What are you especially sensitive to, the way the princess was sensitive to the pea?
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To clarify the first one: kids trained to expect that (1) every problem has a correct answer or a known set of correct answers + (2) the adults know what it is (and how to correctly find it) tend to become very anxious about reasoning from first principles or experimenting freely
There's another important loss when kids become procedural worksheet-fillers and discrete task-doers: they never develop intuitions for what sometimes works, what might have worked, what deceptively *seems* to work — and consequently, they never really build out a model
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For example, a "good" student might well be able to solve a sheet of square root equations *and* give a perfectly reasonable description of what a square root is **without** being able to tell you why such a thing is called a SQUARE root.
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...it may never even occur to such a child to make the obvious connection to the square shape. To her, squares and square roots are about multiplying and 2s and lines over numbers. What would that have to do with a square?
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I spent some time with my niece, just as she started school, “doing sums” as she described it. Goal was to try to give her a sense of quantity distinct from particular ways of doing basic arithmetic - to give her some intuition of her own ASAP.
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Six years later she’s top of her class for everything and wants to be an astrophysicist. Don’t know if I helped much, but I couldn’t have hindered much either!
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