Educational Studies in Mathematics

, Volume 98, Issue 1, pp 95–113 | Cite as

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

  • Maura Iori


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.


Learning mathematics Mathematical object Semiotic representation Representation register Semio-cognitive approach Professional teacher training 



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.


  1. Chevallard, Y. (1985). Transposition didactique: Du savoir savant au savoir enseigné [Didactic transposition: From academic knowledge to taught knowledge]. Grenoble: La Pensée Sauvage.Google Scholar
  2. D’Amore, B. (2001). Concettualizzazione, registri di rappresentazioni semiotiche e noetica [Conceptualization, registers of semiotic representations and noetics]. La matematica e la sua didattica, 15(2), 150–173.Google Scholar
  3. D’Amore, B. (2006). Concepts, objects, semiotic and meaning: Investigations of the concept’s construction in mathematical learning (Doctoral dissertation). Constantine the Philosopher University, Nitra, Slovakia. Retrieved from
  4. D’Amore, B., & Fandiño Pinilla, M. I. (2009). La formazione degli insegnanti di matematica, problema pedagogico, didattico e culturale [Mathematics teachers’ education: A pedagogical, didactic and cultural problem]. In F. Frabboni & M. L. Giovannini (Eds.), Professione insegnante (pp. 145–154). Milan: Franco Angeli.Google Scholar
  5. D’Amore, B., Fandiño Pinilla, M. I., & Iori, M. (2013). Primi elementi di semiotica: La sua presenza e la sua importanza nel processo di insegnamento-apprendimento della matematica [First elements of semiotics: Its presence and importance in mathematics teaching-learning process]. Bologna: Pitagora.Google Scholar
  6. D’Amore, B., Fandiño Pinilla, M. I., Iori, M., & Matteuzzi, M. (2015). Análisis de los antecedentes histórico-filosóficos de la “paradoja cognitiva de Duval” [Analysis of the historical and philosophical antecedents to “Duval’s cognitive paradox”]. Revista Latinoamericana de Investigación en Matemática Educativa, 18(2), 177–212.CrossRefGoogle Scholar
  7. Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61(3), 293–319.CrossRefGoogle Scholar
  8. Duval, R. (1988a). Ecarts sémantiques et cohérence mathématique: Introduction aux problèmes de congruence [Semantic disparities and mathematical coherence: An introduction to the problems of congruence]. Annales de Didactique et de Sciences cognitives, 1(1), 7–25.Google Scholar
  9. Duval, R. (1988b). Approche cognitive des problèmes de géométrie en termes de congruence [A cognitive approach to the geometrical problems in term of congruence]. Annales de Didactique et de Sciences cognitives, 1(1), 57–74.Google Scholar
  10. Duval, R. (1993). Registres de représentations sémiotique et fonctionnement cognitif de la pensée [Registers of semiotic representations and cognitive functioning of thought]. Annales de Didactique et de Sciences Cognitives, 5(1), 37–65.Google Scholar
  11. Duval, R. (1995). Sémiosis et pensée humaine: Registres sémiotiques et apprentissages intellectuels [Semiosis and human thought: Semiotic registers and intellectual learning]. Bern: Peter Lang.Google Scholar
  12. Duval, R. (2006a). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.CrossRefGoogle Scholar
  13. Duval, R. (2006b). Quelle sémiotique pour l’analyse de l’activité et des productions mathématiques? [What semiotics for the analysis of mathematical activity and productions?]. In L. Radford & B. D’Amore (Eds.), Semiotics, Culture and Mathematical Thinking [Special Issue]. Revista Latinoamericana de Investigación en Matemática Educativa, 9(1), 45–81.Google Scholar
  14. Duval, R. (2009). «Objet»: Un mot pour quatre ordres de réalité irréductibles? [Object: A word for four irreducible orders of reality?]. In J. Baillé (Ed.), Du mot au concept: Objet (pp. 79–108). Grenoble: PUG.Google Scholar
  15. Godino, J. D. (2009). Categorías de análisis de los conocimientos del profesor de matemáticas [Categories to analyze the mathematics teacher’s knowledge]. UNIÓN, Revista Iberoamericana de Educación Matemática, 20, 13–31.Google Scholar
  16. Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM–The International Journal on Mathematics Education, 39(1–2), 127–135.CrossRefGoogle Scholar
  17. Hoffmann, M. H. G. (2006). What is a “semiotic prospective,” and what could it be? Some comments on the contributions to this special issue. Educational Studies in Mathematics, 61(1–2), 279–291.CrossRefGoogle Scholar
  18. Iori, M. (2015). La consapevolezza dell’insegnante della dimensione semio-cognitiva dell’apprendimento della matematica [The teacher’s awareness of the semio-cognitive dimension of learning mathematics] (Doctoral dissertation). University of Palermo, Italy. Retrieved from
  19. Janvier, C. (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: L. Erlbaum Associates.Google Scholar
  20. Mason, M. (2010). Sample size and saturation in PhD studies using qualitative interviews. Forum: Qualitative Social Research, 11(3). Retrieved from
  21. Morse, J. M. (1991). Approaches to qualitative–quantitative methodological triangulation. Nursing Research, 40(2), 120–123.CrossRefGoogle Scholar
  22. Sáenz-Ludlow, A., & Presmeg, N. (2006). Guest editorial: Semiotic perspectives on learning mathematics and communicating mathematically. Educational Studies in Mathematics, 61(1–2), 1–10.CrossRefGoogle Scholar
  23. Santos, L., Berg, C. V., Brown, L., Malara, N., Potari, D., & Turner, F. (2012). CERME7 Working group 17: From a study of teaching practices to issues in teacher education. Research in Mathematics Education, 14(2), 215–216.CrossRefGoogle Scholar
  24. Sbaragli, S., & Santi, G. (2011). Teacher’s choices as the cause of misconceptions in the learning of the concept of angle. International Journal for Studies in Mathematics Education, 4(2), 117–157.Google Scholar
  25. Schoenfeld, A. H. (2016). Making sense of teaching. ZDM Mathematics Education, 48(1), 239–246.CrossRefGoogle Scholar
  26. Short, T. L. (2007). Peirce’s theory of signs. New York: Cambridge University Press.CrossRefGoogle Scholar
  27. Tashakkori, A., & Teddlie, C. (1998). Mixed methodology: Combining qualitative and quantitative approaches. Thousand Oaks, CA: Sage.Google Scholar
  28. Tashakkori, A., & Teddlie, C. (2003). Handbook of mixed methods in social & behavioral research. Thousand Oaks, CA: Sage.Google Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

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

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