Metarepresentational competence in early grades: External representations of data and their components

The paper discusses a qualitative study on metarepresentational competence in 30 students of grade 1 to 4 (aged 6 to 9). Through clinical interviews and without prior instruction, students constructed 192 representations of data and explained their components. Four invariant components were identified in the representations and explanations of the students: variable, frequency, base-linear, and linearity-graph. Within the diversity of representations, the results show the invariant components and the aspects of invention, functioning, critique, and learning of the metarepresentational competence. In this way, we contribute to a body of literature on competence to represent, ensuing an approach that values the variety of representations that give meaning to discovering, communicating, and reasoning about the relationships in data in the first years of schooling.