On Mon, Oct 15, 2012 at 4:53 PM, Louis Talman <firstname.lastname@example.org> wrote:
> > > On Mon, Oct 15, 2012 at 3:00 PM, Robert Hansen <email@example.com> wrote: > >> >> On Oct 15, 2012, at 1:04 PM, Louis Talman <firstname.lastname@example.org> wrote: >> >> >> The ability to do so is important, because proof is central to >> mathematics. Those who can't distinguish between good argument and bad >> argument certainly ought not to be teaching mathematics. Even those who >> *can* do so but don't understand that proof is central to mathematics (and >> this includes many who mistakenly think that they want to major in >> mathematics) ought not to teach mathematics. (And the reason, I suspect, >> that the latter category includes so many who discover too late that they >> don't really want to study mathematics, is that too many of them make it >> through to become mathematics teachers. Allegedly, anyway.) >> >> >> Agreed. >> >> >> The aim of the test seems to be to test whether students can >> differentiate good arguments from bad arguments. >> >> >> The aim? The target is fine (as you wrote above), the aim is very poor. A >> survey format? >> >> I would have asked... >> >> 1. Is this proof correct? >> 2. If not, why?-- >> > > As usual, you asked something other than what you meant. You asked if the > test "is mathematics". It most certainly is. > > Whether it's a good test of mathematics is quite another question, and one > you didn't ask. >
To the above let me add: The survey format shares the flaws of other multiple guess formats. No such test can really probe the depths of a student's understanding of proof. Such probing requires that a student write something and that the student's writing be read by a knowledgeable person. Anything less amounts to determining the condition of a car by measuring only the pressure in its tires.
--Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver