[Numeracy 177] Re: Application vs. Theory

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Michael Gyori tesolmichael at yahoo.com
Mon Feb 15 21:54:36 EST 2010

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 - http://opinionator.blogs.nytimes.com/2010/02/14/the-enemy-of-my-enemy/ - 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 

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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