[Numeracy 183] Re: Application vs. Theory

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Carol King cking at lyon.k12.nv.us
Tue Feb 16 13:12:20 EST 2010

Thank you both for eloquently stating the problem. Carol


From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On
Behalf Of Michael Gyori
Sent: Monday, February 15, 2010 6:55 PM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 177] Re: Application vs. Theory

Greetings all,

Indeed: when we teach the "abstract" to those who reside in the
"concrete," we are at high risk of losing them. On a cognitive level,
we will only succeed in teaching the abstract if it becomes meaningful
(one could say "cognitively concrete"). We revert back to the key
pedagogic notion of scaffolding (essentially a Vygotskian version of the
"zone of proximal development").

Cognitively, something as concrete as a computer is "abstract" (in the
sense of removed from what is known) in the eyes of an individual who
has never seen one, let alone heard of one. Alternatively, say for
mathematicians, the notion of two negatives forming a positive is
"concrete" (i.e., "real") in that is fully and transparently meaningful
within their respective cognitive realms.

The link that Susan included in her post preceding the one below -
- is worth a read. It points to ways that the abstract can be "made
concrete," with the caveat that, with respect to the author's examples,
they tap into the learners' background knowledge.

I find myself quite concerned with pedagogic stances and approaches that
are content with a plateauing of learning experiences by not going
beyond the "well, that's the way it is, so just learn and apply the
rules." Ultimately, our learners will rise to our expectations, or else
engage in learned helplessness if whatever is good enough becomes the
learning goal.


Michael A. Gyori

Maui International Language School

www.mauilanguage.com <http://www.mauilanguage.com/>


From: Susan Jones <SUJones at parkland.edu>
To: numeracy at nifl.gov
Sent: Mon, February 15, 2010 2:30:45 PM
Subject: [Numeracy 174] Re: Application vs. Theory

In my experience, it's when we "speak abstract" to students who live in
concrete that we lose them.

Generally when we "teach theory" what we actually teach is further
reinforcement that math is an arcane ritual in which we are to perform
symbolic rites and written incantations with certain inscrutable
patterns until they satisfy The Master. When I am writing those symbols
down, they're connecting to all kinds of things in my mind... real
applications... when my students read word problems, they are often not
connecting the processes to somethign real; it's just adding a layer of
complexity to the symbol manipulation. I work hard to help them see the
connection, but that generally requires a whole lot more drawing and
wishing I were a graphic artist ;)

Susan Jones
Academic Development Specialist
Center for Academic Success
Parkland College
Champaign, IL 61821
sujones at parkland.edu

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