Management of semiotic representations in mathematics: Quantifications and new characterizations

Federica Ferretti 1, Alessandro Gambini 2, Camilla Spagnolo 3 *
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1 University of Ferrara, Ferrara, ITALY
2 Sapienza University of Rome, Rome, ITALY
3 Free University of Bozen-Bolzano, Bolzano, ITALY
* Corresponding Author
EUR J SCI MATH ED, Volume 12, Issue 1, pp. 11-20. https://doi.org/10.30935/scimath/13827
Published Online: 25 October 2023, Published: 01 January 2024
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ABSTRACT

As highlighted in the literature, one of the main difficulties in mathematics is the management of different semiotic representations. This difficulty occurs in verticals throughout schooling and is often an obstacle to the proper learning process of mathematics. The present study aims to investigate the different facets of these difficulties with regard to mathematical tasks in secondary school. In particular, questions from Italian large-scale mathematics assessments are analyzed and interpreted through the theoretical lens of Duval’s (1993) theory. Statistical analyses on a robust national sample allow a framing of the main difficulties and provide valuable information in this field.

CITATION

Ferretti, F., Gambini, A., & Spagnolo, C. (2024). Management of semiotic representations in mathematics: Quantifications and new characterizations. European Journal of Science and Mathematics Education, 12(1), 11-20. https://doi.org/10.30935/scimath/13827

