Evaluating students' abilities to construct mathematical models from data using latent class analysis

Abstract

Analyzing and interpreting data is an important science practice that contributes toward the construction of models from data; yet, there is evidence that students may struggle with making meaning of data. The study reported here focused on characterizing students’ approaches to analyzing rate and concentration data in the context of method of initial rates tasks, a type of task used to construct a rate law, which is a mathematical model that relates the reactant concentration to the rate. Here, we present a large-scale analysis (n = 768) of second-semester introductory chemistry students’ responses to three open-ended questions about how to construct rate laws from initial concentration and rate data. Students’ responses were coded based on the level of sophistication in their responses, and latent class analysis was then used to identify groups (i.e. classes) of students with similar response patterns across tasks. Here, we present evidence for a five-class model that included qualitatively distinct and increasingly sophisticated approaches to reasoning about the data. We compared the results from our latent class model to the correctness of students’ answers (i.e. reaction orders) and to a less familiar task, in which students were unable to use the control of variables strategy. The results showed that many students struggled to engage meaningfully with the data when constructing their rate laws. The students’ strategies may provide insight into how to scaffold students’ abilities to analyze data.