Hi, michel paul escribió: [...] > But creating a suite of simple functions like that would be easy > enough but also challenging enough for most of them, plus these > functions could then easily be configured with @interact. > > Another example of what I'm trying to get at with this 'functional > decomposition' theme: standard deviation. We can define standard > deviation as: > > def stdev(L): return sqrt(variance(L)) > def variance(L): return mean(squares(deviations(L))) > def deviations(L): return [(x - mean(L)) for x in L] > def squares(L): return [x^2 for x in L] > def mean(L): return sum(L)/len(L) > > We are not just blindly coding the typical formula for standard > deviation here. It's a concept map, and it works! (It's also the > population rather than the sample formula, but that's easily adjusted.) > Thanks for the example of concept mapping :-). I will try it in my contexts.
[...] > Right, I don't mean to say that discussion of the problem becomes > irrelevant or even that written discussion is irrelevant. I mean that > certain kinds of arguments will become irrelevant. I'm trying to get > at another sense for what it means to 'show one's work'. If one's > work is to construct a set of functions that will solve a problem, > then one's work works! It could make the discussion of 'showing work' > more meaningful. Instead of writing the math out by hand and using > the calculator to handle the grunt work, I'd rather throw away the > calculator and focus on how to get the kids to construct, articulate, > a computational analysis of a situation. [...] What I have done, not with kids, but with undergraduate students, is to use the heuristics of George Polya in the solution of the problem, but is in the same spirit of what have been said here. Argumentation and analysis is first, calculation/computation comes after that. That's why I try to use a scientific document processor linked with Sage as a primary interface. Some times we don't use Sage at all. Cheers, Offray -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
