But how many high school calculus teachers spend their evenings doing calculus? (What would that even mean?) Can you imagine a geometry teacher spending his evenings writing faux-formal proofs with modus ponens? Do algebra teachers even use algebra? Do they depend on it?
Can you trust a teacher who doesn’t use what he teaches? Who has never used what he teaches?
Can you trust a teacher whose only connection to a subject is teaching it?
How can such a teacher know if what he’s teaching is valuable, or how well he’s teaching it? (“Curricula” and “exams”, respectively, are horrendous answers to those questions.)
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