Problem solving and coordinate systems: It's not all about complicated calculations
T.S. Volkwyn, J. Airey, B. Gregorčič, F. Heijkenskjöld and C. Linder,
Uppsala university
A great deal of work has been carried out on student approaches to problem solving in physics.
One of the seminal findings of this body of work highlights the ways in which expert
physicists carefully model physics problems, in order to gain a better understanding
of the system at hand.
Only after this modelling stage do experts move on to select the simplest method for
problem solution (van Heuvelen, 1991). Students, on the other hand, have been shown
to have a tendency to overvalue mathematical representations, missing out the important
conceptual understanding of the system, preferring to quickly move over to a “Plug and
chug” mathematical approach (Tuminaro, 2004). It has also been suggested that novice
students may hold the alternative conception that coordinate systems are fixed (e.g.
the x-axis is always drawn to the right, with the y-axis pointing up) (Volkwyn, Airey,
Gregorčič, Heijkenskjöld and Linder, 2017).
Clearly such a conception will be a major hindrance to the simplification and
solution of physics problems.
In this presentation we describe a laboratory exercise in which we allowed students to experience the expert process of problem solving in physics together with the movability of coordinate systems by exposing them to a situation where careful positioning of coordinates removes the necessity for any mathematical calculation whatsoever.
We designed an open-ended laboratory task, in which students working in pairs were tasked with finding the magnitude and direction of the Earth’s magnetic field using a mediating tool—the IOLab. This device is equipped with a magnetometer and wirelessly sends information on the Cartesian components of the field to a display, in real time. Although solving the laboratory task is possible by following a purely mathematical approach without moving the IOLab, this yields a potentially laborious calculation and does not challenge the alternative conception that coordinate systems are fixed. The first pair of students attempted this approach and quickly became bogged down in complicated calculations, requiring intervention from the laboratory assistant. The second pair of students took a much more exploratory approach to the problem. In their interactions with the IOLab device they eventually devised a strategy where they moved the IOLab so that one of the coordinates was aligned with the field. At this point the direction and magnitude of the field could simply be determined by observation (reading off the value on screen and noting the orientation of the IOLab device). In doing so the students came to experience themselves as holding a movable coordinate system.
We claim that our experimental design opens up the possibility for students to learn three key disciplinary affordances of coordinate systems; (i) they are not fixed in an up/down, right/left orientation, (ii) they are at the service of physicists, and (iii) physicists always position their coordinate systems in such a way as to make the problem easy to solve.
References
- Tuminaro, J. (2004). A Cognitive framework for analyzing and describing introductory students' use of mathematics in physics PhD Thesis: University of Maryland.
- van Heuvelen, A. (1991). Learning to think like a physicist: A review of research-based instructional strategies. American Journal of Physics, 59(10), 891-897.
- Volkwyn, T. S., Airey, J., Gregorčič, B., Heijkenskjöld, F., and Linder, C. (2017). Physics students learning about abstract mathematical tools when engaging with “invisible” phenomena. PERC proceedings 2018 https://www.compadre.org/per/perc/proceedings.cfm. In American Association of Physics Teachers Physics Education 2017 Summer Meeting, Cincinnati, OH, July 26-27 (pp. 408-411). American Association of Physics Teachers. DOI:10.1119/perc.2017.pr.097