The end result is a group of students who have “succeeded” in high school calculus without really having the proper foundations, a tower built on sand. It is quite possible for students to learn the mechanics of many categories of calculus problems and to answer questions correctly on exams without really understanding the concepts. To quote the MAA’s report:
In some sense, the worst preparation a student heading toward a career in science or engineering could receive is one that rushes toward accumulation of problem-solving abilities in calculus while short-changing the broader preparation needed for success beyond calculus.
.. The college course covers the same material in a quarter of the time; students must therefore have solid skills in algebra and geometry along with good study and work habits to succeed.
.. The rush to AP Calculus has instructed students in the techniques for solving large classes of standard calculus problems rather than prepare them for success in higher mathematics.
.. But if we want to advance STEM education and continue to produce a high-quality technical workforce we must confront this issue. We need to stop the rush to calculus and focus instead on a thorough grounding in algebra, geometry and functions.
Calculus is one of the great intellectual achievements of the last 400 years; shortchanging it by reducing its beauty and utility to a list of problems to be checked off a rubric does a disservice to everyone.