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$\begingroup$ I give this presentation to kids of all levels middle school and up. The goal is to help them think about math in a different way. I'm not sure if it is exactly what you are looking for, but I thought it might be helpful. youtube.com/… $\endgroup$– johnnybCommented Mar 2, 2020 at 18:14
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1$\begingroup$ This book is quite good, but assumes high-school math, and is aimed at college students. Still you might find it useful: Velleman, Daniel J. How to prove it: A structured approach. Cambridge University Press, 2019. $\endgroup$– Joseph O'RourkeCommented Mar 5, 2020 at 2:04
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3$\begingroup$ That is a VERY ambitious program. If your 12 and 13-year-olds can handle proofs and formal logic, you might have a look at my proof-checking freeware and the accompanying tutorial that are available at my homepage dcproof.com It introduces students to the basic methods of proof. Each line of proof that the student enters is verified immediately after it is entered. Feedback is instantaneous. It is impossible to write a invalid proof. $\endgroup$– Dan ChristensenCommented Mar 5, 2020 at 3:15
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