A typical intro math course is stuffed with concepts. Advanced students can handle it. Maybe average students too, if they understand everything on the first pass. (This never happens, of course.) Poorer students are doomed, without heroic effort.

Why are the courses so full? One reason is the expert’s blind spot. If you’re a math prof, you were good at math as an undergrad. You were one of those advanced students. You went to grad school, and got even better.

As you learned, some mathing became automatic. That is, you learned it so well that your subconscious does it for you, with no attention from the conscious you. Just like riding a bicycle. You can do it without paying attention to every step.

Recall that your consciousness does not have direct access to your subconscious. This means that you could be doing some math without knowing how you do it. Like riding a bicycle. If someone asked you how to ride a bicycle, you would have to think about it for the first time in years. Don’t do it while riding, or you might have an intimate moment with the pavement.

Experts regularly underestimate how difficult it is to learn their subject. It seems so easy to them, so obvious. Want a badly designed intro math course? Give the task to a math expert who knows nothing about learning.

We’ll talk more about the expert’s blind spot in the section on course design.

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