The fall semester may be just about over, but for too many calculus students, the relief of being done with finals is tempered by a loss in math confidence — especially if they’re female, reports a recent study by the Mathematical Association of America (MAA).
Funded in part by the National Science Foundation and edited by professors from Macalester College, University of Michigan–Ann Arbor, and San Diego State University, the five-year study surveyed 213 colleges and universities, 502 instructors, and more than 14,000 students. The study, released in October, found that there was not only a drop in math confidence after taking Calculus 1, but also a drop in math enjoyment, and an increased sense of worry among students that they couldn’t handle new material. This was reported by students at every kind of institution, from the Ivy Leagues to community colleges.
Women were far more prone to this kind of thinking than men.
Students are not wrong to feel this way, since the study showed that, on average, only half got the grades usually needed (that is, an A or a B) to do well in Calculus 2 (Calculus 1 is equivalent to Calculus AB; at some schools Calculus BC is equivalent to Calculus 1 and 2, or a year of college calculus, though some schools structure their courses differently). At community colleges and state universities, the proportion of A and B students was even lower.
This may not seem like such a big deal, since only about 700,000 students out of 20 million take college calculus every year. But those calculus students aren’t all math majors; according to the study, barely two percent are. Nor are they in physics or other hard sciences; those disciplines account fors just four percent of calculus-taking students. Five percent go into computer science, seven percent go into finance, and five percent become teachers. The bulk of calculus students go into engineering (31 percent) or the biological or medical sciences (30 percent).
“Calculus occupies a unique position as gatekeeper to the disciplines in science, technology, engineering, and mathematics (STEM),” wrote the authors of the study. “At least one term of calculus is required for almost all STEM majors. For too many students, this requirement is either an insurmountable obstacle or — more subtly — a great discourager from the pursuit of fields that build upon the insights of mathematics.”
While the MAA study only covers the past five years, this is not a new problem. Math educators first began talking about the calculus-aversion phenomenon in earnest in the late 1970s. Robert White, a noted meteorologist and former president of the National Academy of Engineering, said college calculus needed to stop being a “filter” and turn into a “pump.” A 1988 report by the MAA, “Calculus for a New Century: A Pump not a Filter,” launched a movement to reform how calculus is taught in schools. Sadly, according to this most recent study, the movement hasn’t made much progress, but the researchers have hopes that this new study will help.
“Calculus is still a filter, but until 2010 we knew very little about who takes it, how it is taught, or what makes for effective calculus programs that promote rather than inhibit students’ continuation into successful careers in science and engineering,” they wrote.
So, what can help?
The study found that taking calculus in high school, even passing the AP exam, was no guarantee of success in college. Only students who got a 4, or even better, a 5, saw benefit, and the study reveals that students with top scores often manage to skip Calculus 1 altogether, taking themselves out of the pool.
And what about before that?
A really good precalculus course is vital, according to the study, whether in high school or college. It also showed that taking precalculus in college as opposed to in high school is no guarantee that students will be prepared for calculus, and that in some cases college precalculus may even prevent them from taking calculus altogether. According to the study, this is because they either failed the class, were too discouraged, or unprepared to go on to calculus — which then kept them from majoring in STEM fields.
Once a student is enrolled in calculus, the study found (unsurprisingly) that the instructor plays a huge role in student success. Effective instructors, the authors wrote,
Create a positive atmosphere in which the instructors encourage students to ask questions; maintain a positive attitude towards students’ mistakes; keep reasonable pacing of the lecture to ensure all students are on the same page, with time for individual, pair, or group work; set high standards and clear expectations that all students can meet, and have availability to answer student questions and respond to students needs.
Effective instruction, the study found, is not necessarily affected by class size, though smaller classes do allow the teacher to get to know students better. Also, the level of education of the teacher isn’t a guarantee of that instructor’s ability to teach (that is, not everyone needs a math doctorate). Finally, using tech in class, such as calculators or math software, was not much more effective than using pencil and paper.
And while the teacher is crucial, so are others: Having additional support, from tutors to math labs to alternate courses (some universities offer a longer class, or calculus aimed at specific non-math majors) can help. So can making students feel like they are important parts of the math community, particularly during their first year.
That said, the authors of the study acknowledge that there are no easy solutions, particularly in an economic climate that has squeezed most math departments. The authors point to increased enrollment and budget cuts, as well as an inability to support and retain women, minority students, economically-disadvantaged students, and first-generation students. The authors also acknowledge, however, that there is more need than ever to make changes. This is particularly true given high expected growth rates in STEM fields.
But things can change.
“Our colleges and universities want students to succeed. For high school teachers and administrators, this report may open their eyes to the obstacles and struggles our universities face and the very challenging environment students encounter as they make the transition to post-secondary education.