Competition Math is NOT an All-Encompassing Holy Grail of Math Learning or General Problem Solving

Skill development all comes down to building domain-specific chunks in long-term memory. The way you increase your ability to make mental leaps is not actually by jumping farther, but rather, by building bridges that reduce the distance you need to jump.

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Last I checked, there’s a lack of research evidence that people can actually increase their “raw” working memory capacity and generalization ability through training general problem-solving skills…

but there IS research evidence that you can effectively turn long-term memory into an extension of working memory if you acquire domain-specific foundational skills and develop them to the point of automaticity.

And as you layer more advanced skills on top, those foundational skills naturally get compressed into more generalizable neural representations that can be applied more flexibly across different contexts.

It seems like skill development all comes down to building domain-specific chunks in long-term memory that allow you to bring more information into working memory without actually increasing the amount of cognitive effort you have to put forth to rehearse that neural activation.

In other words, the way you increase your ability to make mental leaps is not actually by jumping farther, but rather, by building bridges that reduce the distance you need to jump.

Now, I do expect that students who do well in competition math will tend to have some inherent cognitive “jumping” advantages (e.g., higher working memory capacity & generalization ability), and those cognitive advantages are advantageous in other fields.

But I don’t think it’s the competition math training itself that confers the cognitive jumping advantage.

There are a lot of people who view competition math as some kind of all-encompassing holy grail of math learning and I just don’t agree at all. I just view it as another subject.

Of course, competition math will force a consolidation of underlying skills, but so will layering on higher math skills that are more relevant to your area of interest.

I’m not saying competition math is zero ROI, I’m just saying that when you build a tower of skills, there’s a lot to be gained by building towards a direction that’s particularly relevant to your future.

Like, sure, competition math will aid your abilities in higher math and to some extent translate to other quantitative problem solving domains…

but you know what will aid your abilities MORE in higher math and translate MORE to other quantitative problem solving domains?

Skilling up directly in higher math and those quantitative problem solving domains ;)

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