Abstract
In this article we carry out a critical account of a previous research on the influence of unknown (mathematically irrelevant) keywords present in a mathematical problem in solving the problem by young students. The research, proposed in the early ’90s, was repeated in similar ways between the end of 2019 and the beginning of 2020 aimed at: (1) establishing whether the empirical results of the first research are confirmed or reliable; (2) checking whether more modern theoretical tools lead to research results different from those obtained in the first research; (3) showing how a broad, particularly heterogeneous theoretical framework is able to provide interpretations or explanations of the phenomenon under study; (4) linking the theoretical tools available in the ’90s (Brousseau’s theory of didactical situations) to the theoretical tools provided by subsequent theories or research approaches (in particular, Luis Radford’s theory of objectification and Duval’s semio-cognitive approach). The results of the research carried out between 2019 and 2020 confirm and enrich with details the results of the research carried out in the ’90s, due to the new analysis and interpretation tools available to research in mathematics education. Tools of theories that are partially comparable and partially compatible with Brousseau’s theory of didactical situations. Nevertheless, a dialogue in a hermeneutic key, or a non-epistemological comparison between these theories is extremely important to access more refined and effective interpretative keys of the phenomenon under study, as the present research suggests.