Wayne Bishop says: >I especially noticed that in sophomore proof-based geometry where I never could understand fellow students whom I considered to be very bright needed a lot of help from me (a great self-esteem builder) when I could not understand their difficulties.
This is just a guess, but perhaps one reason proof based geometry is nearly extinct in our schools is because it is too much of a shock for most mere mortals to be presented with that style of thinking without sufficient prior preparation.
In the course I had in high school, with the teacher who turned out to be one of the best I ever had, logic was treated exclusively for several weeks before we ever mentioned the words "point" or "line".
I see no reason that modus ponens should not be known to students before they ever enter high school.
>One of the participants - currently a geometry teacher of such - announced to the class (with no appearance of guilt, just healthy ignorance) that he insisted that his students replicate the T- style proofs following exactly the same steps as the solutions manual because, otherwise, he could not tell if they were correct or not. Almost the antithesis of the goal of the course.
Sadly, this kind of insanity is not limited to proof based geometry.