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Teachers’ awareness of the semio-cognitive dimension of learning mathematics

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Abstract

While many semiotic and cognitive studies on learning mathematics have focused primarily on students, this study focuses mainly on teachers, by seeking to bring to light their awareness of the semiotic and cognitive aspects of learning mathematics. The aim is to highlight the degree of awareness that teachers show about: (1) the distinction between what the institution (school, university, society, etc.) proposes as a mathematical object (not in itself but as the content to be learned) and one of its semiotic representations; (2) the different aspects of a semiotic representation that the student able to handle the representation and the student who handles the representation with difficulty may focus on; (3) the semiotic conflicts generated by the contents of semiotic representations that are similar to each other in some respect. For this purpose, in this study, the semio-cognitive approach introduced by Raymond Duval was complemented with the semiotic-interpretative approach of the Peircean tradition. By embracing the pragmatist research paradigm, the methodology was based on the research questions, which guided the selection of the research methods within a qualitatively driven mixed methods design. The research results clearly show the need for a review of professional teacher training programs, as regards the role the semiotic handling plays in the cognitive construction of the mathematical objects and the learning assessment.

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Notes

  1. As regards the knowledge, beliefs, practices, and the affectivity of the teacher, see for example, Davis and Simmt (2006).

  2. By semiotic conflict (Godino, Batanero, & Font, 2007) we mean the emergence of a discrepancy between the interpretations of the content of a semiotic representation by two parties (people or institutions).

  3. “A representation is that character of a thing by virtue of which, for the production of a certain mental effect, it may stand in place of another thing. The thing having this character I term a representamen, the mental effect, or thought, its interpretant, the thing for which it stands, its object” (Peirce, CP 1.564, ca. 1893).

  4. On mathematics teacher education and professional knowledge, see for example: Godino (2009), Santos et al. (2012), Schoenfeld (2016).

  5. “Qual” = qualitative, “quan” = quantitative, “+” stands for concurrent, “→” stands for sequential; uppercase letters indicate a high priority, while lowercase letters indicate a low priority of methodological approach in the mixed study (Morse, 1991; Tashakkori & Teddlie, 1998).

  6. Many examples and didactic reflections about the handling of such representations and the pitfalls that can be hide behind their use could be found in D’Amore, Fandiño Pinilla, and Iori (2013).

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Acknowledgements

My heartfelt thanks go to all the teachers who have agreed to participate in this research. Special thanks go to Professor Raymond Duval, for his valuable scientific contributions, helpful clarifications, and suggestions during the research. Very special thanks go to Professor Bruno D’Amore, without whose help this work would never have been possible.

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  1. Nucleo di Ricerca in Didattica della Matematica (NRD) at the University of Bologna, Bologna, Italy

    Maura Iori

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  1. Maura Iori
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Correspondence to Maura Iori.

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Iori, M. Teachers’ awareness of the semio-cognitive dimension of learning mathematics. Educ Stud Math 98, 95–113 (2018). https://doi.org/10.1007/s10649-018-9808-5

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