New Ph.D.: Plugging numbers into a formula isn't physics 

When physics students perform calculations involving everything from rocket trajectories to the spread of sound waves, they do so through mathematical representations. However, even if students have a firm grasp of mathematics, it's far from guaranteed that they can connect graphs and equations to the reality they describe. That is an issue, said Muhammad Aswin Rangkuti, who recently defended his Ph.D. at the Department of Science Education, University of Copenhagen.  

"Most students treat physics as mathematics, where a formula is a mathematical tool, they can use. But they don't necessarily understand the physical phenomenon behind the formula," said Muhammad Aswin Rangkuti. 

"They might plug numbers into a formula and get a result. But that doesn't mean anything by itself. It's not physics, it's mathematics." 

If students don't understand the physical phenomena they're calculating, they will struggle to find meaning in the subject and relate their calculations to the real world, argued Muhammad Aswin Rangkuti. 

"Students don't see equations as meaningful when they're merely tools for solving problems. We need to help them develop a different perspective on formulas and help them see what lies beyond them." 

Going beyond mathematics 

In his research, Muhammad Aswin Rangkuti has explored how to help students see beyond mathematics when it comes to the 1-D wave equation, which describes a wave's dependence on time and place. 

The equation encompasses all wave phenomena — from ocean waves to electromagnetic waves — and is therefore widely used in physics. 

"I asked students how they would explain the equation to their fellow students. None of them were able to do it. They could recite the mathematical description, but they don't know why it looks the way it does," said Muhammad Aswin Rangkuti. 

The researcher also presented the students with various functions and asked if they satisfied the wave equation. 

"Mathematically, the students can figure that out. But when asked which functions actually represent waves in a physical situation, they have no idea." 

Surprisingly meaningful 

Muhammad Aswin Rangkuti developed four tutorials aimed at gradually enabling students to make sense of the meaning of the 1-D wave equation. The result was that many students changed how they used the equation. 

"The goal was to get students to ask why? Why does the formula look the way it does, and what does it tell us? And this should be part of your understanding if you want a deep understanding of physics," said Muhammad Aswin Rangkuti. 

“After the tutorials some students said, they never thought they could explore so much physical meaning from only one physics equation.” 

Not all students came through the tutorials with the same revelation, but Muhammad Aswin Rangkuti still hope, they’ll look at other physics equations differently in the future. 

Changing student perspective 

The research shows, that it is possible to give students a deeper understanding of the tools they are learning. And it should be more common in classrooms to focus on these aspects of physics, said Muhammad Aswin Rangkuti. 

Students don't see equations as meaningful when they're merely tools for solving problems.

"We see that students talk about physics as being extremely difficult. People consider it the hardest subject, compared to biology, chemistry, and mathematics. It's a problem, and I think it stems from the way we teach physics," he says. 

At all levels of education, there's a tendency to teach mathematics and physics as separate entities. Therefore, students tend to view physics and mathematics as two distinct subjects, even though they're deeply interconnected. 

"I'd like to see math teachers and physics teachers collaborate more to integrate their teachings and make both subjects more meaningful for students. If we can teach physics better, it will change students' perspective on the subject."