Measurement and uncertainty in the first-year physics laboratory: towards probing students' conceptual understanding of the mean - Majiet, Nuraan (University of Cape Town, 2021)
Physics is about sense-making. The world we live in and experience through our sensory modalities is highly complex. In order to make sense of this complexity we reduce the experiences to a more simplified form. The way in which this is achieved is through modelling. Physics consists of both theory and experiment, thus modelling in physics consists of two components: (1) conceptualization and mathematization (theory) which involves ontological innovation and introducing variables and (2) designing experiments which leads to measurements (experiment). We can then compare our theoretical predictions with our measurements. The present work is primarily focused on aspect (2) dealing with the modelling of experiment. First year physics courses include a teaching component directed at the key aspects that relate to experimentation. This includes the key concepts with regard to measurement and uncertainty. However, these have proved to be challenging aspects of a first-year curriculum and students often resort to rote methods. Student understanding of measurement and uncertainty was explored in detail in a series of studies that were carried by a collaboration between UCT and the University of York. This work showed that students exhibited a wide variety of ideas with regard to all aspects regarding data, ranging from data collection to data processing. Based on their theoretical constructs that explained this variation in terms of point and set paradigms, they concluded that the purpose of teaching was to move students from the point to the set paradigm. Despite the fact that they created an instrument (Physics Measurement Questionnaire (PMQ)) to measure such a shift, it is not clear that the measured shift reflects actual conceptual change. This is particularly so insofar as combining multiple readings into a single number such as the mean is concerned. While many of the questions on the PMQ do attempt to probe student thinking, the question regarding the mean is in fact purely calculational. Therefore, the nature of the responses does not allow one to fully determine to what extent the calculation follows from an appropriate model or whether it is simply an arithmetic step that is carried out without any model in mind. While calculating the mean might be regarded as a step forward for students who were previously classified as point thinkers it can be argued that this is in fact a retrograde step from a modelling perspective in that the step can be described as "model abandonment". Thus, rather than the mean being a stepping stone to further understanding of uncertainty, it could in fact prevent such a learning trajectory. As seen from the PMQ it is not easy to pose questions that probe what model, if any, students have in mind when calculating the mean. The present work thus aimed to explore the degree to which it was possible to identify to what extent students used the mean with some model in mind. The starting point for the work was the PMQ. Questions were posed in the same manner but with the aim of eliciting the reasons why students perceive the mean to be the appropriate way to proceed during data analysis. To what extent is it possible to probe students' modelling approaches in the first-year laboratory? Is it possible to design a non- interview methodology in order to identify their reasons for using the mean? To investigate this a number of questions were constructed and administered to two small groups of students, 20 and 30 respectively, as part of a two step iterative developmental research process. The questions were administered to first-year physics students at the University of Cape Town. The final questionnaire consisted of four questions. The two data collection probes were taken directly from the PMQ and placed at the beginning of the questionnaire for control purposes and the two pilot questions were adapted from the Using Repeated Distance (UR) Probe in the PMQ. UR was reformulated into two questions with an explanation component; one question investigated what students use as the final result in a purported experiment and the other looked at what they predicted as the next value. The analysis comprised careful investigation as to the "Level of Informativeness" provided by the questions followed by a cross probe analysis where the Level of Informativeness allowed for this to be done. The present studies that were carried out indicated that there was no straightforward way to elicit information as to whether the student had some model in mind or not. However, a number of insights into the way forward were gained. These included the way in which questions could be framed around the issues of the mean that allowed for some level of inference to be made. While some further work still remains insofar as this is concerned, we suggest that these questions be included in future versions of the PMQ.