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> those who were underperforming weren’t struggling with the fundamental concepts in the class, but with algebra: the problems were caused by not having an intuitive understanding of, for example, the difference between f(x+a) and f(x)+a.

Those taking that class have spent years trying to learn algebra and still don't get it so we are already trying this.

> I’m no great teacher, but I was able to get all but one of the office hour regulars up to speed over the course of the semester.

Most likely they just memorized the new algebra rules as well. There are lots of studies showing how hard it is to teach students anything tangible, instead most will just try to memorize everything you say.

See for example: https://www.amazon.com/Academically-Adrift-Limited-Learning-...

The linked book was published in 2011 -- lacking the US context, has the situation changed in the past 6 years?

I've thought for some time that the idea of understanding is bass ackwarkds - understanding comes after learning how to do something mechanically, particularly in maths. Don't know if that's a learning theory though

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