What lies behind a graph?

Interpreting graphs is an important skill for chemistry students. Graphs that show a distribution of states, such as the Maxwell—Boltzmann (MB) distribution, are particularly difficult. Students studying chemistry at a higher level encounter more complex examples when they learn about probability distributions in quantum mechanics. It is crucial they understand what is required to read them.

In a recent study, Jon-Marc Rodriguez’ research team probed students’ abilities to explain the MB distribution and make predictions based on their understanding. The authors note a recent shift in chemistry education research away from cataloguing students’ misconceptions to characterising the reasoning behind those misconceptions, with a view to helping students make more effective use of their existing knowledge. This informed their research methodology, which explored the knowledge students used to engage with the MB distribution.

The research team interviewed 12 undergraduate students at a US college. They asked the students to describe and sketch what happens in a sealed flask of neon at room temperature, and then when it is heated to 100°C. The researchers then prompted students to describe what a MB distribution curve showed, and asked them to sketch the curve at a higher temperature. Finally, they showed the students a distribution graph with two curves depicting different temperatures and asked them to explain which curve corresponded to the higher temperature, and the faster reaction.

The researchers analysed the specific features of the graphs and prompts the students attended to, and the knowledge students used. They noted times when certain pieces of knowledge activated other ideas, and identified fragmented knowledge by the absence of such links. From this, they created ‘resource graphs’ – maps of each student’s knowledge. The analysis also identified inferences students were able to make successfully based on their engagement with the questions.

The findings show that students are more able to make inferences if they view the MB graph as a distribution rather than as a process. Students who view it as a process assume covariation between quantities on the axes. For example, they may assume that as speed increases, the number of molecules decreases. This leads to faulty knowledge application when responding to questions. Additionally, students need to read the peak as an indication of particles grouping, rather than as an event, in order to apply other ideas.