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 <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>