The importance of structure, clarity, representation, and language in elementary mathematics instruction

This article presents a study that investigated potential misconceptions presented in third grade mathematics classrooms and the association of these potential misconceptions with Mathematical Knowledge for Teaching (MKT) and standards-based teaching practices (as measured by the Mathematics Scan). A sequential explanatory mixed methods model was used to analyze the frequency of potential misconceptions presented via instances of lack in teacher clarity or misuse of representations as well as the association to MKT and M-Scan scores. A qualitative multiple case study design was then used to identify patterns in lessons where potential misconceptions were often present as opposed to lessons where no potential misconceptions were presented. The results document the prevalence of potential misconceptions related to representations and language use. These potential misconceptions were most frequently conveyed through a lack of clarity or overgeneralization. Teachers who had higher frequencies of potential misconceptions were found to relate to lower MKT and M-Scan composites. This supports professional development and policy initiatives in mathematics education of the importance of teachers’ content knowledge for mathematics teaching.