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]]>Meanwhile, every current Geometry book I’ve used has placed the Distance Formula well before the Pythagorean Theorem. For instance, in Pearson’s current edition of Geometry, the Distance Formula is in section 1-7, while the Pythagorean Theorem is in section 8-1. And, stunningly, the Distance Formula section STILL REFERENCES the Pythagorean Theorem.

How are students supposed to make connections between facts when the facts aren’t even presented in a logical order?

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]]>I guess my question is the following: Given that any normal teacher-led, classroom acquired, piece of knowledge is – in itself – just a shallow ‘fact’ in the moment it is delivered/received/stumbled-upon, is the proposal that – with nothing more than a thorough smattering of shallow knowledge, the brain will automatically assimilate these different bits of knowledge into webs of understanding which will – by their own accord – become insights and, indeed, lead to ‘profound’ realisations/appreciations etc…? (whatever ‘profound’ might mean given this discussion).

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