by Stephen Perencevich
I have a couple of thoughts on expectations of mathematics. Linda McIsaac complains that when students enter the workforce they are not trained in the use of spreadsheets or Pareto Diagrams or in the ways of Total Quality Management. She may be right on this score, but I don't think that such topics should be taught in mathematics courses.
When I was in high school vocational courses were offered, except that back then we had courses in carpentry and printing. I actually took a course in machine shop in which I learned how to use machine tools such as the lathe and drill press, an excellent application of my mathematics skills. If students are lacking in vocational skills, why not offer courses which address the problem directly?
Spreadsheets, TQM, word processors, data bases, and the like all have somewhat of a mathematical component, but let's face it: they are not rocket science. If a student has taken a rigorous mathematics curriculum, learning such skills would border on the trivial. How do professional learn such skills? Not in mathematics courses. A few hours spent at the keyboard with the manual at your side is normally sufficient.
Algebra, geometry, precalculus, and calculus all are (or at least should be) purely mathematical. Virtually any person should be able to achieve competence (if not mastery) of these subjects in four years of study. If new approaches and the use of hand-held calculators help students to learn mathematics better, then I say bring them on. But let us keep some perspective.
The foundations of mathematics have been successfully passed from one generation to the next for millennia, before the invention of the calculator or the light bulb, before the invention of the printing press or even the pencil. The real impediment to students learning mathematics is their own lack of motivation. How can anyone with any motivation at all spend twelve years in school and not be able to add fractions or solve a simple linear equation? Mathematics is not easy, and no amount of curriculum reform, pedagogical reform, or use of technology will make it so. The only way to learn high school mathematics is to engage the material on a non-trivial level.
Most of the proposed solutions to the motivation problem involve enticing students with future economic benefits or convincing students that the topics will be useful in their "real life." These approaches are doomed to failure. We are, after all, talking about teenagers. They have a hard time thinking past next weekend. The connection they see between present actions and future consequences is tenuous at best. Motivational strategies which offer rewards to be realized only in the long term are clearly ineffective.
Stephen Perencevich can be reached by e-mail at: Stephen_Perencevich@webster.senate.gov.