[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
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  Chicago, Illinois 60611          upd at cs.luc.edu for undergrad admin
                                   aharrin at luc.edu as professor

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