by
Trizor (797662) <
trizor@gmail.com> on Saturday August 26 2006, @11:42PM (
#15987653)
As one of the 20 (My fifth grade teacher actually read Piaget and showed it to me and labeled me as such) I look at my classmates and see that now (12th grade) they still struggle with symbolic concepts because they were codeled with the concrete for much too long. The example is physics, where the solutions are often entirely symbolic, many students have trouble with manipulating and thinking abstractly in symbols. However in earlier classes they are encouraged to plug in concrete values as soon as they learn them, and I was actually repremanded for using symbols (My Father is a Professor of Physics and when helping me with math homework at a young age insisted on my use of symbols instead of concrete numbers.) in Chemistry I when we were working with heating and cooling and temperature. While the concrete numberse were initially easily grasped by the class, problems quickly arose when they forgot the meaning of each number because it changed problem to problem and began to forget the theory behind what they were doing. The result was that every single class member could work any type of problem they had seen previously on memory of the motions to go through, but had no clue as to what they were doing and could not solve any new type of problem based on the theory they knew. In short: While they may still be developing the ability to understand abstractions, the sooner they begin learning the better they will be for life. You’ll be doing them a favor by introducing them to the concept of a variable and a general solution.
