Conceptual framework assessment of knowledge integration in student learning of measurement uncertainty

In this study, a conceptual framework of measurement uncertainty was developed and used to guide the development of a multiple-choice concept test for the assessment of students’ knowledge integration in learning measurement uncertainty. Based on assessment data and interview results, students were identified into three levels of knowledge integration including novice, intermediate, and expertlike. The reasoning pathways of students at different levels revealed a progression of reasoning from a rudimentary surface level to a deep understanding that can be mapped in the conceptual framework. This work demonstrates the possibility of identifying a quantitative categorization scheme to model knowledge integration as well as its utility in teaching and learning. Overall, the assessments and interviews revealed common and persistent difficulties in students’ understanding of measurement uncertainty. In addition, students at different levels of knowledge integration demonstrate unique types of knowledge states that can be represented in the conceptual framework, making it a useful tool for analyzing different reasoning pathways and knowledge structures.

Figure 1

Conceptual framework for the measurement uncertainty. Solid arrows represent experts’ conceptual pathways while dashed-line arrows represent novices’ reasoning.

Figure 2

Students’ performance across different designs of contextual configurations. The error bars represent standard errors.

Figure 3

Plot of typical and atypical questions across total scores (with error bars denoting standard error) for all students in this study. The frequency of total score distribution is shown as a bar chart in the background. An absolute count of students falling into each range is shown on the right axis.

Figure 4

Plot of what, how, and why questions across total scores (with error bars denoting standard error) for all students in this study. The frequency of total score distribution is shown as a bar chart in the background. An absolute count of students falling into each range is shown on the right axis.

Figure 5

Scree plot of the eigenvalues of the correlation matrix of the measurement uncertainty test.