Those of us who regularly deal with entering college freshmen are all too familiar with their inadequate math preparation. But in fact, high school mathematics has been ramped up quite a bit in terms of content. What happened? An article in the American Physical Society discusses this paradox. The author of the article, Dr. Joseph Ganem, is a professor of physics at Loyola University, Maryland. He is also a parent of children in high school. He noticed that over the years, the math homework his children were assigned required his frequent intervention. Since this is a parent with a Ph.D. in physics, he had no trouble helping them. But what about the many other students who do not have such an educated parent or access to tutoring services? Sounds like many students are just muddling through their jr. high and high school math without retaining much of anything. He points to two major flaws in the high school curriculum:

1. Confusing difficulty with rigor. It appears to me that the creators of the grade school math curricula believe that “rigor” means pushing students to do ever more difficult problems at a younger age. It’s like teaching difficult concerti to novice musicians before they master the basics of their instruments. Rigor–defined by the dictionary in the context of mathematics as a “scrupulous or inflexible accuracy”–is best obtained by learning age-appropriate concepts and techniques.

(emphasis mine)Attempting difficult problems without the proper foundation is actually an impediment to developing rigor.

[….]2. Mistaking process for understanding. Just because a student can perform a technique that solves a difficult problem doesn’t mean that he or she understands the problem. …

Pushing students too early to do algebra is not really the answer to our perennial problem of students being noncompetitive in the global mathematical landscape. We ought to invest in better teacher prep programs in colleges and provide better incentives for pursuing a career in K-12 teaching. And the math that is taught should be focused and connected, not just a drill based collection of disconnected topics, nor the latest reform program designed by math educators from the education college.