I'm not sure how this fits in, but is clear to me that for at least some students who rebel at using letters (and it may be just an aversion to letters for these students) that they are treating number symbolically; e.g. ultimately canceling it out when appropriate and never performing actulal arithmetic with the numbers (like adding 2 + 3 to get 5, they will cancel in the sense of (2/2 = 1) or 3+(-3)=0, operations you'd be able to do with symbols; but for some unknown reason to me, putting in a symbol that looks like an arabic numeral gets them past a barrier that using a latin letter fails to do.
I'd comment that using many graphing packages do not help as you often have to explicitly put in a number for a parameter in the formula you are plotting in order to get the computer/device to actually make the plot. I wonder if this is affecting the situation being discussed here to the detriment of flexibility in thinking for our students.
Joel R
| -----Original Message-----
| From: phys-l-bounces@mail.phys-l.org [mailto:phys-l-bounces@mail.phys-
| l.org] On Behalf Of John Clement
| Sent: Wednesday, May 16, 2012 8:28 PM
| To: Phys-L@Phys-L.org
| Subject: Re: [Phys-L] The great barrrier (was Proportional reasoning)
|
| Thinking Science starts with understanding variables. So perhaps the
| problem is more basic, the understanding of variables. I doubt that it
| is
| just a simple aversion to using letters. It most probably is a deeper
| problem. So just making them use letters will not fix it.
|
| John M. Clement
| Houston, TX
|
| >
| > I's not just that, in my experience. The great barrier seems
| > to be the
| > use of algebra. Even at the third year college level, after
| > a bunch of
| > calculus courses, I've had students who rebel at the use of
| > letter symbols
| > instead of numbers. While I agree that numerical examples
| > can oftern be
| > helpful, the transition to symbolic reasoning seems not to be
| > sufficiently
| > accomplished in most math (and physics, and chemistry) courses. That
| > omission, then leaves the student unable to generalize the
| > insight that
| > could be gained from specific numerical examples.
|
|
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