The K-12 system keeps sending us students who can't do algebra. Here's how to fix that.

As leaders of science and engineering departments at a public university, we have front row seats to the outcomes of America’s approach to kindergarten-12th grade (K-12) math education. We see incoming students’ math placement test results, and we also witness firsthand their performance in our classes.

In our view, proposals to slow the pace of instruction are not necessarily troubling (although the devil is always in the details). But our chief concern is that whatever the standards might be, students must face meaningful checkpoints to ensure that they actually meet the standards before advancing to the next step.

Most students tell us — promisingly — that they took calculus or pre-calculus as high school seniors. Alas, placement tests show that in a typical fall semester, nearly half of entering physical science and engineering students have not developed algebra skills appropriate to college-level calculus. They end up falling behind, taking courses in high school-level algebra and trigonometry, rather than learning calculus.

This wouldn’t have happened if the K-12 system had taken a more gradual approach to honing core skills.

A false perception of progress appears to be the main problem. People are understandably happy when more students move rapidly into calculus, a class that was a rarity for earlier generations of high schoolers. Given perennial educational concerns over getting more students into science and engineering, who could blame anyone for feeling good when more students take advanced math? As a consequence, every math student gets to be above average in Lake Wobegon, and society gets to believe that our economy’s need for technical professionals is being met.

Alas, too many students aren’t ready. Both the placement tests and classroom experience indicate that many have not yet mastered algebra to the degree necessary for calculus. It’s not really the students’ fault — they went through a system that prized rapid progression rather than gradual, in-depth practice. Thus, many students know algebra to an extent, but not well enough to reliably spot their own mistakes or tackle complex problems. The situation is akin to knowing a language well enough to answer simple questions but not well enough for sophisticated conversation.

Science and engineering textbooks are packed with algebraic expressions. Attempting to study these subjects without strong algebra skills is akin to reading and discussing Tolstoy in the original Russian while still struggling with verb tenses.

The stakes, however, go well beyond misunderstanding literary devices. One cannot design airplane wings, analyze statistical data, develop encryption tools, or perform countless other technical tasks essential in modern society unless one can use algebraic formulas as deftly as a literary scholar parses metaphors.

The solution is simple: slow down. Reinforce half-finished foundations. Give high school students at the end of junior year the same math placement tests that colleges administer to incoming freshmen, and let the ones with algebra deficits take courses that meet their needs, rather than rushing them into calculus. More gradual math progress won’t look as good on the college applications, but it will lead to more students actually taking and passing calculus in their first year of college, instead of delaying calculus to play catch-up.

Of course, a policy reform is only as good as its feedback systems. In our university departments, we rely on medium-term to long-term data to inform educational decisions. We track student performance in subsequent classes, keep in touch with alumni, and seek input from the industries that hire our graduates. We learn what we’re doing well and what we should improve.

California’s public high schools should likewise receive data on how their graduates perform in their first year of college, especially at public universities with missions to serve California’s high school graduates. Special attention should go to whether graduates who attempt math-intensive majors place into and pass the appropriate freshman math classes. Introductory calculus classes follow very similar curricula across all 23 Cal State campuses, enabling data collection and meaningful comparisons for high schools that send significant numbers of students to the CSU system.

The steepest cost of our proposal is forsaking idealism, moving away from the lofty but unrealistic goal of getting students into calculus as rapidly as possible. Sustainable progress is more about firm foundations than fast results.

Better that a college student start in calculus and succeed than aim to finish calculus in high school, fail to develop core skills, and repeat algebra in college. Our country needs scientists and engineers whose math skills are competitive in a global high-tech economy. High schools, in turn, need appropriate information and incentives to ensure that those skills are developed.

Alex Small is a professor of physics and astronomy and Yasser Salem is a professor of civil engineering at California State Polytechnic University, Ponoma.