Examples of Cue-based Activation and Formation of Knowledge

The first example is a study on student understanding of potential energy diagrams. Students were given a question shown in the left part of Figure bellow, in which three different potential well was provided along with two plots of wavefunction. Students were asked to describe where the electron would be most like found based on the provided wavefunction. The correct way to answer this question is to find the probability density distribution based on the wavefunction, which would show that the electron is most likely found around the mid points between 0 and ±L. The results from surveys and interviews using this question show that a significant part of students (40%) have interpreted the potential well, which represents a 1-dimensional quantum system such as an electron in a E-field, as a 2-dimensional physical system such as a gravitational well and used the vertical dimension to represent the position of the electron. Most of the remaining students (45%) gave no answers to the question.

Using the cue-based association, we can see that the context of a potential well is new to the students; however, part of the cues such as the shape of the 2-dimensional well is familiar and therefore can be matched with a classical system such as a hole in the ground. The feature of the energy levels also appears similar to the structure of a ladder which is consistent with the system of a hole in the ground. The cue of the quantum wavefunction and the correct association with the probability density is found to have a much smaller probability (~5%) to be activated with the population we studied. From this example, we can see that certain cues of the representation for a quantum system are similar to the ones of classical systems and can activate students into using the knowledge that are associated with the classical systems. However, students often have low confidence on using the activated knowledge. As indicated by interview data, many of the students who didn’t answer the questions also are activated with the classical knowledge but considered those not applicable. Most of the students who applied the classical knowledge have low confidence – it is just something they can think of.

The following slides show another example on the topic of potential steps where students are cued with classical type of understanding (going down or up a hill) by the features of step-down and step-up of the diagram and apply these classical understanding to interpret the quantum context.