What do you think the importance of formal logic is in early (ish) mathematical education?

Most of mathematics is formalised by axioms in the language of logic, but in my experience formal logic is covered superficially, if at all in middle/ high school education. Thoughts?I believe that formal logic can be instrumental in early mathematics education to faciliate students' learning of how to reason mathematically and develop higher order thinking skills that are useful particularly for geometry and problem solving. I believe a prerequisite to formal logic is for students to have mastered fundamental mathematical foundations. Once they have grasped the fundamentals, they are then able to apply syllogisms, inferences, deductive and inductive reasonsing, etc. in such a manner that the logic is mathematically valid.

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