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The worlds’ game: collective language manipulation as a space to develop logical abilities in a primary school classroom

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Abstract

This paper presents a Vygotskian research device that focuses on collaborative activities based on the manipulation of linguistic objects in a primary school classroom, with 8–9-year-old children. Through social exchanges among the different points of view, the children were engaged in a dynamic process of building and negotiating mathematical meanings. How the children may become aware of the possibility that the same language can have different interpretations as well as some aspects of the distinction between syntax and semantic is analyzed. The analyzed activity is the “worlds’ game,” the final step of a didactic path based on the construction and manipulation of a procedural language. The content analysis of the elicitation interviews allows to reconstruct children’s reasoning, individually developed during and after the activities. From a qualitative analysis, it emerges how almost all the children reached a good level of awareness and mastery about the possibility that the same language can have different interpretations and, therefore, about some aspects of the difference between syntax and semantics.

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Notes

  1. The concept of cadre can be defined as a symbolic scaffolding legitimizing a system of actions and meanings upon which the actors rely in order to establish and see certain features of their relationship (Perret-Clermont and Nicolet 2001).

  2. The introduction of the positional notation, the transition from rhetoric algebra to a symbolic one, the differential calculus through Leibnitz’s symbolism, the increasingly widespread the use of variables, and quantifiers induced by the arithmetization of analysis are all stages of language’s evolution in this direction (Ferrari and Gerla 2015).

  3. A reflective process that enhances the awareness of the actors involved in the learning/teaching dynamics and, therefore, can help them identify the errors and distortions that characterize their strategies to solve problems (Cesari Lusso et al. 2015).

  4. For example, the development of abilities such as identifying problems, devising more or less formal languages to encode, process procedures to resolve them, and developing skills in describing these procedures unambiguously (Gerla et al. 1990).

  5. According to Vermersch (1994), the traces are the material signs produced by the children during the activities, such as intermediate and final written notes and outcomes.

  6. The Elicitation Interview is a method based on techniques for the formulations of the re-launchings (questions, reformulations, silences) aimed at facilitating and attending the a posteriori verbalization (in the sense of putting into words) of a particular experience (Vermersch 1994).

  7. This procedure required a segmentation of the corpus data into semantic units, through the classification of lexical units relating to the same subject, carried out by the authors of the paper.

  8. Classified as a unit of analysis that refers to the same theme or topic.

  9. Classified as a unit of analysis that assumes, in the context unit, the same meaning or similar meanings.

  10. The children chose the initials of words representing the instructions because, as they asserted during the collective discussions, this choice helped them to better remember the instruction

  11. An example of equivalence rule is AI = F, since both the words represent “no moving” and so they produce the same effect regarding the final position of the path. So, the word AIA is equivalent to the word A (Coppola et al. 2011b, 2014).

  12. For example, both in the yellow and orange worlds, the equivalence rule LELO= F holds, whereas this rule does not hold in the blue world. Therefore, the words LELO and F are equivalent both in the yellow and orange worlds, but they are not equivalent in the blue world.

  13. In transcribing the interviews, we used some of the Jefferson’s norms (Jefferson 1985), as (0.5) to indicate the length of the pause in seconds; (.) to indicate a shorter pause than 0.5 s. In the Extracts, we used I for the interviewer and the initial letter of the children’s name for the children.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Cristina Coppola

  2. Dipartimento di Scienze Umane, Filosofiche e della Formazione, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Monica Mollo & Tiziana Pacelli

Authors
  1. Cristina Coppola
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  2. Monica Mollo
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  3. Tiziana Pacelli
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Corresponding author

Correspondence to Cristina Coppola.

Additional information

Cristina Coppola. Researcher in Mathematics Education. Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132 – 84084, Fisciano (Salerno), Italy. E-mail: ccoppola@unisa.it, http://www.unisa.it/docenti/cristinacoppola/ind

Current themes of research:

Future teachers’ attitudes and emotions towards mathematics. The study of different aspects regarding the relationship between mathematical logic and language, with particular attention to the development of logical tools in primary school children, to the semiotic coordination with secondary school children in mathematical learning processes and to undergraduate students’ reasoning in logical tasks. The use of e-learning in mathematics education.

Most relevant publications in the field of Psychology of Education:

Coppola, C., Mollo, M., Pacelli, T. (2015). The development of logical tools through socially constructed and culturally situated activities. In M.V., Dazzani, M., Ristum, G., Marsico, & A.C., Bastos A.C. (Eds). (in press). Looking at Inside and Outside the Educational Contexts through Cultural Lens. Charlotte, N.C. USA: Information Age Publishing.

Coppola C., Mollo M., Pacelli T. (2014). Manipolazione di un linguaggio socialmente costruito in una classe di scuola primaria: costruzione del concetto di equivalenza, L’insegnamento della matematica e delle scienze integrate, Vol.37 A, n. 1, pp. 7-33.

