Momentum in Physics Ed

Math, specifically calculus, is a barrier to many natural sciences, technology and engineering fields. Physics, which is math-heavy, often proves similarly challenging to students who wish to pursue STEM degrees.

A new way of teaching introductory, calculus-based physics holds some promise for students who struggle with math, however. The curriculum involves two major changes from the way this standard course is typically taught. Whereas most courses begin with instruction on forces and vector mathematics, this begins instead with energy -- which, proponents say, better plays to students’ intuition. The course also asks students to do more calculus themselves, to make sure they understand it.

The two adjustments are related and “reinforce one another,” said Christopher Fischer, engineering physics director and associate chair of physics and astronomy at the University of Kansas, as beginning the course with energy rather than forces “automatically requires more calculus.”

Fischer co-wrote a recent study that demonstrated that this calculus-enhanced “energy-first” curriculum resulted in higher gains on the Force Concept Inventory exam, a basic physics assessment, for all students. It also improved later performance in engineering courses for students who entered college with lower ACT math scores.

In other words, the study says, “the downstream benefits were largest for students with lower math abilities who also pose a larger retention risk.” The new curriculum, therefore, “has the potential to improve student retention by specifically helping the students who need help the most, including traditionally underserved populations who often have weaker mathematics preparation.”

Fischer said he and his co-authors believe that organizing the course in this way “may be helping students to overcome the well-documented math transference barrier to learning physics.” It’s well-known that forces and associated vector mathematics “pose a significant learning curve for students,” he added, and delaying them allows students to focus “more on learning the physics.”

A ‘Positive Feedback Loop’

That creates “a positive feedback loop” in which students improve their physics and math skills at the same time, Fischer said. He and colleagues also believe the approach is exportable to any institution of any size. Fischer wrote a textbook series that introduces classical mechanics using the concept of energy conservation first, before forces. And he and his colleagues have made lecture slides, in-class exercises and homework assignments that do the same -- all of which they’re willing to share upon request.

Fischer's co-authors, all from physics at Kansas, are Sarah LeGresley, assistant teaching professor; Jennifer Delgado, associate teaching professor; Christopher Bruner, Ph.D. candidate; and Michael Murray, professor. Physical Review Physics Education Research published the study.

Neither the new course or the traditional course are lecture-based, as both use active learning. Before coming to class, for example, students read a textbook section or watch a video on a given topic. About 20 minutes of the class is devoted to a professor’s presentation, and students work together to solve multiple problems during the rest of the class session. Students then do graded homework assignments.

The new curriculum, however, which began in 2015, develops classical mechanics using the concepts of energy and energy conservation before introducing the concept of force. “Our intention in structuring the curriculum in this way was to provide students a common conceptual and mathematical scaffold for solving a wide variety of problems,” the paper says. We “hoped to help students understand the concepts that underpin the mathematical strategies and associated equations rather than the strategies themselves.”

An Energy-First Approach

An energy-first approach is probably best described as Hamiltonian mechanics, the authors say. In terms of math, it relies more heavily on both differential and integral calculus than the traditional force-first curriculum.

For example, in the enhanced PHSX 211 course, as opposed to 210, students use calculus routinely when covering one-dimensional and two-dimensional translational motion, circular motion, rotational motion, and oscillatory motion.

“We hoped that this repeated use of calculus through the curriculum would help students improve their fluency with applying calculus to solving physics problems,” the study says. The authors further “believe this curriculum empowers students to derive their own equations for describing systems and solving problems, rather than relying solely on equations derived by others.”

While the paper has generated buzz, it has some critics. Among them is Suzanne White Brahmia, an assistant professor of physics at the University of Washington, who has written about the need for “mathematizing,” or translating between the concrete and abstract, to be a bigger part of the physics curriculum. She had several concerns, including that the new intervention was carried out in a course with so many fewer students than the control.

“I would be very cautious about promoting it as breakthrough evidence,” Brahmia said, calling the study “interesting but not at all convincing.”

It’s “entirely possible that well-taught, smaller courses with more contact hours could achieve the same results,” she added. “There is lots of evidence for that.”

True: the curriculum group had fewer that half the students in the comparative traditional curriculum class. The paper acknowledges this -- and the fact that its scope, of just one, unnamed Midwestern university, was limited. But Fischer said he and his colleague tried to control variation in class size by having the same ratio of faculty members and undergraduate teaching assistants to students in each class.

The revised course also involves 25 extra minutes of class time twice a week. So, the paper says, it’s “possible that this extra time results in improvements in student learning.” The authors plan to assess the impact of differences in class size and contact hours in a future study.