A Math Makeover: Closing the Gap Between High School and College Math
By Tao Pang
In his Back Page article in the October APS News, Joseph Ganem has correctly identified the widening gap between high school and college math. Here I want to focus on the poor outcomes of college math classes and suggest a few strategies that can be adopted to improve the situation.
Over nearly two decades, I have witnessed a steady decline of math readiness of college students in my general physics classes. How bad is it? A couple of years ago, I started conducting a math background survey in my general physics classes. The survey questions included all necessary math elements for the course and the results indicated that nearly half of these students could not carry out simple arithmetic operations.
According to a recent report from the Brown Center on Education Policy at the Brookings Institution, researchers have found that the misplaced math student in eighth-grade algebra class is at the level of third grade if not worse. My math survey result is consistent with the findings of the Brown Center; half of the college students have not learned more math since third grade.
There is also a sharp contrast found between the students well-prepared in math and the others. For example, the students who had 50% or more correct answers in my math survey showed a strong correlation between knowing more math and learning more physics. Thus students better prepared in math do better in college classes and will more likely finish their degrees.
What can we do to improve the situation? First is how to improve the preparatory math education. Certain basic concepts, such as the order of arithmetic operations, fractions, percents, and square roots, taught at elementary school or middle school, should be reinforced over the course of the math education in high school and beginning college classes. Geometry is a fundamental subject that needs to be reinforced in beginning college mathematics before trigonometry is taught.
A two-tier precalculus course can help both well-prepared and lost students. A placement test can be used to admit students into fast-track one-semester precalculus. Others should take a one-year course that will give them more time to catch up without delaying them from taking the course. Adequate resources should be directed to math education by hiring more competent teaching assistants for the classes. Assign the best instructors to teach these courses and award them with merit, reduced teaching or service load, or teaching assistance. Mandate recitation for the slow-paced course. The goal of recitation is to help students one by one to catch up in arithmetic, prealgebra, or whatever is needed to move them to a better level in math. For some, this may just mean that they will learn how to add and multiply, and that’s it. For others, this can be an opportunity for them finally to learn how to solve an equation.
How can we improve the learning of the students in a typical physics class given their weak math background and time constraint? A quick overview of the basic skills in mathematics at the beginning of the course is a good starting point. A small number of well selected exercises can be helpful, too. A similar review, with calculus included, can also be devised for students taking a calculus-based physics course. A handout that summarizes the math needed is another effective tool. A set of well compiled web links suits this generation of students even better.
In my general physics class, I usually take a three-step approach to a subject. I start with some cartoons and sketches to illustrate a new concept. Then I try to describe the concept as accurately as possible in words. The final step is to introduce the concept with the necessary mathematics combined with examples. About half of my students can follow immediately in this third step after the preparation of the first two steps. The other half will need extra help, which usually is not readily available or may cost students financially. Each college should concentrate on this problem by creating individual tutoring programs for the students.
If we help students make up the math that they should have learned, we will close the gap between high school and college math. Knowing that the enemy of higher education in physics is the lack of math, we can win the war for student retention by strengthening math education on all fronts.
Tao Pang is Chair and Professor at the Department of Physics and Astronomy, University of Nevada, Las Vegas and author of the book: An Introduction to Computational Physics, published by Cambridge University Press.