2020.10.11 12:11
how I think teaching should be done
Based on my experience teaching adults and children programming and mathematics, I think teaching needs to be different from how it is often done. Usually, people think that teaching is about explaining things well. I argue that it is different - that usually, it is not about explaining at all, but about building intuition through appropriate exercises. Let's say someone has a problem solving this task:
In classes VIa, VIb, VIc, and VId, money was collected for theater tickets. Class VIa contributed 180 PLN, VIb - 120 PLN, and classes VIc and VId each contributed 150 PLN. The tickets turned out to be cheaper than expected, costing a total of 500 PLN. How should the remaining money be divided among the classes?
When I face such a problem (meaning, when someone does not know how to approach it), I do not explain anything. Instead, I wonder how it is that I can immediately see how to solve it, while someone else cannot. What intuition is this person lacking? Where do problems arise? Then I come up with some small exercises that target these weak points, build the necessary intuitions, and for the next month, from time to time, without rush, I occasionally throw in such warm-up problems. For example: there are three men and two women in a team. What fraction of all people are men? What fraction of all hands in this team are men's hands? What fraction of eyes in this team are men's eyes? What fraction of fingers in this team are men's fingers (here you need to be careful not to choose a body part that only one gender has). What fraction of spinal vertebrae in this team are men's vertebrae (while we do not know how many vertebrae a normal person has, we know it does not depend on gender)? The team (still the same) organized a fundraiser for a party. Everyone contributed the same amount (but we do not know how much). What fraction of the money is men's money? And so we calmly practice until the solution to the first problem becomes obvious.
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