Photo: In two of the study classes, students work in small groups.

(Photo by WSU Photo Services).

 
Calculus is the New York of the academic curriculum. If you can make it there, so the feeling goes, you can make it anywhere.

Trouble is, most students can’t.

“All across the United States, precalculus is a challenge,” said Sandy Cooper, associate professor in the WSU math department. About 40 percent of students who enroll in precalculus withdraw or fail, she said. And among students who take precalculus at WSU and then go on to take calculus, only 50 percent succeed on their first attempt.

 “That’s a huge concern,” Cooper said, because calculus is the de facto gatekeeper — the Ellis Island, as it were — that keeps students out of engineering, math and physics. Other majors that require precalculus or calculus courses include biological and earth sciences, business, economics, architecture and construction management. 

Four test classes
Cooper and Jo Clay Olson, an assistant professor in the department of teaching and learning, teamed up last spring to begin what they believe will be one of the most in-depth research projects devoted to better understanding not only why students fail calculus courses, but what can be done to help them.

“What we will be learning this year is where we really need to be focusing our attention,” Cooper said. “What we want to see from this is where our time is best spent.”

This semester the math department is offering 13 sections of precalculus, but four sections have been modified to look at both pedagogy and class size.

 The control section, a lecture-based course, is being taught by a skilled instructor who is successful at engaging students in the material within the traditional format, Cooper said.

In another section, students are working in groups of three or four, with the teacher acting as “the guide on the side” rather than “the sage on the stage.” In a third section, the teacher has a more central role, as in a lecture-based class, but students work in pairs and spend a significant amount of time in class working together on problems.

The fourth section is also lecture-based, but there are only about 40 students in the class, about half the size of a regular precalculus class.

Each class is being videotaped at least twice during the semester, and researchers are taking detailed notes regarding class interactions and teaching methods.
 
Transferable knowledge
In addition to the qualitative data, Cooper and Olson are compiling a mountain of quantitative data. Each precalculus test is being deconstructed, question by question and step by step, to determine precisely which mathematical concepts are required to successfully work though the problem. That information is being shared with course instructors to help them during the semester, but it is also the raw data that will inform what the researchers hope will be several papers on the topic.

One of the things they are looking at, Olson said, is which questions require a fundamental understanding of a particular concept and which questions require an advanced understanding.

One hypothesis for why such a high percentage of students who pass precalculus go on to fail calculus is that students in precalculus learn enough to have a basic understanding, but never internalize the information to the point that it is “transferable” to other applications.

Inspired to learn
“Cramming doesn’t work,” Cooper said. “These are really important tools that students are acquiring. It’s the language that they are going to speak from here on out.”

“And they need to be fluent,” Olson added.

The math department is funding two-thirds of this research project and the Office of Undergraduate Education is funding the rest.

Olson said the impetus for the comprehensive research design grew out of Jean Lave’s appearance on the Pullman campus in September 2006. Lave, a professor at U.C. Berkeley, is a well-known social learning theorist who has written extensively about “communities of practice.”

“She got us to dream and think outside the box,” Olson said.

Use it or lose it – in high school
More students study calculus in high school than in college, but only about a third of them get college credit for their efforts, says David Bressoud, president of the Math Association of America.

In a paper published online in April 2007, Bressoud states that, in 2004-2005, about 400,000 college students and 500,000 high school students studied calculus. But only about a third of the high school students placed high enough on math placement tests to skip the course in college.

One problem might be that the high school course simply isn’t as rigorous as a college course, said Sandy Cooper, associate professor of math at WSU. But it also might be that some high school students take precalculus or calculus as juniors and then take no math during their senior year.

That doesn’t work for most students.

“It’s like a language,” she said. “If you don’t use it, you lose it.”

Still, she said, those high school classes are not necessarily a waste of time, even if students end up repeating them. That early introduction can help students build a deeper understanding once they get to college.