High-school mathematics education taught us to hand-execute algorithms to manipulate symbols into equivalent forms. The rules of arithmetic, then the rules of algebra, properties of trigonometry, more algebra, then the obscure edge-case tricks of integration and differentiation. That is 100% of &quot;math&quot; to any high school graduate. Nothing remotely related to reasoning about monads.<p>There is no reason at all that a straight-A high school math student should be expected to be even slightly good at writing proofs.