On Fri, Jan 1, 2010 at 3:26 PM, michel paul <mpaul...@gmail.com> wrote: > After reflecting on the responses I received last year (and happy new one!), > here is a condensed version of points I'd like to express to my > administration: > > Given the ubiquitous nature of freely available and powerful computational > technology in our culture, what should high school students learn? > I believe they should learn math in a way that simultaneously empowers them > to make the most effective use of this technology. > Fluency in graphing calculator use is not sufficient for contemporary > computational literacy. In fact, it is neither necessary nor sufficient. > The only possible reason for insistence on their continued use would be > founded in an interest in promoting the product. The AP and SAT exams > promote the use of these products. QED. > A problem in promoting the use of such products is the limited understanding > of mathematics they encourage. > The standard of mathematical and computational literacy required (not > necessarily by current state standards, but in the larger world) by today's > high school students can be addressed through the judicious study of > computational language. > Not all programming activity leads to mathematical insight. However, a > central core of what we call programming is in fact a form of pure > mathematics, and many aspects of this way of thinking are in fact relevant > for the high school math curriculum. The sooner America gets on task on > this, the better off we'll be. We can begin to address the deficiencies in > both our secondary mathematical and technological literacy simultaneously. > > Again, please let me know if I'm off base with any of this. Is any of this > irrelevant or tangential? > > In my initial list > >>7. Instead of spending so much time teaching kids how to isolate variables >> in equations, perhaps it would be better for them to learn how to construct >> suites of simple interacting functions? > > I think is clearly a mistaken expression. It should not be 'instead of > ..'. Rather, > >>7. In addition to learning how to isolate variables in equations (and >> explaining their reasoning), kids also need to learn how to construct suites >> of simple interacting functions to model and test ideas. > > Again, please correct me if I'm off, but I think this is one of the central > differences between what we do in traditional high school math classes vs. > what one does using a computational language/environment - construction. > When using something like Sage, most of one's effort is not engaged in > 'solving equations' but in constructing computational models of ideas, and > this is important for today's math students to learn to do. Our traditional > curriculum doesn't touch that kind of stuff - or only rarely. > > I completely agree with and appreciate the importance of getting them to > isolate variables in symbolic formulas. I think that's where a lot of > problems arise in students' understanding of what algebra even is (and I > think the emphasis on calculators has promoted this misunderstanding) - they > think it's all about finding particular numeric solutions for individual > equations or for systems of, at most, 2 or 3 equations. Then, when it's > purely symbolic, their reaction is "Why are there so many letters? Why > can't you use more numbers?" But this really is where they need to focus. > The reasoning required to manipulate symbolic expressions is directly > related to the reasoning required for computational constructions. > > There seems to be lots of agreement about the importance of writing in > math. Perfect. I hope this can be a major point in persuading my > administration that integrating something like Sage - not treating it like > it's something foreign - would be extremely valuable. Again, kids could > create their own math reports in Sage, little mini-papers, that would > actually do stuff while explaining ideas. > > And along with writing - reading. I deeply appreciate the recommendation > that if kids learn to read a math text that everything else becomes > secondary. Yeah, that's great. I'm going to make a point of incorporating > that into my classes. > > As for 'concept maps' I will replace the example of the quadratic formula > with the example of standard deviation. I think that conveys the point > better. > > What I now need is a simple, direct, knock-down, and hopefully fatal > argument against the entrenched position that 'graphing calculators are > enough'. That's really the whole source of the opposition I constantly face > in the high school world the AP and SAT are considered sacred and anything > 'else' is too much. > > My position has been that, no, this is not some other layer on top of the > math, this IS math itself, this is how mathematicians do things these days. > > How accurate am I in making statements like that? I want to create as > effective and accurate an argument as I can.
Definitely many mathematicians use computers, but that is not how *all* mathematicians do things these days. In any case, as my wife is a teacher in the public school system, I am not convinced that administrators are swayed by accurately stated facts. They know their mission is teaching kids and if you can convince them the school system do a better job educating kids using computer programming then you can connect teaching programming to their mission. Hopefully, that is something they can grasp. I think Kirby Urner http://www.4dsolutions.net/ocn/index.html has thought about tese things. You might want to email him directly (I'm sure he is not on this list) to see what his opinions of your proposal is. > > Also - has it become the norm for college math departments these days to use > some form of CAS, whether Mathematica, Maple, MatLab, or Sage? Or do only > some use these things? If it has in fact become the norm, and if we think > we're trying to prepare kids for the world they'll be entering, well, why > NOT show them these things? > > Again, thanks very much for the constructive dialog on this. > > Happy New Year. > > - Michel Paul > > -- > > 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. > -- 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.
