Philosophy for Children and mathematical argumentation: A multimodal analysis in second grade primary school

Authors

  • Andrea Maffia University of Bologna
  • Elisabetta Pisani Istituto Comprensivo di Montefelcino
  • Mariangela Scarpini University of Parma

DOI:

https://doi.org/10.60923/issn.1970-2221/22841

Keywords:

mathematical argumentation, Philosophy for Children, multimodality, gestuality, Toulmin's model

Abstract

Argumentation is a fundamental component of mathematical thinking, yet in school practices it does not seem to be given sufficient space, which is instead largely reserved for the memorization of formulas and rules.   Through the lenses of Philosophy for Children — that enhances critical, creative and reflective thinking through the creation of a community of inquiry — this paper investigates children’s argumentations in second grade following the resolution of an open problem concerning the cube and its nets. The analysis of the data collected uses a multimodal approach that integrates verbal and non-verbal. The results highlight how gestures, artefacts and interactions are fundamental resources for supporting and expanding children's mathematical thinking in a dialogical context that not only is possible even at this young age and in a mathematical context, but it does also prove to be fruitful.

References

Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investigación en Matemática Educativa, 9(1), 267-299.

Arzarello, F., & Paola, D. (2007). Semiotic games: The role of the teacher. In W. Jeong-Ho, L. Hee-Chan, P. Kyo-Sik Park, S., Dong-Yeop (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (pp. 17-24). PME.

Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70, 97-109.

Arzarello, F., & Sabena, C. (2014). Analytic-structural functions of gestures in mathematical argumentation processes. In L. D. Edwards, F. Ferrara, D. Moore-Russo (Eds.), Emerging Perspectives on Gesture and Embodiment in Mathematics (pp. 75-103). Information Age Publishing.

Baccaglini-Frank, A., Di Martino, P., Maffei, L., Mariotti, M., Pezzia, M., Signorini, G., & Zan, R. (2013). Quaderni Invalsi. Ambito: Relazioni e Funzioni. INVALSI.

Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 147-176.

Ball, D. L. (1995). Transforming pedagogy: Classrooms as mathematical communities. A response to Timothy Lensmire and John Pryor. Harvard Educational Review, 65, 670-677.

Bartolini Bussi, M. G., Boni, M., & Ferri, F. (1995). Interazione sociale e conoscenza a scuola: La discussione matematica. Centro Documentazione Educativa.

Bikner-Ahsbahs, A., & Prediger, S. (Eds). (2014). Networking of theories as a research practice in mathematics education. Springer.

Boaler, J., & Humphreys, C. (2005). Connecting mathematical ideas. Heinemann.

Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. Journal of the Learning Sciences, 10, 113164.

Corazza, P. (2021). Come ripensare l'intelligenza collettiva nell'epoca digitale? Spunti di riflessione a partire da Philosophy for/with Children e pedagogia degli oppressi. In S. Demozzi (Ed.), Contesti per pensare. Riflessioni su pedagogia, indagine filosofica e comunità di ricerca (pp. 101-115). Franco Angeli.

Daniel, M. F. (2013). Engaging in critical dialogue about mathematics. Analytic Teaching and Philosophical Praxis, 34(1), 58-68.

Daniel, M. F., Lafortune, L., Mongeau, P., & Pallascio, R. (2003). Philosophy for Children Adapted to Mathematics: A Study of its Impact on the Evolution of Affective Factors. Analytic Teaching, 23(1), 10-25.

Daniel, M. F., Lafortune, L., Pallascio, R., & Schleifer, M. (1999). Philosophical reflection and cooperative practices in an elementary school mathematics classroom. Canadian Journal of Education, 24(4), 426-440.

Daniel, M. F., Lafortune, L., Pallascio, R., & Sykes, P. (1994). A primary school curriculum to foster thinking about mathematics. Analytic Teaching, 15(1), 29-40.

Demozzi, S. (2021). Il tempo dell'infanzia come possibilità di educazione al pensiero. In S. Demozzi (ed.), Contesti per pensare. Riflessioni su pedagogia, indagine filosofica e comunità di ricerca (pp. 17-31). Franco Angeli.

Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103-131.

Ferrara, F., Robutti, O., & Edwards, L. D. (2014). An exploratory study of multimodalities in the mathematics classroom. In L. D. Edwards, F. Ferrara, D. Moore-Russo (Eds.), Emerging perspectives on gesture and embodiment in mathematics (pp. 105-124). Information Age Publishing.

Kennedy, N. S. (2007). From philosophical to mathematical inquiry in the classroom. Childhood & Philosophy, 3(6), 289-311.

Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29-63.

Lipman, M. (2005). Educare al pensiero. Vita e Pensiero.

Lipman, M. (2018). L'impegno di una vita: Insegnare a pensare. Mimesis.

Maffia, A., & Sabena, C. (2015). Networking of theories as resource for classroom activities analysis: The emergence of multimodal semiotic chains. Quaderni di Ricerca in Didattica, 25(2), 405-417.

Mariotti, M. A. (2022). Argomentare e dimostrare come problema didattico. UTET Università.

McNeill, D. (1992). Hand and mind: What gestures reveal about thought. University of Chicago Press.

MIUR. (2012). Indicazioni Nazionali per il curricolo della scuola dell'infanzia e del primo ciclo di istruzione. https://sial.school/wp-content/uploads/2022/04/Indicazioni_Annali_Curriculo_Italiano.pdf.

Morin, E. (2004). Educare per l'era planetaria. Armando Editore.

Nigris, E. (2015). Le domande che aiutano a capire. Mondadori.

Pallascio, R. & Simmt, E. (2002). Philosophy for children on Mathematics. In E. Simmt, & B. Davis (Eds.), Proceedings of the 26th annual meeting of the Canadian mathematics education study group (pp. 43-58). CMESG/GCEDM.

Peirce, C. S. (1984). Le leggi dell'ipotesi. Bompiani.

Radford, L., & Sabena, C. (2014). The question of method in a Vygotskian semiotic approach. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 157-182). Springer.

Rapanta, C., & Felton, M. K. (2022). Learning to argue through dialogue: A review of instructional approaches. Educational Psychology Review, 34(2), 477-509.

Reuter, F. (2023). Explorative mathematical argumentation: A theoretical framework for identifying and analysing argumentation processes in early mathematics learning. Educational Studies in Mathematics, 112(3), 415-435.

Sabena, C. (2011). Studiare la multimodalità dell'insegnamento-apprendimento: Focus sui gesti. L'insegnamento della Matematica e delle Scienze Integrate, 34(3), 333-342.

Sabena, C. (2018). Exploring the contribution of gestures to mathematical argumentation processes from a semiotic perspective. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, & B. Xu (Eds.), Invited Lectures from the 13th International Congress on Mathematical Education (pp. 541-559). Springer International Publishing.

Sabena, C., Maffia, A., & Krause, C. M. (2016). L'analisi semiotica in ottica multimodale: Dalla costruzione di un quadro teorico al networking con altre teorie. Relazione al XXXIII Seminario Nazionale di ricerca in didattica della matematica Giovanni Prodi. AIRDM

Santi, M. (2006). Ragionare con il discorso. Il pensiero argomentativo nelle discussioni in classe. Liguori.

Santi, M., & Oliverio, S. (2016). Educating for Complex Thinking through Philosophical Inquiry. Liguori.

Schoenfeld, A. H. (1989). What’s all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189-215). Erlbaum.

Schwarz, B., & Prusak, N. (2016). The importance of multi-modality in mathematical argumentation. In F. Paglieri, L. Bonelli, & S. Felletti (Eds.), The psychology of argument (p. 387-406). College Publications

Scipione, L. (2021). Conversare, discutere, dialogare: Contesti e pretesti per l'esercizio del pensiero. In S. Demozzi (Ed.), Contesti per pensare. Riflessioni su pedagogia, indagine filosofica e comunità di ricerca (pp. 65-79). Fran-co Angeli.

Scipione, L. (2022). Pretesti filosofici. Discutere e argomentare nella scuola primaria. Anicia.

Selleri, P. (2016). La comunicazione in classe. Carocci.

Striano, M. (1999). Quando il pensiero si racconta. Meltemi.

Tibaldeo, R. F. (2015). Un felice connubio di razionalità e libertà: La pratica "riflessiva" della "Philosophy for Children" (P4C) di Matthew Lipman. Itinera, (10), 362-376.

Toulmin, S. (1975). Gli usi dell'argomentazione. Rosenberg & Sellier.

Vygotskij, L. S. (2007). Pensiero e linguaggio. Giunti.

Zan, R. (2007). Difficoltà in matematica. Springer.

Published

2026-06-30

How to Cite

Maffia, A., Pisani, E., & Scarpini, M. (2026). Philosophy for Children and mathematical argumentation: A multimodal analysis in second grade primary school . Ricerche Di Pedagogia E Didattica. Journal of Theories and Research in Education, 21(1), 121–145. https://doi.org/10.60923/issn.1970-2221/22841

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Articles