There's this thing where some educators argue students must be thinking of the precise educational point at all times, and that anything else is a distraction. That's what's happening here. But it is, in my view, the wrong approach, because it completely does away with association, and focuses on rote memorization. But which outcome is better: a memorized fact about the underground railroad, or a person associating biscuits with the underground railroaf every time they make biscuits, for the rest of their life? The same, though less obvious, point can be applied to mathematics. "Were they thinking about math concepts? No, they were thinking about rectangles, lines, and shading." But those are math concepts - just not formalized notational math. Abstract concepts not associated with ground truth are lost, not only forgotten, but never useful in the first place.
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