[Xie asked me this question with regards to the "Three Consecutive Integers" Algebra PoW, and I suggested that this might be a good place to post it. -Annie]
Dear seasoned teachers,
Supposed if you tried to explain a solution of Algebra to the clever students of PreAlgebra, they might got the way of thinking, but not believed absolutely. They might ask how do you know it ALWAYS work?
Then you might say that variables can respect for any numbers, so it was true. If they would still doubt then, or ask you to give a proof that they might understand, even ask for giving by the method of reduction to absurdity. How to explain ALWAYS clearly to them?
Theory? Experiment? Or other wonderful words? What are you going to do?