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4

I'd probably introduce the idea of proof with arithmetic questions that very much seem true based on simple specific examples but would need to be proven. Usually the classic even-odd proofs like the following: If we let $n$ be an integer... If $n^2$ is odd, then $n$ is odd. If $n^2$ is even, then $n$ is even. $n^2$ is odd if and only if $n$ is odd. And ...


3

Note: I'm currently learning proofs myself, but I wonder if a good book on mathematical proofs might be useful towards this goal. That along with a 1:1 experienced mathematics tutor. Books in this genre include How to Prove it by Velleman, How to Think Like a Mathematician by Houston, the Book of Proof by Hammack, and Mathematical Proofs a Transition to ...


2

Since it has not been mentioned by name in the other answers, I'll say that once we model the x and y coordinates of a point on the unit circle as $\left(\cos(\theta),\sin(\theta)\right)$ (marked by a ray through the origin), I define the tangent as the slope of that ray. Since they've found the slope of a line so many times before, my students end up ...


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