sentences could you tell your earlier self (the self that hadn’t solved the problem yet) that would make the solution really easy?”. This is essentially a shorter version of Gladwell’s Outlier idea. It is deliberative practice rather than just practice per se, and makes sure you are actually learning from the right kind of practice.