A student can earn a good grade in calculus, walk into a physics class and suddenly feel like none of it makes sense.
The equations may look familiar. The math may even be something the student has already practiced. But figuring out which idea applies, how to set up the problem and what the answer means in the physical world can be much harder.
It is like a new driver learning the rules of the road, then having to apply them in real traffic.
John Thompson, a professor of physics at the University of Maine, studies that disconnect.
“The mathematical computation is typically the easiest part,” Thompson said. “Setting up the math problem that you have to do, and then understanding what it means at the end, are the hard parts, because they involve both mathematical and physical reasoning combined in often unfamiliar ways to students.”
Thompson is leading UMaine’s participation in a new National Science Foundation research project with colleagues at California State University, Fullerton and the University of Washington. The team will study how physics students use knowledge from math courses and then develop practical teaching materials to support students bridge the mathematics and its applications more effectively.
If the research succeeds, physics instructors around the country could have practical teaching tools they can add to existing courses to help students connect calculus with the problems they are trying to solve.
A critical point for physics students
The stakes are higher than one difficult homework assignment.
The project will focus largely on a second-year course that teaches physics majors to apply the mathematics they will need to complex physics problems in more advanced classes. Similar courses are offered at colleges and universities across the country, and Thompson said they can come at a critical point in a student’s education.
For many physics majors, it is one of the first times they are taking a class mainly with other students in their major. Doing well can strengthen their confidence and sense that they belong in physics. Struggling can cause them to question whether they should remain in the field.
“It builds their identity as a physicist and their sense of, ‘I belong here,’” Thompson said.
That makes the research partly about keeping capable students in physics.
In physics, the symbols and equations represent something happening in the real world. A variable may stand for distance, time, force, speed or energy. Students have to know how to work through the math, but they also have to understand what the math is describing.
If students repeatedly struggle to use math they have already learned, they may begin to believe they are simply not good at physics.
“We want to support the students,” Thompson said. “We don’t want to just say, ‘Oh, well, I guess you can’t hack it.’”
Finding where the connection breaks down
The researchers will interview students and instructors, observe classes and review student work to identify where the biggest gaps appear. They also want to understand what instructors expect students to know when they enter these courses and how those expectations compare with what students can actually apply.
Thompson said the issue is not with math instruction. Math and physics use many of the same ideas, but each discipline applies them differently. The researchers want to better understand what happens when students move from one context to the other.
The next step is to turn those findings into something instructors can use.
Rather than redesigning an entire course, the team plans to create various activities — some shorter, some longer — aimed at specific points where students commonly get stuck. These would help students see how a mathematical idea they already know applies to a physics problem, or how to bring in extensions of familiar math to a problem.
“It might be a 10-minute thing,” Thompson said. “Here’s a good exercise for students to do.”
The materials could also help instructors recognize common misunderstandings and suggest questions they can ask to guide students toward a better understanding and to build their physics-specific reasoning skills.
The team plans to test the activities in their own classrooms, improve them based on what they learn and eventually make them available to other instructors.
An impact beyond the physics classroom
The potential impact could extend beyond physics. Students in chemistry, engineering and other science and technology fields also have to take knowledge from one course and apply it in another.
Thompson said that ability to transfer knowledge is part of the broader purpose of college.
“To me, college is about learning to think and reason more effectively no matter the major,” he said. “Reasoning quantitatively is crucial in science, and we’re hoping to improve that skill for our students.”
If the research works as intended, students could enter advanced science courses better prepared, more confident in what they already know and less likely to leave a field because they struggled to connect ideas taught in different classrooms.
Ultimately, success could show up in a much simpler moment: a student seeing — and recognizing — familiar mathematics in a physics problem and realizing they already have the tools to begin.
“Oh, yeah, we did that in calculus,” Thompson said. “All right, now I know what I’m doing.”
Contact: David Nordman, david.nordman@maine.edu
