Handbook

Point and Set Paradigm []

Research on students' understanding of measurement uncertainties has identified two paradigms, see Tab. 1: the point and set paradigm [1]. These paradigms describe two extremes in students' viewpoints regarding measurement data. This part starts with a description of the two paradigms which will then be used as a foundation to talk about students' difficulties regarding measurement uncertainties.

Point Paradigm []

In the point paradigm, students think about measurements as being single isolated events that, given the right instrumentation and practice, lead to the "true value" that can be measured in an experiment. Measurement uncertainties are the result of imperfections in the measurement instruments and/or procedures that can, in principle, be eliminated.

Set Paradigma []

In contrast, in the set paradigm, students look at a dataset as a whole. The fluctuations in the measurements are used to determine the measurement uncertainty and are, hence, an indication of the data quality. Students let go of the idea of a true value but rather try and determine the ⓘ uncertainty intervaluncertainty interval: The range of values spanned by the mean and the uncertainty. which can be seen as a set of values. Hence, a result of a measurement can never be a single value but rather a range of values.

Table 1: Some contrasting characteristics of the point and set paradigms.

Point Paradigm Set Paradigm
Every experiment has a "true value" that can be determined when taking the correct procedures with the correct equipment. In an experiment, a certain measurand can be determined. This measurand is a precise as possible description of what is to be measured.
Uncertainties can be eliminated, avoided, or reduced to zero. They are a sign of something having gone wrong. Uncertainties are omnipresent in every experiment. The goal is to control them, reduce them to a desired level, and to quantify them. They are an indication of the quality of an experiment.
Repeated measurements are taken to: confirm an outcome, practice measuring, and be able to calculate a mean value. Repeated measurements are taken to estimate the spread in measurements and quantify the measurement uncertainty.
The mean value represents the "true value" of an experiment. Every measurement result—regardless if it comes from a single measurement or multiple measurements—contains a best value (often the mean value) and an uncertainty interval (the range of values) around it.

Goal []

Research has repeatedly found that the vast majority of students, even at the university level, are firmly located in the point paradigm. The goal of many first-year lab courses is to shift students' thinking from the point toward the set paradigm. Research has also shown that this is best done by first addressing the fundamental underpinnings of measurement uncertainties [2, 3], before moving toward statistical procedures. This approach is also chosen in the Digital Learning Environment (DLE) that was developed for students in secondary education.

Table 1 shows some contrasting ideas associated with the point and set paradigms that students have. The concepts in this table will be further elaborated on in the next subsections.

Relevancy of measurement uncertainties []

Depending on the goal of the experiment, the evaluation of the measurement uncertainty is a necessity for the success of the experiment. In all cases where conclusions are data-based, an analysis of the measurement uncertainty is required. In other instances, e.g., when the relation between two variables is to be illutrated or when general trends are shown, this evaluation is not needed at all. To read more about this, see Kok et al., [4].

For teaching strategies on measurement uncertainties, see Holz and Heinicke [5].

https://www.youtube.com/watch?v=uMvT02mHkss

Literature