Analysing theories of meaning in mathematics education from the onto-semiotic approach

Abstract

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.

KEYWORDS:

• Meaning
• semiotics
• epistemology
• mathematics education
• onto-semiotics

Acknowledgements

Research carried out as part of the research project PID2019-105601GB-I00/AEI/10.13039/501100011033 and FQM-126 Research Group (Regional Government of Andalusia, Spain).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 A sign is always constituted by one (or more) elements of an EXPRESSION PLANE conventionally placed in correlation with one (or more) elements of a CONTENT PLANE […]. A semiotic function is performed when two functives (expression and content) enter into mutual correlation. (Eco, 1991, pp. 83–84).

2 Sáenz-Ludlow and Kadunz (2016, p. 3) represent the triadic sign with the word SIGN (in capital), to distinguish it from the representamen or vehicle-sign component. They indicate that understanding the process of meaning construction involves understanding the active role of the interpreting Person in the reconstruction of the real Object of a SIGN from the keys and indications provided by the sign vehicles, which only indicate certain aspects of the real Object.

3 Godino et al. (2011) describe different meanings of natural numbers from the institutional point of view. Batanero and Díaz (2007) identify various meanings of probability.

Additional information

Funding

This work was supported by Research project: [Grant Number PID2019-105601GB-I00].