Investigating Relational Understanding: The Quality of Learners’ Argumentations

Tasks related to relational understanding are useful for arguing about basic mathematical structures and relationships, and for encouraging long-term mathematical thinking. It has been determined that learners in primary school have considerable difficulties arguing about these relationships. Based on these findings, a study was conducted in which the written argumentations of tasks targeting relational understanding provided by 72 learners aged ten to thirteen were evaluated. The tasks covered various mathematical topics and were divided into tasks involving pattern continuation, explorative argumentation and persuasive argumentation. Responses were evaluated by an inductive-deductive coding scheme. The results showed that learners can describe the relationships, but often struggle to explain the underlying reasons for their occurrence. In comparison to exploring and describing the relationships, the quality of the persuasive argumentations in particular was low. There were no substantial weaknesses in any specific aspect of the argumentations, such as structure or linguistic precision. Nevertheless, performance differed to some extent between tasks addressing different mathematical content, which may point to argumentation as a more domain-specific than domain-general competence. However, given the limited number of tasks per content area, this interpretation remains tentative and warrants further investigation. The findings provide tentative indications of variation across mathematical content areas, but do not allow firm conclusions about the domain-specificity of argumentation competence. Future research should employ multiple tasks per domain and longitudinal designs to disentangle content-related from task-specific effects and to examine how persuasive argumentation competence develops over time.