Fostering Representational Flexibility in the Mathematical Working Space of Rational Numbers

The study focuses on the cognitive level of Mathematical Working Space (MWS) and the component of the epistemological level related to semiotic representations in two mathematical domains of rational numbers: fraction and decimal number addition. Within this scope, it aims to explore how representational flexibility develops over time. A similar developmental pattern of four distinct hierarchical levels of student representational flexibility in both domains is identified. The findings indicate that the genesis of the semiotic axis in fraction and decimal addition is not automatic, but a long process of developmental steps that could be referred to as MWS1, MWS2, MWS3, MWS4 (final). There is not a clear and stable correspondence between developmental levels of representational flexibility and school grades. Didactical implications in order to foster representational flexibility in the MWS of fraction and decimal addition are discussed.