Three things really made me stop and think while reading Skemp’s article. The first one was the difference between knowing how to do it and knowing why it works. I’ve learned that a lot of the time in math, I’ve memorized a formula or approach to get the right answer without really knowing what was going on. The second was the example where students got the area question wrong because the measurements were in different units.They knew the formula, but as soon as the question changed a little, the rule they memorized wasn’t enough. The third thing that stood out to me was Skemp’s example of knowing a few routes around a town versus actually having a mental map of the whole town. That made his argument much easier for me to understand because if you know the map, you can figure out where to go even when you haven’t taken that exact route before.
I agree with Skemp for the most part. “I think it’s better in the long run to know why something works rather than just memorizing rules. At the same time, I don’t think memorization is necessarily a bad thing. Skemp also admits that sometimes it’s best to learn a simple rule first, so you can get started and build confidence. I think the best learning method is a mix of the two: learn how to do something first, but don’t stop there, learn why it works eventually too.
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