[Edu-sig] a non-rhetorical question
Andrew Harrington
aharrin at luc.edu
Mon Jul 9 20:55:26 CEST 2007
On the algebra/geometry questions:
As a longtime math professor in a past life, it is my observation of
students going forward from high school, and of students long ago when I
was in high school myself, and tutored a lot of peers, that there are
several effects in the algebra/geometry discussion. It seems to me that
there are many students who process visual and spatial information very
well, who just 'get' geometry, and may have a very hard time with the
pure symbol manipulation in algebra. Of course constructing a geometric
proof does involve getting into symbolism, and some who learn to get
motivation for that from the spatial images in geometry, then have an
easier time with algebra.
I have no hard data, but only a great deal of examples.
I also hypothesize that some students who are capable of learning symbol
manipulation, but need practice, do well getting that experience in
algebra, and then are less overwhelmed taking geometry later by the
added requirement to have spatial intuition.
As to the natural order of brain maturation for processing symbols vs
spatial relationships, I leave that to others.
Andy Harrington
Jay Bloodworth wrote:
> On Sun, 2007-07-08 at 21:46 +0200, Laura Creighton wrote:
>
>> Do you have many students who are good at geometry and still rotten
>> at algebra? Also what do they say when you ask them 'what don't
>> you understand here?'
>>
>
>
> I wouldn't say rotten, but it's not unusual to have students who do
> significantly better in geometry than algebra. Again, it could just be
> a year of brain maturity that makes that so.
>
> "What don't you understand?" Usually if a kid can answer that they
> don't have a problem:
>
> Ex: 2x + 3y + 5x = 7x + 3y
>
> Kid 1:
> "Why don't you understand?"
> "Where did the 7x come from?"
> "From combining like terms. I added 2x and 5x."
> "What are like terms?"
> "Terms with the same variables to the same powers. 2x and 5x both have
> x to the first power and no other variables."
>
> versus
>
> Kid 2:
> "Why don't you understand?"
> "I just don't get it."
>
> Not a great example, because most students can do a little better with
> like terms than Kid 2. But the point is that the "don't get it" kids
> I'm talking about can't really tell you what they don't get. They see a
> string of symbols on line one and another on line two and claim to see
> no connection between them. And though I can often ask a series of
> questions to determine what they don't get and to explain it - "Do you
> see where the 3y comes from? Good. How about the 7x? Okay, do you see
> the 2x and 5x? etc." - they'll still say they don't get it.
>
> That was probably a longer yet less complete answer than you were
> looking for. Nonetheless, I hope it helps.
>
> Jay
>
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--
Andrew N. Harrington
Computer Science Department Director of Academic Programs
Loyola University Chicago http://www.cs.luc.edu/~anh
512B Lewis Towers (office) Phone: 312-915-7999
Snail mail to Lewis Towers 416 Fax: 312-915-7998
820 North Michigan Avenue gdp at cs.luc.edu for graduate admin
Chicago, Illinois 60611 upd at cs.luc.edu for undergrad admin
aharrin at luc.edu as professor
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