How analogies helped novice students think about superposition states and collapse in quantum mechanics

Abstract

In my active learning course on quantum mechanics, students build their knowledge by following the scientific process as outlined by the Investigative Science Learning Environment. In this course, open-ended questions on the effect of measurement (collapse) failed to elicit meaningful responses from students. Meaningful responses are crucial for the next steps of testing students’ ideas using hypothetico-deductive reasoning. I wanted to help the students in this process with a pictorial representation. To arrive at a pictorial representation that would have meaning for students, I first asked them to provide their analogies for a superposition state. A common suggestion was the mixture of colours, but other, more inventive analogies were also suggested. I developed a pictorial representation based on the colour analogy. I reformulated the questions on collapse using this representation and a more concretized formulation. The ability of students to meaningfully answer the questions increased to the point where it was possible to complete also the testing part of the process. In the article, I discuss the analogies that students suggested and what underlying ideas known from literature they could represent. I provide the derived representation, the reformulated questions and evidence of how this helped students articulate their answers and helped identify students’ productive ideas that they could not clearly articulate in words. This enabled students to arrive at conclusions about the effect of measurement following the scientific process. This study contributes to the literature by providing student-generated analogies, using a pictorial representation derived from student-generated analogies, and showing an example of an efficiently formulated question on a difficult topic that is able to elicit meaningful responses.