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Re: What's in an expression?

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  • Subject: [mg132427] Re: What's in an expression?
  • From: Murray Eisenberg <murray at>
  • Date: Wed, 12 Mar 2014 03:29:20 -0400 (EDT)
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On certain strictly symbol-manipulation questions, giving a 
multiple-choice question can give too much of a clue as to the correct 
answer. This is most especially the case with symbolic integration, 
where the student need only differentiate each of the possible answers 
and compare with the integrand.

Getting students to explain, even to organize, their work, is often like 
pulling teeth. Terrific if one can do it.

Certainly the ideal is not just to have students explain what they're 
doing and why, but to given them much meatier problems. The reality, 
especially in the mass-enrollment calculus courses today, is that 
there's too often inadequate resources for reading such written work, 
whether on paper or in Mathematica documents. Just the paper-shuffling 
(or file-shuffling) is often out of the question.

In any case, the questioner was asking about testing a basic symbolic 
skill, and for that having the student just provide an answer is often 

If a contemporary on-line homework system is being used, then the 
instructor can even include a couple of questions in an assignment where 
the student, using a palette or keyboard shortcuts for special symbols, 
types out an explanation; such a system makes it easy for the instructor 
(or TA or other human grader) to go right through all the students' work 
in a very efficient manner, without having to handle paper while doing 
so and, especially, not have all the time-wasting distraction of handing 
papers back in class.

On Mar 11, 2014, at 3:37 AM, djmpark <djmpark at> wrote:

> You could have multiple choice questions, or you could use pattern 
> with alternatives that you would hope would catch the acceptable 
> But why not, in this day and age, give students something better? Why 
> have the students write short mathematical essays in notebook form on
> various topics where they might explain how they got an answer and the
> principles behind it? Of course, that means the teacher would have to
> actually read the notebooks, and the student would also have to learn how to
> write readable and clear presentations.
> David Park
> djmpark at
> From: sam.takoy at [mailto:sam.takoy at]
> Hi all,
> I'm building a little Mathematica system that checks answers entered 
> students. Suppose the question is "what is Sin'[x]?" ad the student
> responds: Sin'[x] which is "correct", but not the intended answer 
> 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 
> 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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