<html><head><style type="text/css"></style></head><body><div style="font-family:times new roman,new york,times,serif;font-size:12pt"><div>I would agree with Albert if notions could only be divided into two parts (and the unsophisticated human brain loves this kinds of "either-or" distinctions). I was careful to identify at least three divisions in my initial post. The two of interest are "fluent, but not pro" and the one that Albert mentioned "pro". I'm interested in the first of these "fluent, but not pro", because this is where learners are doing the "real deal" and not any other kind of deal. This is the level that is necessary for a Jeffersonian democracy in which "the ultimate repository of the powers of the society lie in the hands of the people" and "if their discretion is not sufficient, the remedy is not to take these powers from them but to better inform their discretion through education". A good goal for the larger system -- which has to include not just what people need in their practical life, but also what they need to understand the issues of their society, how their society works, what their responsibilities as citizens need to be, etc. For example, in the 21st century, a fluent (but not "pro") understanding of science, and of the way that science looks at knowledge and knowing is needed to be a "holder of the ultimate powers of the society". A good and reasonable goal for a modern society (like the US) would be to have 70% to 80% of the citizens have this medium level of fluency. This reasonable medium level of fluency requires some real ability to do and to think within the different domains. (I trust this will not be controversial in a world whose understanding and response to AIDS, to climate problems, and to many other systemic difficulties has been wildly different depending on the level of understandings of the mathematics and science of these systems in the different societies.) Tip O'Neal once said that "All politics are local" -- and one large goal for "real deal education" would be to change that in a large enough way to move the societies and their citizens out of just trying to maximize their various localities to the detriment of the finite and critical larger "outside of tribe" issues. </div><div style="font-family: times new roman,new york,times,serif; font-size: 12pt;"> A good heuristic is to make a scheme for the real deal (and to take care of the local practical needs as part of these). A bad heuristic is to make a scheme for the practical needs and hope that the real deal will somehow happen because the simpler needs are part of the larger real deal (this just hasn't happened, and likely just won't happen). Part of the reason here is that the larger real deal is rather different epistemologically, whereas the practical smaller parts often are reachable by training existing commonsense reasoning. An analogy that is not too strained is that people made things with bricks for thousands of years before the arch was invented -- there was almost no route via "brick thinking" to the arch, despite that arches can be made from bricks. Best wishes, Alan <div style="font-family: arial,helvetica,sans-serif; font-size: 10pt;"><hr size="1">From: Albert Cahalan <acahalan@gmail.com> To: droujkova@gmail.com; iaep <iaep@lists.sugarlabs.org> Sent: Thursday, May 7, 2009 2:55:09 AM Subject: Re: [IAEP] versus, not Maria Droujkova writes: > 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. I don't think this is a proper expectation. Gym class isn't expected to create pro or Olympic athletes. Music class isn't expected to create pop stars. Native language class isn't expected to create a J. K. Rowling, Shakespeare, or Tom Clancy. Math isn't any different. A student who is **solidly** prepared for calculus is doing well. This would include word problems with a minimum of 4 steps, some algebra, geometry, trigonometry, etc. Here in the USA, most students get nowhere near that level. For the very best students we may hope for completing calculus early enough to use it for physics, followed by statistics with calculus. Maybe one could throw in a tiny bit about game theory or aliasing. A desire to have students "make mathematics" can't be allowed to get in the way of ensuring that non-ideal students learn the existing math that they need. Math isn't just for people like Euler. _______________________________________________ IAEP -- It's An Education Project (not a laptop project!) <a ymailto="mailto:IAEP@lists.sugarlabs.org" href="mailto:IAEP@lists.sugarlabs.org">IAEP@lists.sugarlabs.org</a> <a target="_blank" href="http://lists.sugarlabs.org/listinfo/iaep">http://lists.sugarlabs.org/listinfo/iaep</a> </div></div></div> </body></html>