Strategies of Pre-Service Mathematics Teachers when Articulating Representations of a Function

Background: Several investigations have shown the difficulties that preservice mathematics teachers present in articulating the elements of a function, in particular, its different representations. Objective: To analyse pre-service mathematics teachers’ articulation of semiotic representations and partial meanings of the notion of function. Design: This research uses qualitative design. Setting and participants: The respondents’ sample comprised 37 pre-service mathematics teachers from a Chilean university. Data collection and analysis: To collect the information, interviews were applied based on the answers given by the pre-service teachers when solving problem situations that involve functional relationships, of which they had to produce and connect their representations, both with conceptual elements and with the sociocultural context. The information was processed using the content analysis technique. Results: The results show a good state of development of the mathematical dimension of the participants’ didactic-mathematical knowledge. Regarding didactic knowledge, while some managed to articulate the partial meanings of function and the representations produced adequately, others show limitations, by not putting at the service of mathematical knowledge the knowledge with which they can potentially carry out teaching situations, establishing few connections between the elements of the representations produced, with corresponding conceptual and sociocultural elements. Conclusions: There is a need for implementing strategies that allow pre-service teachers to articulate partial meanings and representations of a function with conceptual and sociocultural elements that leads them to envision potential teaching activities of this concept.