On Mon, Oct 15, 2012 at 4:53 PM, Louis Talman <talmanl@gmail.com> wrote:


On Mon, Oct 15, 2012 at 3:00 PM, Robert Hansen <bob@rsccore.com> wrote:

On Oct 15, 2012, at 1:04 PM, Louis Talman <talmanl@gmail.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.)

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

  <http://rowdy.mscd.edu/%7Etalmanl>