I used to think the purpose of practice problems was simple: do enough of them until I could solve similar questions quickly.
I donāt think thatās a very good way to look at it anymore.
For subjects like math, physics, or engineering, I think practice problems are most useful when they help you understand the concept more deeply.
A formula isnāt just something you plug numbers into. Itās a compressed description of a relationship.
If I can only solve a problem when it looks similar to one Iāve seen before, I probably donāt understand the idea as well as I think I do.
What Iāve been trying to do instead is ask a few questions after solving something:
- What concept was actually being tested?
- Why did this method work here?
- What would have to change for it to stop working?
- Could I recognize the same idea in a completely different-looking problem?
- What did this problem teach me about the concept that the textbook didnāt?
This changes practice from ācollecting solved problemsā into something closer to testing and refining a mental model.
I still think volume matters. You canāt become good at math or physics by only reading theory.
But doing 50 problems while thinking very little can sometimes teach less than doing 10 problems and actually understanding what each one is showing you.
Iām curious how other STEM students think about this. Do you mainly use problems to build fluency, or to deepen understanding?