Software designed to help physicists tackle complicated mathematics seems to be encouraging students to focus on the wrong aspects of scientific problems.
Interested in how students use computer programs to solve problems, physicists Thomas Bing and Edward Redish of the University of Maryland, College Park, analysed videos of teams of students as they worked on their assignments. Among other tools, the students used , a program that crunches not only numbers but also symbols, enabling it to do algebra and calculus.
By solving equations that might take days to solve with a pencil and paper, Mathematica frees up researchers to explore larger questions and to explore more problems. But this comes at a cost, Bing and Redish warn.
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Using Mathematica for physics involves two stages: choosing a strategy for solving the problem, and then implementing that strategy by typing in a few lines of computer code. Although the second stage can require formidable mathematical ability, it is the first that trains a student in physics.
The researchers found that Mathematica encourages students to focus on the second, programming stage, at the expense of the first (). 鈥淢athematica affects the kind of reasoning they use,鈥� says Bing. 鈥淭hey focus on computational aspects of the problem, while suppressing the connection with the physics.鈥�
During an assignment in which students used Mathematica to solve a problem in quantum theory, their first answer was infinity. This was obviously wrong, but instead of going back to check whether they had chosen a sensible strategy, they repeatedly came up with new ways to program the same strategy, and failed to solve the problem. Students might get trapped in this 鈥渟ticky mindset鈥� even when doing the calculation by hand, but Mathematica鈥檚 speed at doing calculations makes it more likely, Bing and Redish say.
This is a common problem, according to researchers who study the psychology of how people interact with computational devices. 鈥淲e often see,鈥� says Elspeth McKay of the RMIT University in Melbourne, Australia, 鈥渢hat automated thinking tools tend to block people鈥檚 capacity to see or know the broader context of the problem they face.鈥�
