Abstract
There is a consensus that the items proposed by the Program for International Student Assessment (PISA) program allow us to focus on the outcomes of the processes of appropriation and transformation of learning tools at the end of compulsory schooling, particularly regarding the key competencies for lifelong learning and citizenship in digital societies. Taking into account these assumptions, this paper focuses on a fine-grained analysis of the dynamics of students’ performance when they are confronted with a question from the mathematics domain in PISA 2012, through the example of the Climbing Mount Fuji item (question 1). In the context of the interaction dynamics (between a student and a research assistant), twelve 15-year-old students from Naples (Campania, Italy) were requested to think aloud when answering the question 1 of the item. Verbatim transcripts of the interactions are analyzed from the point of view of the PISA framework, the mathematical educational framework, and the socio-psychological approach based on didactic contract. The results show that the students involved in this task commit themselves in a complex reasoning, relying on mathematical requirements (e.g., different mathematical procedures) in an attempt to resolve ambiguities in the text, also referring to their everyday school life, activated by the didactic contract implied by the scenario of the question. The interweaving of PISA performances, mathematical procedures, and the socio-psychological approach to test assessment is discussed as a tool for a better understanding of teaching and learning activities.
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Notes
The outer-most box in Figure 1.1 (OECD 2013a, p. 25) shows that mathematical literacy takes place in the context of a challenge or problem that arises in the real world. In this framework, these challenges are characterized in two ways. The context categories, which will be described in detail later in this paper, identify the areas of life from which the problem arises. The context may be of a personal nature, involving problems or challenges that might face an individual or one’s family or peer group. The problem might instead be set in a societal context (focusing on one’s community—whether it be local, national, or global), an occupational context (centered on the world of work), or a scientific context (relating to the application of mathematics to the natural and technological world).
The didactic contract (Brousseau 1997/2002, pp. 31–32) implies the determination, which is neither written nor clearly stated, of the respective roles of the student and the teacher in the classroom and in relation to knowledge. Brousseau also said that the didactic contract is a “relationship which explicitly determines for a small part, but especially implicitly, what each partner, the teacher and the students, is responsible for managing and in one way or another will be responsible to the other.”
Across the OECD countries, a more socio-economically advantaged students score 38 points higher in mathematics—the equivalent of nearly one year of schooling—than a less advantaged students (OECD 2013b, p. 13).
More information about the project may be found in the following: https://www.coe.int/t/dg3/socialpolicies/socialcohesiondev/trends_EN.asp; Series of publications Trends in social cohesion, No. 9
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Patrizia Selleri. Department of Psychology, Alma Mater Studiorum University of Bologna, Via Berti Pichat, 5, 40100 Bologna, Italy. E-mail: patrizia.selleri@unibo.it
Current themes of research:
Social interaction and cognitive development. Classroom discourse. Social representations of development, education, learning and teaching. Dynamics of diffusion of scientific knowledge and common sense. Quality of life.
Most relevant publications in the field of Psychology of Education:
Selleri, P. (2016). La comunicazione in classe. Roma: Carocci (new edition)
Carugati, F. & Selleri, P. (2014). Social development and the development of social representations: two sides of the same coin? In A. Antonietti, E. Confalonieri & A. Marchetti (Eds.) Metarepresentation and narrative in educational settings: where cognitive and social development meet (pp.15–54). New York: Cambridge University Press.
Carugati, F. & Selleri, P. (2014) Piaget, Vygotskij and European approach in social psychology of education: a space for virtous dialogue? In T. Zittoun & A. Iannaccone (Eds.) Activities of thinking in social spaces (pp. 43–61). New York: Nova Science Publishers, Inc.
Selleri, P. & Carugati, F. (2013). Taking care of children and pupils: agreements and disagreements in parents’ and teachers’ social representations. In G. Marsico, K. Komatsu, A. Iannaccone (Eds.) Crossing boundaries: intercontestual dynamics between family and school (pp. 229–260). Charlotte, N.C., Publisher: IAP: Information Age Publishing Inc.
Scalone, L., Tomasetto, C., Matteucci, M.C., Selleri, P., Broccoli, S., Pacelli, B., Cavrini G. (2011). Assessing quality of life in children and adolescents: development and validation of the Italian version of the EQ-5D-Y. Italian Journal of Public Health, 8, 331–341.
Felice Carugati. Alma Mater Studiorum University of Bologna (retired). Bologna, Italy. E-mail: felice.carugati@unibo.it
Current themes of research:
Socialization processes in institutions and the families. Social and personal identity. Social interaction and cognitive development. Social representations of development, education, learning and teaching. Dynamics of diffusion of scientific knowledge and common sense. Social dynamics in assessment and evaluation of teaching, learning and social institutions. Dissemination of information and communication technologies in educational contexts, distance education in higher education.
Most relevant publications in the field of Psychology of Education:
Carugati, F. & Perret-Clermont, A-N. (2015). Learning and instruction: social-cognitive perspectives. In J. D. Wright (editor-in-chief), International encyclopedia of the social & behavioral sciences, 2nd edition, Vol 13. (pp. 670–676) .Oxford: Elsevier.
Carugati, F. & Selleri, P. (2014). Social development and the development of social representations: two sides of the same coin? In A. Antonietti, E. Confalonieri & A. Marchetti (Eds.) Metarepresentation and narrative in educational settings: where cognitive and social development meet (pp.15–54). New York: Cambridge University Press.
Carugati, F. & Selleri, P. (2014) Piaget, Vygotskij and European approach in social psychology of education: a space for virtous dialogue? In T. Zittoun & A. Iannaccone (Eds.) Activities of thinking in social spaces (pp. 43–61). New York: Nova Science Publishers, Inc.
Miguel, I., Pires Valentim, J., & Carugati, F. (2013). Social representations of the development of intelligence, parental values and parenting styles: a theoretical model for analysis. European Journal of Psychology of Education. https://doi.org/10.1007/s10212-012-0160-3.
Carugati, F. (2013). Commentary: Crossing boundaries between everyday and research contexts: extending the conversation. In G. Marsico, K. Komatsu, & A. Iannaccone (Eds.). Crossing boundaries: intercontestual dynamics between family and school (pp.171–183). Charlotte, N.C. Publisher: IAP: Information Age Publishing Inc., Charlotte, N.C.
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Selleri, P., Carugati, F. Errare humanum est! A socio-psychological approach to a “Climbing Mount Fuji” PISA question. Eur J Psychol Educ 33, 489–504 (2018). https://doi.org/10.1007/s10212-018-0373-1
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DOI: https://doi.org/10.1007/s10212-018-0373-1