Friday, May 2, 2008

Abstract and concrete

The New York Times, often the least un-bad of the bad lot that is the press in this country, had an interesting article on pedagogy in mathematics this week.

They reported on a finding that students at the university level learn better in an abstract setting than in a setting where they are taught using concrete examples and are expected to understand the abstract as a unifying them of the specific examples.

I have to say that I am not surprised: I have always found that I need lots of examples in order to start forming a general conclusion (often lots more than one might imagine necessary) and I can imagine that the study might have used far too few examples prior to testing.

Of course, it is an open question how much influence the research will have: after all, it is just one data point, and there are lots of schools of pedagogy which insist on teaching the concrete and encouraging the students to develop to the general: which the research suggests is an inferior technique.

Even more worrying: the article suggests that students are better off studing the abstract than studying the concrete and then studying the abstract: this is somewhat more surprising, unless the concrete examples are (as sometimes happens) chosen to be rather too baby-ish for students.

Yours, in the abstract,

1 comment:

awareness said...

Though math isnt my forte, what i do love is problem solving and critical analysis.....which i guess falls abstractly under the math umbrella now doesnt it? My brain does work from the abstract down to the concrete....i think this is the case for most adult learners, because the underlying need is to be able to grasp onto some new piece of information and pull it down to a place where it can be linked to prior learning and then applied in life.
This is how I usually approach teaching a new lesson/theory....make it big and abstract-ish and then hone it through examples that the participants can relate to while encouraging them to do so.


ps. have you dropped by to see some of the pics i've posted of the area flooding? Don't know how upriver has fared......but if you follow the link to my friend Charles' blog, you'll see many many pics of downtown Fredericton. The worst is downriver towards Oromocto and Jemseg.....all under water along the valley. There isn't even a market this weekend....