http:\/\/www.funbrain.com\/guess\/index.html<\/a><\/p>\nYou guess a number between 1 and 100 (or 1 and 10) and the computer tells you if the answer is higher or lower than the guess.\u00a0 This process repeats until you guess correctly or you run out of turns.\u00a0 You have 7 guesses for 1 to 100.\u00a0 My recollection from my Computer Science graduate work was that a binary search is the optimal strategy for this type of problem.\u00a0 So, your first guess would be 50.\u00a0 If the computer said lower, you would then guess 25.\u00a0 If the computer said higher, your next guess would be 75.\u00a0 This allows you to rapidly hone in on the answer.<\/p>\n
When I asked my colleague if she taught the kids this strategy, her response was that she never teaches kids strategies but always lets the kids find their own strategies.<\/p>\n
I really questions this approach, which seems to be an extreme interpretation of the constructivist philosophy of education.\u00a0 From wikipedia, Constructivism<\/strong> is a theory of knowledge, which argues that humans generate knowledge and meaning from their experiences.\u00a0 If taken to its limits, teachers never actually teach anything but provide the materials and experiences so that children can discover everything for themselves.<\/p>\nIn my experience, it is an excellent practice to give students a chance to explore problems on their own without giving them the answer or the strategy to get the answer.\u00a0 However, not all algorithms are the same.\u00a0 We know from the field of computer science, that algorithms can be mathematically evaluated as to their efficiency.\u00a0 Of course, they need to be correct too!\u00a0\u00a0 Some teachers (and I am not sure if my colleague is one or not), seem to feel that all ways of getting the answer are equivalent and equally valid.\u00a0 This is clearly not true.\u00a0 So we should encourage different ways of getting the answer but we should also be evaluating them as to which methods are better than others.\u00a0 I think it is misguided in the attempt to preserve self esteem to say that all methods are equally good.\u00a0 Some even think that getting a correct answer is not important, but only the method.\u00a0 I would say that both are important.<\/p>\n
I also think that we most definitely need to teach kids strategies and methods after giving them time to explore on their own.\u00a0 To not do so robs students of all the mathematical work that has gone before them.\u00a0 You would not get very far in math without understanding what has gone before us.\u00a0 So I teach specific problem solving strategies and computational algorithms.\u00a0 Frankly, some students would never arrive at good algorithms if never shown to them.\u00a0 Children also construct knowledge from what we teach them.\u00a0 In my view, they need to make sense of not just their own ideas but the ideas of those that have been gone before them.\u00a0 That can be done in a hands on way with math manipulatives with young children.<\/p>\n","protected":false},"excerpt":{"rendered":"
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