<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "> On 07 May 2009, at 11:55 , Albert Cahalan wrote: <blockquote type="cite">Maria Droujkova writes: </blockquote><blockquote type="cite"> </blockquote><blockquote type="cite"><blockquote type="cite">I think it may be useful to distinguish tracks, and destinations to </blockquote></blockquote><blockquote type="cite"><blockquote type="cite">which they lead. The real deal destinations are to make mathematics: </blockquote></blockquote><blockquote type="cite"><blockquote type="cite">coin definitions and refine them, pose problems, form conjectures, </blockquote></blockquote><blockquote type="cite"><blockquote type="cite">construct example spaces, create models and so on. Activities with </blockquote></blockquote><blockquote type="cite"><blockquote type="cite">real deal destinations invite students to make mathematics; this is </blockquote></blockquote><blockquote type="cite"><blockquote type="cite">the part where I get pretty "religious" and I suspect Tim does, as well. </blockquote></blockquote><blockquote type="cite"> </blockquote><blockquote type="cite">I don't think this is a proper expectation. </blockquote><blockquote type="cite"> </blockquote><blockquote type="cite">Gym class isn't expected to create pro or Olympic athletes. </blockquote><blockquote type="cite">Music class isn't expected to create pop stars. Native language </blockquote><blockquote type="cite">class isn't expected to create a J. K. Rowling, Shakespeare, </blockquote><blockquote type="cite">or Tom Clancy. </blockquote><blockquote type="cite"> </blockquote><blockquote type="cite">Math isn't any different. </blockquote><blockquote type="cite"> </blockquote><blockquote type="cite">A student who is **solidly** prepared for calculus is doing well. </blockquote><blockquote type="cite">This would include word problems with a minimum of 4 steps, </blockquote><blockquote type="cite">some algebra, geometry, trigonometry, etc. </blockquote><blockquote type="cite"> </blockquote><blockquote type="cite">Here in the USA, most students get nowhere near that level. </blockquote><blockquote type="cite"> </blockquote><blockquote type="cite">For the very best students we may hope for completing calculus early </blockquote><blockquote type="cite">enough to use it for physics, followed by statistics with calculus. </blockquote><blockquote type="cite">Maybe one could throw in a tiny bit about game theory or aliasing. </blockquote><blockquote type="cite"> </blockquote><blockquote type="cite">A desire to have students "make mathematics" can't be allowed to </blockquote><blockquote type="cite">get in the way of ensuring that non-ideal students learn the existing </blockquote><blockquote type="cite">math that they need. Math isn't just for people like Euler. </blockquote> I agree 100% with that statement Albert. It would be irresponsible in the extreme. In fact, probably, such a policy decision would likely destroy civil society. I might take a bit of an issue with the use of the term "non-ideal" but this is a silly detail not worth quibbling about because we all know which students we are talking about. My question for everyone is, can we come to agree that not only is Albert's statement true, but the following statement is at the same time also true: "A desire to have students learn the existing math they need can't be allowed to get in the way of nurturing those students who aspire to become mathematicians one day." Yes ? Great ! So now we all agree there is a critical need to make sure that, even if we have to move heaven and earth to do it, we must all make friends with each other and work together so that the learning system can support both kind of student! Because if we don't... we're all going to still be stuck with our existing system when we revisit this argument next year, and the next year, and the year after that. And we must all agree that this is very important because this existing learning system of ours... this system is really great because it manages to at the same time, simultaneously:  * Produce students who are NOT able to do the elementary mathematics needed to thrive in our complex society. AND  * Produce students who are NOT getting access to critical instruction during the years they are most likely to integrate the math at a level allowing them to produce the work of an Euler one day instead of wasting their talents & postdoctoral qualifications helping the management at Lehman Brothers et al accidently the entire economy. Wow! If Phys Ed teachers are able to help the non-ideal kids like me learn to throw a ball and still support the kids who will pitch major league one day surely it can't be that hard ? On this note I'll sit down now and let Rabbi Eliezer lead the class in prayer:  <a href="http://lesswrong.com/lw/3h/why_our_kind_cant_cooperate/">http://lesswrong.com/lw/3h/why_our_kind_cant_cooperate/</a> - antoine -- <a href="http://7degrees.co.za">http://7degrees.co.za</a> "Libré software for human education." </body></html>