Logic for high schoolers
In algebra 1, we want to prove the sum of a rational and irrational is irrational. However, the student must know what proof by contradiction is before seeing this proof. In geometry, we want to prove that corresponding angles implies parallel lines. This also requires proof by contradiction. Because of this, I propose teaching how to use proof by contradiction before algebra 1, or including a section on mathematical logic within algebra 1.
In geometry, once we see proof of a conditional statement, we want to ask whether the converse is true. Therefore, we should teach what conditional, converse, and biconditional statements are, before high school geometry.
I think a basic logic course should be taught before algebra 1, for the reasons above. This course should include propositional logic and various proof methods, but should exclude proof by induction. Could we teach natural deduction proofs at this stage? I need more evidence.