College Students’ Solutions to Linear Functions Problems: Identifying and Interpreting Common Mistakes

Among the domains of math knowledge that college students need to master for success in college and future careers (Conley et al., 2011), students’ performance is lowest in the topic of linear functions (LF) (Britton & Henderson, 2009; Mielicki et al., 2019). Important benefits can result from analyses of performance on assessments that focus on students’ ability to solve description, graph, and table LF problems and, specifically, uncovering the types of errors students make to help understand and ameliorate their struggles with this domain of mathematics. This Master’s thesis project focused on exploring and modeling the cognitive underpinnings of common errors in LF problems to enable subsequent instructional research aimed at ameliorating major conceptual and/or procedural difficulties underlying performance. Empirical evidence showed that students performed considerably better on description items compared to table and graph items. Errors in the latter two problem types were mapped to the interpretation and construction aspects of the problem-solving process. Interpretation errors are predominantly observed in graph problems and errors in both interpretation and construction processes were observed for table problems. These error patterns reflected systematic inductive failures that were attributed to the overgeneralization of relevant conceptual and procedural knowledge based on familiar structural features that are conditional on the form in which the information is presented. The quantitative and qualitative analyses of the item level and student level responses can be used to inform the design of instructional interventions such as using worked examples.