ABSTRACT
The main objective of this chapter is to show how the combination of a priori analysis of mathematical tasks, protocol analysis, and thinking-aloud methods can generate empirical insights and contribute to theory development on mathematical learning. First, a description of these classical methods and their functional characteristics is provided. Second, based on the socio-constructivist approach, a combination and re-conceptualisation of these methods is proposed, which allows to develop a more nuanced unit of analysis for studying students’ solving of mathematical tasks. Third, empirical examples in which three students engage with a PISA item are used to illustrate the significance of the methodological approach. Combining the fine-grained analysis of the students’ activity on the task with the examination of their verbal reports allows tracing the dialogic processes associated with the construction of the task. In particular, the task is co-constructed through both an inner dialogue of the student with himself and a social practice embedded in school socialisation. Integrating the three methods could represent a methodological innovation that allows us to re-conceptualise the socio-constructivist approach to mathematical learning and conceive an extended unit of analysis, making visible the role of social practices embedded in everyday school life for mathematical thinking.
