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Re: What's in an expression?

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  • Subject: [mg132426] Re: What's in an expression?
  • From: Richard Fateman <fateman at>
  • Date: Wed, 12 Mar 2014 03:29:00 -0400 (EDT)
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On 3/11/2014 12:16 AM, Murray Eisenberg wrote:
> One way, which doesn't involve looking at the form of the student's
> symbolic answer, is something employed by a at least one of the popular
> on-line homework systems: evaluate the "correct" answer at a number of
> judiciously chosen numerical values of x, evaluate the student's answer
> at the same values of x, and check that they're the same (within fuzz).

For some clases of expressions you can use elements of a finite field, 
in which case there is no fuzz.

This problem has been address at least as early as the 1960's.

There is
a major flaw in the logic behind the question.

Namely, it requires students to (a) derive the correct answer and then
(b) understand the computer syntax and type the answer into the computer 

You probably want to test (a),  but you will also test (b).  In fact,
telling a student he/she is wrong, when they only error is a type-b 
error seems to me to be disheartening if not destructive.

If you sufficiently simplify the task, I suppose it becomes
simultaneously do-able and quite dull, and you can find a discussion by
dullards on stack-overflow.

Another possible flaw is that just typing the question in, and 
evaluating, should get the right answer without the student knowing it.

> Otherwise, you may have to deal with a myriad of possible forms in which
> the student might submit an answer without actually doing what you want.

> On Mar 10, 2014, at 4:38 AM, sam.takoy at wrote:
>> Hi all,
>> I'm building a little Mathematica system that checks answers entered
> by students. Suppose the question is "what is Sin'[x]?" ad the student
> responds: Sin'[x] which is "correct", but not the intended answer
> (Cos[x]). I'm wondering if there is a general way to approach this sort
> of problem. In particular, is there a way to find out whether a given
> expression includes certain elements (like Derivative)?
>> Thank you in advance,
>> Sam
> Murray Eisenberg                                murray at
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 240 246-7240 (H)
> University of Massachusetts
> 710 North Pleasant Street
> Amherst, MA 01003-9305

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