REFERENCES

  • Atkin, J. M. (1998). The OECD study of innovations in science, mathematics and technology education. Journal of Curriculum Studies, 30(6), 647-660. https://doi.org/10.1080/002202798183369
  • Breakspear, S. (2012). The policy impact of PISA: An exploration of the normative effects of international benchmarking in school system performance. OECD Publishing. https://doi.org/10.1787/5k9fdfqffr28-en
  • Callingham, R., & Bond, T. (2006). Research in mathematics education and Rasch measurement. Mathematics Education Research Journal, 18(2), 1-10. https://doi.org/10.1007/BF03217432
  • Campbell, C., & Levin, B. (2009). Using data to support educational improvement. Educational Assessment, Evaluation and Accountability, 21(1), 47-65. https://doi.org/10.1007/s11092-008-9063-x
  • Casalvieri, C., Gambini, A., Spagnolo, C., & Viola, G. (2023). The concept of derivatives through eye-tracker analysis. In Proceedings of the 15th International Conference on Computer Supported Education (pp. 378-385). https://doi.org/10.5220/0011941100003470
  • D’Amore, B. (2003). La complexité de la noétique en mathématiques ou les raisons de la dévolution manquée [The complexity of noetic in mathematics or the reasons for failed devolution]. For the Learning of Mathematics, 23(1), 47-51.
  • De Lange, J. (2007). Large-scale assessment and mathematics education. In F. K. Lester Jr (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1111-1142). Information Age Publishing.
  • Doig, B. (2006). Large-scale mathematics assessment: Looking globally to act locally. Assessment in Education: Principles, Policy & Practice, 13(3), 265-288. https://doi.org/10.1080/09695940601035403
  • 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 [Annals of Didactics and Cognitive Sciences], 5, 37-65.
  • Duval, R. (1998). Signe et object (I). Trois grandes étapes dans la problématique des rapports entre répresentation et objet [Sign and object (I). Three main stages in the problem of the relationship between representation and object]. Annales de Didactique et de Sciences Cognitives [Annals of Didactics and Cognitive Sciences], 6, 139-163.
  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103-131. https://doi.org/10.1007/s10649-006-0400-z
  • Duval, R. (2008). Eight problems for a semiotic approach in mathematics education. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom, and culture (pp. 39-61). Sense Publishers. https://doi.org/10.1163/9789087905972_004
  • Eurydice, I. U. I. (2016). La valutazione delle scuole in Europa: Politiche e approcci in alcuni Paesi europei [School evaluation in Europe: Policies and approaches in some European countries]. Eurydice Italia.
  • Facciaroni, L., Gambini, A., & Mazza, L. (2023). The difficulties in geometry: A quantitative analysis based on results of mathematics competitions in Italy. European Journal of Science and Mathematics Education, 11(2), 259-270. https://doi.org/10.30935/scimath/12590
  • Ferretti, F., & Bolondi, G. (2021). This cannot be the result! The didactic phenomenon ‘the age of the earth’. International Journal of Mathematical Education in Science and Technology, 52(2), 194-207. https://doi.org/10.1080/0020739X.2019.1670366
  • Ferretti, F., & Giberti, C. (2020). The properties of powers: Didactic contract and gender gap. International Journal of Science and Mathematical Education, 19(8), 1717-1735. https://doi.org/10.1007/s10763-020-10130-5
  • Ferretti, F., & Santi, G. (2023). Teachers’ subjectification as a dialogue with standardized assessment. For the Learning of Mathematics, 43(2), 19-21.
  • Ferretti, F., Santi, G. R. P., & Bolondi, G. (2022). Interpreting difficulties in the learning of algebraic inequalities, as an emerging macro-phenomenon in large scale assessment. Research in Mathematics Education, 24(3), 367-389. https://doi.org/10.1080/14794802.2021.2010236
  • Gambini, A., Desimoni, M., & Ferretti, F. (2022). Predictive tools for university performance: An explorative study. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2021.2022794
  • Garuti, R., & Martignone, F. (2019). Assessment and argumentation: An analysis of mathematics standardized items. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the 11th Congress of the European Society for Research in Mathematics Education (pp. 4075-4082). Freudenthal Group & Freudenthal Institute, Utrecht University, and ERME.
  • Giberti, C., Santi, G., & Spagnolo, C. (2023). The role of metaphors in interpreting students’ difficulties in operating with percentages: A mixed method study based on large scale assessment. European Journal of Science and Mathematics Education, 11(2), 297-321. https://doi.org/10.30935/scimath/12642
  • Hart, L. C., Smith, S. Z., Swars, S. L., & Smith, M. E. (2009). An examination of research methods in mathematics education (1995-2005). Journal of Mixed Methods Research, 3(1), 26-41. https://doi.org/10.1177/1558689808325771
  • INVALSI (2018). Quadro di riferimento delle prove di INVALSI di matematica [Reference framework for the INVALSI mathematics tests]. https://invalsiareaprove.cineca.it/docs/file/QdR_MATEMATICA.pdf
  • Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14-26. https://doi.org/10.3102/0013189X033007014
  • Kanes, C., Morgan, C., & Tsatsaroni, A. (2014). The PISA mathematics regime: Knowledge structures and practices of the self. Educational Studies in Mathematics, 87, 145-165. https://doi.org/10.1007/s10649-014-9542-6
  • Kloosterman, P., Walcott, C., Brown, N. J. S., Mohr, D., Pérez, A., Dai, S., Roach, M., Hall, L. D., & Huang, H.-C. (2015). Using NAEP to analyze eighth-grade students’ ability to reason algebraically. In J. A. Middleton, J. Cai, & S. Hwang (Eds.), Large-scale studies in mathematics education (pp. 179-207). Springer. https://doi.org/10.1007/978-3-319-07716-1_9
  • Looney, J. W. (2011). Integrating formative and summative assessment: Progress toward a seamless system? OECD Publishing.
  • Mazza, L., & Gambini, A. (2023). The phenomenon of the gender gap among gifted students: the situation in Italy based on analysis of results in mathematics competitions. Teaching Mathematics and its Applications: An International Journal of the IMA, 42(2), 170-186. https://doi.org/10.1093/teamat/hrac009
  • Meinck, S., Neuschmidt, O., & Taneva, M. (2017). Workshop theme: “Use of educational large-scale assessment data for research on mathematics didactics”. In G. Kaiser (Ed.), Proceedings of the 13th International Congress on Mathematical Education (pp.741-742). Springer. https://doi.org/10.1007/978-3-319-62597-3_132
  • MIUR. (2012). Indicazioni nazionali per il curricolo della scuola dell’infanzia e del primo ciclo di istruzione [National indications for the curriculum of nursery school and the first cycle of education]. Le Monnier.
  • Presmeg, N., Radford, L., Roth, W. M., & Kadunz, G. (2016). Semiotics in mathematics education. Springer. https://doi.org/10.1007/978-3-319-31370-2
  • Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Danish Institute for Educational Research.
  • Schoonenboom, J., & Johnson, R. B. (2017). How to construct a mixed methods research design. Kölner Zeitschrift für Soziologie und Sozialpsychologie [Cologne Journal of Sociology and Social Psychology], 69(Supplement 2), 107-131. https://doi.org/10.1007/s11577-017-0454-1
  • Spagnolo, C., Capone, R., & Gambini, A. (2021a). Where do students focus their attention on solving mathematical tasks? An eye tracker explorative study. In M. Prasitha, N. Changsri, & N. Boonsena (Eds.), Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education (pp. 89-96). PME.
  • Spagnolo, C., Giglio, R., Tiralongo, S., & Bolondi, G. (2022). Formative assessment in LDL workshop activities: Engaging teachers in a training program. In B. Csapó, & J. Uhomoibhi (Eds.), Proceedings of the International Conference on Computer Supported Education (pp. 560-576). Springer. https://doi.org/10.1007/978-3-031-14756-2_27
  • Spagnolo, C., Giglio, R., Tiralongo, S., Bolondi, G. (2021b). Formative assessment in LDL: A teacher-training experiment. In Proceedings of the 13th International Conference on Computer Supported Education (pp. 657-664). https://doi.org/10.5220/0010496006570664
  • Tasaki, N. (2017). The impact of OECD-PISA results on Japanese educational policy. European Journal of Education, 52(2), 145-153. https://doi.org/10.1111/ejed.12217