Analysing Theories of Meaning in Mathematics Education from the Onto-Semiotic Approach

The notions of meaning and sense, which are closely related to understanding, play an essential role in educational processes in general and, therefore, in the teaching and learning of mathematics. However, the terms 'meaning' and 'sense' are unevenly used in the theory of language, semiotics, philosophy and psychology. After describing the main characteristics of the referential and pragmatic theories of meaning, in this article, we detail various approaches to the notion of meaning, and present the perspective suggested by the onto-semiotic approach (OSA) of mathematical knowledge and instruction. This proposal partially incorporates the semiotic, ontological and epistemological assumptions of three general semiotic theories (by Hjelmslev, Peirce and Wittgenstein), with a holistic approach to the notion of object, sign and meaning, and takes into account some referential and operational theories, as well as other cognitive and sociocultural theories, about meaning. We also analyse how the meaning of mathematical objects is addressed in three models that have an impact on mathematics education: Frege's logical-realist position, Vergnaud's conceptual triplet and Steinbring's epistemological triangle. We finally suggest some implications for instructional design and teacher education of the OSA holistic approach to the meaning.