For generations,high school students have studied something in school that has
been called mathematics,but which has very little to do with the way mathematics
is created or applied outside of school. One reason for this has been a view of curriculum
in which mathematics courses are seen as mechanisms for communicating
established results and methods — for preparing students for life after school by
giving them a bag of facts. Students learn to solve equations,find areas,and calculate
interest on a loan. Given this view of mathematics,curriculum reform simply
means replacing one set of established results by another one (perhaps newer or
more fashionable). So,instead of studying analysis,students study discrete mathematics;
instead of Euclidean geometry,they study fractal geometry; instead of
probability,they learn something called data analysis. But what they do with binary
trees,snowflake curves,and scatter-plots are the same things they did with
hyperbolas,triangles,and binomial distributions: They learn some properties,work
some problems in which they apply the properties,and move on. The contexts in
which they work might be more modern,but the methods they use are just as far
from mathematics as they were twenty years ago