Date: Apr 26, 2013 4:24 AM Author: Murray Eisenberg Subject: Re: Mathematica-assisted learning was .. Re: Speak errors (was Re: On Apr 25, 2013, at 2:51 AM, Richard Fateman <fateman@cs.berkeley.edu> wrote:

> I think the comparisons are generally with control groups that were being taught

> the same material but without "benefit" of computers. It

> seems to me that comparing the two groups of students on their ability

> to write programs would not be pertinent to the question of whether the

> two groups learned (say) calculus equally well."

If you think that what I'm suggesting is to "write programs" then you simply don't understand the issues here. It's learning mathematical ideas vs. learning to do (largely mindless) mechanical manipulations of symbols.

> On 4/24/2013 3:16 AM, Murray Eisenberg wrote:

>> See interspersed responses:

>> On Apr 22, 2013, at 3:10 AM, Richard Fateman <fateman@cs.berkeley.edu> wrote:

>>

>>> Historically, experiments at higher educational levels to introduce a

>>> computer algebra system into a math course have resulted in consequences

>>> like this:

>>> 1. Students, on average, resented having to learn "something else" (i.e.

>>> using computer program) that wasn't "on the final".

>>

>> Simple solution: let students use the computer for all exams, too. (I've done that.)

> Finding a room with (say) 350 computers, all running (say) mathematica,

> all DISconnected from the internet to avoid collusion, (etc) presents

> certain physical and electronic problems.

>>

>>> 2. On average they learned "no less" than students in the control group

>>> not using computers. But "no more" either.

>>

>> What, exactly, does that mean? By what standards is this being judged?

>

> I think there are a number of peer-reviewed papers in this area; I

> recall one that had to do with a "modern algebra" type course.

> Or this report (1991) regarding calculus and Mathematica

>

> http://library.wolfram.com/infocenter/Articles/3227/

>

> and how students performed in a physics course, it found

>

> " a nonsignificant difference in the mean grades of the two groups "

>

>

> E.g., when comparing with a conventionally taught control group, does

> the comparison test asking

>

> what-if questions that require simulation or calculations, etc.,

>

> beyond the normal capabilities of paper and pencil?

>

> I think the comparisons are generally with control groups that were

> being taught the same material but without "benefit" of computers. It

> seems to me that comparing the two groups of students on their ability

> to write programs would not be pertinent to the question of whether the

> two groups learned (say) calculus equally well.

>

> If you are making the point that you think that students gain something

> by learning to write program for computers, generally, that is something

> I agree with. However, there is scant evidence that introducing

> computers into a conventional course improves learning of that

> conventional course material. You can accuse the instructors of

> lacking imagination, or the students of lacking in ambition, interest,

> curiosity, or the curriculum specifications of lacking in flexibility,

> or the testing process bogus, or the selection of control groups wrong,

> or any other hypothesis that you can come up with to invalidate the

> published results. But other than the anecdotal comments from students

> who really liked (but some hated...) the course, what can you do?

>>

>

> I'm all in favor of technological aids to teaching that work. Finding

> them is not so easy. Proving that they work is hard too. Evidence that

> consists solely of anecdotes from enthusiasts doesn't count. Making neat

> demos is fun for the instructor, but that's not the question here...

>

>

> RJF

>

>

---

Murray Eisenberg murray@math.umass.edu

Mathematics & Statistics Dept.

Lederle Graduate Research Tower phone 413 549-1020 (H)

University of Massachusetts 413 545-2838 (W)

710 North Pleasant Street fax 413 545-1801

Amherst, MA 01003-9305