Date: Oct 15, 2012 6:59 PM
Author: Louis Talman
Subject: Re: Inquiry Based Learning at the University of Michigan Math Dept.
On Mon, Oct 15, 2012 at 4:53 PM, Louis Talman <email@example.com> wrote:
> On Mon, Oct 15, 2012 at 3:00 PM, Robert Hansen <firstname.lastname@example.org> wrote:
>> On Oct 15, 2012, at 1:04 PM, Louis Talman <email@example.com> 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.)
>> 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