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.

Supporting Engagement in Metamodeling Ideas in General Chemistry: Development and Validation of Activities Designed Using Process Oriented Guided Inquiry Learning Criteria

“…Research into chemical kinetics has largely focused on identifying students’ alternative conceptions related to the topic . For example, research indicates students tend to define reaction rate as time , and inappropriately associate stoichiometric coefficients with the exponent within the rate law. ,− Relevant to the activity we developed, students’ reasoning related to the method of initial rates has also been investigated, indicating students need more support in constructing and evaluating models. , Previously published POGIL activities emphasize drawing conclusions from data in kinetics tables, solving problems using the integrated rate laws, and drawing inferences regarding reaction mechanisms. , For the purposes of our activity, the aim was for students to use graphical data in the first learning cycle to construct a definition for reaction order. For the second learning cycle, we guide students in utilizing graphical data and general principles to “invent” the method of initial rates in order to construct a rate law (Figure ).…”

Mapping undergraduate chemistry students' epistemic ideas about models and modeling

“…The literature has shown that construct maps are productive tools for assessing the development of students' knowledge and skills in chemistry (Becker, Noyes, & Cooper, ; Becker, Rupp, & Brandriet, ; Brandriet, Rupp, Lazenby, & Becker, ; Claesgens, Scalise, Wilson, & Stacy, ; Loertscher, Lewis, Mercer, & Minderhout, ; Sevian & Talanquer, ). We thus expect that the set of proposed construct maps will be useful for informing assessment of epistemic knowledge of modeling for both traditional and modeling‐focused curricula.…”

“…A construct map is defined by Wilson (, p. 3) as:

“a well thought out and researched ordering of qualitatively different levels of performance focusing on one characteristic. Thus, a construct map defines what is to be measured or assessed in terms general enough to be interpretable within a curriculum and potentially across curricula, but specific enough to guide the development of the other components.”

Researchers have developed and used construct maps as assessment tools in a variety of studies (e.g., Arya & Maul, ; Becker et al, , ; Brandriet et al, ; Briggs, Alonzo, Schwab, & Wilson, ; N. J. Brown, Furtak, Timms, Nagashima, & Wilson, ; Claesgens et al, ; Loertscher et al, ; Rivet & Kastens, ; Schwarz et al, ; Sevian & Talanquer, ).…”

Research on Students' Understanding of Michaelis-Menten Kinetics and Enzyme Inhibition: Implications for Instruction and Learning

“…As indicated in a topical literature review related to research on the teaching and learning of chemical kinetics, most work has been carried out in a general chemistry context with an emphasis on identifying students' alternative conceptions (1). On the basis of this body of research, students need more support regarding the empirical nature of rate laws and reaction order (2)(3)(4)(5)(6), they tend to conflate chemical kinetics and equilibrium ideas (2, 3, 7-9), and they have difficulty with graphical depictions of rate (4,5,(8)(9)(10). As discussed by Becker et al (2), a contributing factor associated with students' challenges when using these mathematical models lies in a need to use metamodeling ideas more productively, such as understanding the nature and purpose of models and having an appreciation for the role of testing and evaluating models.…”