On Wed, May 6, 2009 at 9:26 AM, Alan Kay <alan.n...@yahoo.com> wrote:
> If the real deals are chosen, then the interesting question is what kinds > of processes will work for what kinds of learners? If it is some non-trivial > percentage of direct instruction, then this is what should be done (and > depending on the learner, this percentage could range from 0% to a > surprisingly high number). However, part of the real deal is being able to > *do* the pursuits, not just know something about them, so all pedagogical > approaches will have to find ways to get learners to learn how to do what > practitioners do who above the two thresholds of "fluency" and "pro". > > Tim Gallwey is one of the best teachers I've ever observed, and he had a > number of extremely effective techniques to help his students learn the real > deal very quickly (and almost none of these were direct instruction -- > partly because, as he liked to say, "The parts of the brain that you need to > do the learning very often don't understand English!"). But if he could see > that the student had gotten on a track that couldn't be influenced by > "guided discovery", then he would instantly tell them to "do it this way". > In other words, he was not religious about his own very successful method, > but instead did what his students individually needed and that worked the > best for them (which happened to be "learning by doing"). > I think it may be useful to distinguish tracks, and destinations to which they lead. The real deal destinations are to make mathematics: coin definitions and refine them, pose problems, form conjectures, construct example spaces, create models and so on. Activities with real deal destinations invite students to make mathematics; this is the part where I get pretty "religious" and I suspect Tim does, as well. Then teachers can help students to search for tracks toward these destinations, by whatever methods work best. Searching for fruitful tracks is a large part of the real deal, of course. But such searching, for field practitioners, does involve referring to past work in the field, and getting "direct instruction" from peers and more advanced colleagues. For example, a kid I observed, trying to extend her model of division to also work on improper fractions looked at a bunch of traditional algorithms in search of ideas. Math Club members attempting to create a definition of multiplication that makes sense to them were directly instructed on some existing definitions, to which they listened with rapt attention. When Tim "would instantly tell them to "do it this way"" it made sense, because "this way" was a track toward some real deal destination. -- Cheers, MariaD Make math your own, to make your own math. http://www.naturalmath.com social math site http://groups.google.com/group/naturalmath our email group http://www.phenixsolutions.com empowering our innovations
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