Your perspective is not PC, of course, but I'm sure you are right. 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. A hellish example, that I may have reported on long ago, was an NSF summer program we had for in-service mathematics teachers. One of the courses was strengthening teachers of proof-based Euclidean geometry. 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.
At 05:32 AM 7/2/2013, Robert Hansen wrote: >I am becoming more and more convinced that you cannot teach it >(logic) any more than you can teach the sense of smell. > >I agree that it is a critical sense, indeed, the critical sense, >because without it there is no chance of developing the intuition, >instinct and habits of mind that I spoke of. But I am convinced that >it is a sense and not something taught. > >That would explain quite well what we see in the world, would it >not? I mean, if logical sense is like, for example, musical sense, >it would explain why only a few are able to thrive with it. > >I distinctly remember in the 4th grade when I first recognized this >sense. It wasn't like an epiphany, I wasn't even trying. It was like >I just opened my eyes. > >Bob Hansen > >On Jul 1, 2013, at 10:53 AM, Joe Niederberger ><firstname.lastname@example.org> wrote: > > > R Hansen says > >> The statements of mathematics (its conclusions) are logical, but > mathematics itself is much much more than just its statements. > > > > People often stress the importance of mathematics by saying that > mathematics teaches critical thinking skills. Aside from "number > sense" I think what they are really talking about, mostly, is the > logical component of mathematics, which is generally implied rather > than explicit. I see no reason why logic should not be taught at an > early age, explicitly. > > > > Cheers, > > Joe N > >