<div class="gmail_quote">On Thu, Jul 2, 2009 at 12:48 AM, Maria Droujkova <<a href="mailto:droujkova@gmail.com">droujkova@gmail.com</a>> wrote: <blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> <div class="im">> From: K. K. Subramaniam <<a href="mailto:subbukk@gmail.com" target="_blank">subbukk@gmail.com</a>> > </div><div class="im">> On Tuesday 30 Jun 2009 11:23:24 pm Alan Kay wrote: >> what is more interesting is how well certain ways of thinking work >> in finding strong models of phenomena compared to others. > This is the part that interests me too ... >> So, if we get >> pneumonia, there are lots of paradigms to choose from, but I'm betting >> that >> most will choose the one that knows how to find out about bacteria and how >> to make antibiotics. > ... and this is where I get stuck ;-), particularly in the context of school > education (first 12 years). Unlike the 3Rs, thinking processes have no > external > manifestation that parents/teachers can monitor, assess or assist. The > economic value of deep thinking is not realized until many years later. The > latency between 'input' and 'output' can be as large as 12 years and > 'evaluation' of output may stretch into decades! </div>I beg to differ here, Subbu. Any time you do any sort of meaningful project with a person of any age, deep thinking manifests itself most strikingly. Here are some household examples: - Deep idea: random events. A toddler pushes a pet bunny off a high place. The mother says that unlike kittens, rabbits can break their legs this way, but the toddler thinks since it did not happen this once, it won't ever happen. The mother takes a glass outside and rolls it down the stairs, several times. It breaks at fourth roll. Toddler experiments with breakable objects more to explore the idea of "sometimes." They keep discussing this big idea of "sometimes" and experimenting. A few years down the road, the mother relates to the kid how this guy was saying, "I smoked all my life and I am fine" - and they laugh at it, together. Probability and statistics comes in later still. Meanwhile, the bunny's safe, and a whole host of dangers that happens "sometimes" are easy to communicate to the toddler. - Deep tool: graphs. Several kids play with graphs qualitatively (a-la <a href="http://thisisindexed.com/" target="_blank">http://thisisindexed.com/</a>). What comes of it? When the 5yo math club members yell too loud, the leader makes a "yelling graph" kids follow up and down in volume, as it's being drawn, thereby obtaining control. When a 10yo experiences a strange math anxiety, she draws a graph of her mood vs. problem solving events, and analyzes it for possible patterns. When a tween and teen group discusses game design, they compare learning curves for apps and games they know and make design decisions correspondingly.</blockquote> <div> i wish I had thought of this for my noisy special class :-) </div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> - Deep collective reasoning: kites. A 3-5 Reggio Emilia group decides to make kites together. Adults provide books and supplies, kids work on patterns and sketch and photograph their ideas. It takes listening and coordinating; their peacekeepers of the day resolve conflicts. Kites change from day to day, becoming increasingly complex.</blockquote> <div> Great examples Maria but Subbu may still be correct - in that some deep thinking takes years to emerge clearly or it might appear then get buried due to peer pressure and then reappear again later, etc. I would say that you are both right. I have heard it mentioned a few times that it takes 10 years for genius to emerge, eg. Mozart started at 5yo but did not display genius until 15yo btw how would the mother know that the toddler did not believe her if the toddler did not voice their dissent? it takes a smart mother to guess that the toddler does not believe and go through the rolling the glass down the stairs routine if the toddler does not object - my general point being that much growth is silent, hard to or almost impossible to observe also see minsky 'society of mind' section 7:10 Genius </div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> Cheers, Maria Droujkova Make math your own, to make your own math. <a href="http://www.naturalmath.com" target="_blank">http://www.naturalmath.com</a> social math site <a href="http://groups.google.com/group/naturalmath" target="_blank">http://groups.google.com/group/naturalmath</a> subscribe now to discuss future math culture with parents, researchers and techies <a href="http://www.phenixsolutions.com" target="_blank">http://www.phenixsolutions.com</a> empowering our innovations</blockquote></div>