>Victor Steinbok writes: > >>Why does it seem that the attitude of any working mathematician >>OR school administrator is that cognitive research is a waste >>of time? > >1) Some working mathematicians have had experience investigating >claims made by advocates of cognitive research and feel, in >retrospect, that the time spent in those investigations was >indeed wasted. Perhaps if proponents of cognitive research >could give us more focused citations (rather than telling us to >go read some books on the theory) and make sure that the works >cited actually bear on the issues in question, we would feel >less like we'd been on a wild goose chase. > >2) Some mathematicians are, I believe, turned off by people who >seem to overstate their case--using the word "know" when they >probably mean "believe", or making absolute claims for which we >are acquainted with counterexamples. > >3) Some mathematicians wish that advocates of cognitive research >(and educational research in general) would do a better job of >practicing what they preach. Think of us as your students; if >we have had difficulty absorbing the principles of your theories >might part of the problem be the way you have tried to teach >them to us? > >Chris Grant
But, now you are saying "some" without "focused citations". Who? What research did they look at? What did the research claim that turned out not to be true? How did they feel it wasted their time? Who said "know" when they really meant "believe"? What counterexamples? (Counter examples might be when the instructor follows the stated situation exactly and it doesn't work - not so easy in a field where human intuition and emotions are flying around and where mathematicians might not be the best at reacting to such actions. )
This game is too easy to play. It goes no where.
The whole idea of recommending books is that they have explanations of the citations as well as the citations themselves. You can either believe the explanations or not, but the citations are all there (bibliography) for you to investigate for yourself, if you so choose.
It seems like a waste of time to me (I could be wrong) to suggest that people, as a first reading, read articles on specific investigations. If I wanted people to understand Galois Theory over Local Fields, I would not ask them to first read Shiratani's "On p-adic Zeta Functions of the Lubin Tate Groups".
People need an overall picture of what they are getting into and then get down to the specifics that catch their attention.
It is simply not that big of a request for all mathematicians to read 5 books or 10 articles on what Cognitive Research has learned about how people learn. "Working" mathematicians are in the classroom teaching our future. They should spend sometime finding out what research is being done and what results are being found on how people learn. It is simply unacceptable to allow their research into learning to solely come from their own teaching and thus conclude that it is the students' fault for not trying hard enough. - Not my opinion, said out loud in many departmental gatherings and e-mailings.
There is new information that says the way we traditionally teach is ineffective. There are results that say the brain is more than a blank slate for us to write on. There are results that say our traditional evaluations are missing the mark.
I gave some specific suggestions for specific books that cite specific research for people to specifically read. I picked the first ones off the top of my head that would fall under the easy-to-read category. There are perhaps better ones. (John Anderson's "The Architecture of Cognition" or Howard Gardner's "Frames of Mind "). I can also suggest articles ("Abstract Planning and Perceptual Chunks: Elements of Expertise in Geometry", Cognitive Science 14: 511-550) to look up and read which are less than easy-to-read, but plenty informative.
As for my students, I teach my students to be responsible for themselves, to question, and to seek out knowledge. Responsibility involves meeting me halfway.