Languages raised by (pre-service) teachers who teach mathematics in multiplication and division tasks

Abstract

DOI: http://dx.doi.org/10.14244/198271991208

By assuming that different languages permeate tasks developed in Mathematics classrooms and that these languages may signal the (lack of) knowledge of agents who participate in them, we bring to discussion in this paper, according to Ludwig Wittgenstein’s premises (2009) about language, how students in an undergraduate Education course deal with multiplication and division operations. Supported by Wittgenstein’s notions of language games, we seek to identify the games which are present in actions of these students as they solve the tasks proposed, and the family resemblances saved among them. Therefore, we analyzed productions of students (scripts in natural language, scripts in mathematical language, scripts in pictorial language), as well as transcripts of recordings of their involvement with the tasks. On one hand, the analysis shows that, despite the occurrence of a variety of languages, the mathematical language seems to validate mathematical knowledge. On the other hand, in students’ productions, the languages keep, in general, family resemblances, from a game to another, to a third game, or within own the game. Despite such similarities, inconsistencies related to the conceptual development of students’ multiplication and division, often sustained in routine expressions in the classroom, lead us to infer that there is a lack of epistemological depth related to these operations, and therefore to the decimal numeration system.

Keywords: Languages, Language games, Family resemblances, Arithmetic operations.