> Actually I find that most of my 11th and 12th graders(all ability levels) > handle this concept just fine. I think it comes to how it is presented.
I absolutely agree. This is what I am trying to bring home all the time: teenagers are normally interested in abstractions and can master them. I quoted Vygotsky because I know his writings better, but I am sure that Piaget had essentially the same opinion on this. Regretfully, some teachers of mathematics don't know enough mathematics to offer their students interesting problems. The students are frustrated and educators misinterpret this frustration as lack of interest in abstractions. Then these educators insist on using cumbersome and fat-fetched `real-world' problems, the students are bored still more, and all the situation gets into a vicious circle.
> The material I am using does an outstanding job of getting the point > across. Try this. Have students go outside to a place where you have > marked off points (in meters, feet or whatever you choose). Give each pair > a stop watch and a set of instructions. One might read like this. Start > at 10 meters and walk along tape at a steady pace for 10 seconds, then jog > for 5 more seconds, then stand still for 3 seconds and turn around and walk > back for 10 seconds. Have them record the marking at each time t(make sure > tape is at least 50 to 100 meters long). Have them go back and put the > data on a graph(meters as a function of time). This is an excellent > representation of displacement and the gradients of each segment represent > the velocities. It really does work well!!!! Try it Andre.
Seimour Papers used such activities in his classes of Logo. But his students were of elementary school age and I think that this is important. For high school students this a ridiculous infantilism. High school age is time for a powerful development of abstract thinking and mastery of formalisms. (This does not exclude athletics, games, picnics etc.)
Andre Toom Department of Mathematics firstname.lastname@example.org University of the Incarnate Word Tel. 210-646-0500 (h) 4301 Broadway 210-829-3170 (o) San Antonio, Texas 78209-6318 Fax 210-829-3153