Last year, Brigham Young University professors taught experimental calculus courses with honors students to test an emerging and controversial way of teaching math. Instead of lecturing, Janet Walter and Hope Gerson, assistant professors in BYU's department of math education, had the students hash out math problems cooperatively.
They explored scenarios from the real world, such as calculating the volume of a region formed around an axis, with the hope of arriving at key math theorems on their own. The professors wanted to study how people learn math - that most abstract, yet essential of academic pursuits.
But some BYU faculty are questioning whether Gerson and Walter's students learned much calculus after they bombed on departmental exams. Even though they were teaching high-achievers in smaller classes, test scores were lower than BYU's overall averages and sunk as the experiment proceeded over the course of three semesters.
"At the end of the day, no matter how much they talk about it, they have to be able to solve the problems. That's where these programs break down," said Lynn Garner, who recently retired after nearly 40 years with BYU's math department. Garner, a former department chairman, authored the textbook that was used for all first-year calculus courses at the time of the experiment.
Gerson and Walter declined to be interviewed. There are metrics for success other than the exam results, but discussing their study prematurely would jeopardize its chance of being published, they said through a BYU spokesman. The scholars, however, did present preliminary findings at a San Diego conference this year.
Gerson and Walter contend there are multiple paths to solving a mathematical problem and students should be encouraged to chart their own way by exploring problems drawn from the real world.
"It sounds great, but it doesn't work," quipped David Wright, a veteran BYU math professor.
Gerson and Walter started their experimental calculus sections during winter semester of 2006 and continued them for the next two semesters. As a condition of approval, the professors used the same textbook as the other BYU calculus sections and administered the departmental final, worth 20 percent of students' grades, required of all 500 students taking calculus each year.
During the first two semesters of Gerson and Walter's experiment, their students' scores were a few points behind the overall averages and a few more behind the honors averages. But by the last section, known as Math 113 or Calculus 2, their scores were nearly 15 points off the overall average, translating to a D grade. In an e-mail to a State Board of Education member, the professors dismissed their students' poor test results because "there was little or no relation between the exam and the published learning outcomes for the course."
But BYU math faculty contacted by The Salt Lake Tribune contend the departmental exam is tailored specifically to measure students' grasp of BYU's standard calculus curriculum.
According to Garner, the exam was instituted in the early 1990s in response to concerns from engineering and physics faculty who insisted that students coming into their programs should all have the same math preparation. Previously, the professors complained that students had divergent understanding of calculus.
"When [Gerson and Walter] proposed those sections, we said it was fine with us as long as they take the uniform final and use the same textbook," Garner said. "Their object was to study how students' attitudes changed during the course. They didn't drill the skills like they do in the other sections."
For the past decade, math instruction in America's schools has become a flash point in a contentious debate pitting "reformist" math educators, who rely on constructivist learning theories, against "traditional" math professors. The Alpine School District became a battleground in this debate several years ago with its embrace of constructivism, derided as "fuzzy math" by its critics.
Constructivists want to replace formulas and algorithms with inquiry-based approaches to learning math, while traditionalists want to stick to lecture-and-drill approaches. Recent research is mixed on constructivism, which has gained traction in math instruction in recent years. An April article published in Science by Ohio State University researchers cast doubt on the use of real-world problems, such as calculating when trains departing different stations will pass each other.
The danger with teaching using this example is that many students only learn how to solve the problem with the trains, said co-author Jennifer Kaminski, a research scientist with Ohio's Center for Cognitive Science, in an OSU press release. If students are later given a problem using the same mathematical principles, but about rising water levels instead of trains, that knowledge just doesn't seem to transfer."