Coppola C., Di Martino P., Pacelli T., Sabena C. (2015). Crucial events in pre-service primary teachers’ mathematical experience. In Beswick, K., Muir, T., & Wells, J. (Eds.). Proceedings of 39th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1). Hobart, Australia: PME.

Coppola C., Di Martino P., Pacelli T., Sabena C. (2012) Primary teachers’ affect: a crucial variable in the teaching of mathematics. Nordic Studies in Mathematics Education, vol. 17 (3-4), 107-123.

Coppola C., Mollo M., Pacelli T. (2011). The concept of equivalence in a socially constructed language in a primary school class, Proceedings of CERME 7, Rzeszów, Poland.

Monica Mollo. Researcher in Psychology of Education. Dipartimento di Scienze Umane, Filosofiche e della Formazione, Università degli Studi di Salerno, Via Giovanni Paolo II, 132 – 84084, Fisciano (Salerno), Italy. E-mail: mmollo@unisa.it

Current themes of research:

Self and identity. Construction of professional identity in university and school teachers. Elicitation interview. Professional practices. Construction of logic/mathematical thinking in children. Social representations. Cultural psychology

Most relevant publications in the field of Psychology of Education:

Savarese G., Fasano O., Mollo M., Pecoraro N. (2015). Tutoramento entre pares e integração universitária da deficiência. in Dazzani, M.V. & Marsico, G. (Eds). (2014). Psicologia Cultural e Contextos Educacionais, Special issue., Revista FACED, Salvador da Bahia: Editoria da Universidade Federal da Bahia.

Cesari Lusso,V., Iannaccone, A., Mollo, M. Tacit Knowledge And Opaque Action In Marsico, G., Ruggieri, R. & Salvatore, S., (Eds). (2015). Reflexivity in Psychology. Yearbook of Idiographic Science Volume 6. Charlotte, NC, USA.: Information Age Publishing.

Savarese G., Carpinelli, L., Fasano O., Mollo M., Pecoraro N. (2013). Study On The Correlation Between Self-Esteem, Coping And Clinical Symptoms In A Group Of Young Adults: A Brief Report. European Scientific Journal October 2013 edition vol.9.

Mollo M., Fasano O., Savarese G., Pecoraro N., Carpinelli L., Iannaccone A. (2013). Studio sulla correlazione tra autostima, coping e sintomatologia clinica in un gruppo di giovani adulti. Abstract book del XXVI Congresso Nazionale Aip - Sezione di Psicologia dello Sviluppo e dell’Educazione, Vita e Pensiero, Milano, 19-21 Settembre 2013.

Mollo, M., (2011) Formare menti. Dimensioni professionali e culturali dell’insegnamento, CUES, Salerno.

Iannaccone, A. Tateo, L. Mollo, M. & Marsico, G. (2008). L’identité professionnelle des enseignants face aux changements, Travail & Formation en Education, vol. 2.

Tiziana Pacelli. PhD in Mathematics. Dipartimento di Scienze Umane, Filosofiche e della Formazione, Università degli Studi di Salerno, Via Giovanni Paolo II, 132-84084 - Fisciano (Salerno), Italy. E-mail: tpacelli@unisa.it

Current themes of research:

Analysis of emotions, beliefs, and attitudes towards mathematics in future primary teachers. The exploration of the relationship between language and the development of logical tools in students at different school levels, in particular through cooperative and linguistic-manipulative activities with primary school children, through activities about semiotic coordination with secondary school children, through logical tasks with undergraduate students. Analysis of the use of e-learning in mathematics education.

Most relevant publications in the field of Psychology of Education:

Coppola C., Di Martino P., Mollo M., Pacelli T., Sabena C. (2013). Pre-service primary teachers’ emotions: the math-redemption phenomenon. Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (PME 37).

Coppola C., Di Martino P., Pacelli T., Sabena C. (2013). Inside teachers’ affect: teaching as an occasion for math-redemption, In: Markku S. Hannula, Päivi Portaankorva-Koivisto, Anu Laine, Liisa Näveri (a cura di), Current state of research on mathematical beliefs XVIII: Proceedings of the MAVI-18 Conference. September 12-15, 2012, Helsinki, Finland. pp. 203-215.

Coppola C., Mollo M., Pacelli T. (2011). An experience of social rising of logical tools: the role of language. International Journal for Mathematics Teaching and Learning.

Andrà C., Coppola C., Pacelli T. (2011). A model for describing reasoning in logical tasks, Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (PME 35).

Coppola C., Mollo M., Pacelli T. (2010). Deduzione come manipolazione linguistica: un’esperienza in una scuola primaria, L’educazione matematica, Anno XXX1, serie 1, vol. 2 no. 3, 5 –22.

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Coppola, C., Mollo, M. & Pacelli, T. The worlds’ game: collective language manipulation as a space to develop logical abilities in a primary school classroom. Eur J Psychol Educ 34, 783–799 (2019). https://doi.org/10.1007/s10212-018-0401-1

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  • DOI: https://doi.org/10.1007/s10212-018-0401-1

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