European Journal of Psychology of Education

, Volume 33, Issue 3, pp 489–504 | Cite as

Errare humanum est! A socio-psychological approach to a “Climbing Mount Fuji” PISA question

  • Patrizia Selleri
  • Felice Carugati


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.


Mathematics PISA framework Mathematical education Didactic contract Socio-psychological approach 



  1. Allalouf, A., Hambleton, R. K., & Sireci, S. G. (1999). Identifying the causes of DIF in translated verbal items. Journal of Educational Measurement, 36(3), 185–198.CrossRefGoogle Scholar
  2. Bottani, N., & Vrignaud, P. (2005). La France et les évaluations internationales. (n.16, Janvier, pp. 172.). Paris: Haut Conseil de l’évaluation de l’école.Google Scholar
  3. Bracey, G. W. (2009). PISA: not leaning hard on U.S. economy. Phi Delta Kappa, 90(6), 450–451.CrossRefGoogle Scholar
  4. Brissiaud, R. (1988). De l’âge du capitaine a l’âge du berger. Quel contrôle de la validité d’un énoncé de problème au CE2? Revue Française de Pédagogie, 82, 23–31.CrossRefGoogle Scholar
  5. Brousseau, G. (1997/2002). Theory of didactical situations in mathematics. New York: Kluwer Academic Publishers.Google Scholar
  6. Carugati, F., & Selleri, P. (2004). Intelligence, educational practices and school reform: organisations change, representations persist. European Journal of School Psychology, 2(1–2), 149–167.Google Scholar
  7. Carugati, F., & Selleri, P. (2014). Piaget, Vygotskij and the European approach in social psychology of education: a space for virtuous dialogue? In T. Zittoun & A. Iannaccone (Eds.), Activities of thinking in social spaces (pp. 43–61). New York: Nova Science Publishers, Inc..Google Scholar
  8. Clements, M. A., Bishop, A. J., Keitel, C., Kilpatrick, J., & Leung, F. K. S. (Eds.). (2013). Third international handbook of mathematics education. New York: Springer.Google Scholar
  9. Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H.-C. (2015). Word problems: a review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6, 348. Scholar
  10. Edelen, M. O., & Reeve, B. B. (2007). Applying item response theory (IRT) modelling to questionnaire development, evaluation, and refinement. Quality of Life Research, 16, 5–18.CrossRefGoogle Scholar
  11. Ericsson, K. A., & Simon, H. A. (1998). How to study thinking in everyday life: contrasting think-aloud protocols with descriptions and explanations of thinking. Mind, Culture, and Activity, 5(3), 178–186.CrossRefGoogle Scholar
  12. Goffman, E. (1967). Interaction ritual: essays on face-to-face interaction. Oxford: Aldine.Google Scholar
  13. Goldstein, H. (2015). Rasch measurement: a response to Payanides, Robinson and Tymms. Response on Rasch model. British Educational Research Journal, 41(1), 176–179.CrossRefGoogle Scholar
  14. Hambleton, R. K. (2005). Issues, designs, and technical guidelines for adapting tests into multiple languages and cultures. In R. K. Hambleton & P. F. Meranda (Eds.), Adapting educational and psychological tests for cross-cultural assessment (pp. 3–38). Mahwah: Erlbaum.Google Scholar
  15. Jungwirth, H. (1993). Routines in classroom discourse. An ethnomethodological approach. European Journal of Psychology of Education, 8(4), 375–387.CrossRefGoogle Scholar
  16. Master, G. N. (1988). Item discrimination: when more is worse. Journal of Educational Measurement, 25(1), 15–29.CrossRefGoogle Scholar
  17. Murat, F., & Rocher, T. (2004). The methods used for international assessments of educational competences. In J. H. Moskowitz & M. Stephens (Eds.), Comparing learning outcomes: international assessment and education policy (pp. 190–214). New York: Routgers Falmer.Google Scholar
  18. OECD. (2013a). PISA 2012 assessment and analytical framework: mathematics, reading, science, problem solving and financial literacy. Paris: OECD Publishing.CrossRefGoogle Scholar
  19. OECD. (2013b). PISA 2012 results: excellence through equity: giving every student the chance to succeed (volume II). Paris: OECD Publishing.CrossRefGoogle Scholar
  20. Owens, T. (2013). Thinking beyond league tables: a review of key PISA research questions. In H. D. Meyer & A. Benavot (Eds.), PISA, power and policy: the emergence of global educational governance (pp. 27–49). Southampton: Symposium Books.Google Scholar
  21. Polya, G. (1945). How to solve it. Princeton: University Press.Google Scholar
  22. Resnick, L. B. (1987). Learning in school and out. Educational Researcher, 16(9), 13–20.Google Scholar
  23. Rochex, J.-Y. (2006). Social, methodological and theoretical issues regarding assessment: lessons from a secondary analysis of PISA 2000 literary tests. Review of Research in Education, 30, 163–212.CrossRefGoogle Scholar
  24. Romagnoli, S., & Selleri, P. (2011). La competenza in cerca d’autore [Competence in search for author]. RicercAzione, 2, 231–236.Google Scholar
  25. Sachs, H., Schegloff, A., & Jefferson, G. (1974). A simplest systematics for the organization of turn-taking for conversation. Language, 50(4), 696–735.CrossRefGoogle Scholar
  26. Säljö, R., & Wyndhamn, J. (1987). The formal setting as context for cognitive activities. An empirical study of arithmetic operations under conflicting premises for communication. European Journal of Psychology of Education, 2(2), 233–245.CrossRefGoogle Scholar
  27. Säljö, R., & Wyndhamn, J. (1993). Solving everyday problems in the formal setting: an empirical study of the school as context for thought. In S. Chaiklin & J. Lave (Eds.), Understanding practice: perspectives on activity and context (pp. 327–342). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  28. Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning. A project of the National Council of Teachers of Mathematics (pp. 355–358). New York: Macmillan Publishing Company.Google Scholar
  29. Schubauer-Leoni, M.-L. (1986). Le contrat didactique: un cadre interprétatif pour comprendre les savoirs manifestés par les élèves en mathématiques [The didactic contract: an interpretative framework for the understanding of the mathematical knowledge displayed by pupils]. European Journal of Psychology of Education, 1(2), 139–153.CrossRefGoogle Scholar
  30. Selleri, P. (2016). La comunicazione in classe [Communication in classrooms]. Roma: Carocci.Google Scholar
  31. Selleri, P., & Carugati, F. (1999). “Ecoutez-moi les enfants”. De la conversation à l’étude des routines scolaires [“Listen to me, kids!”. From the conversation to the study of school routines]. In M. Gilly, J.-P. Roux, & A. Trognon (Eds.), Apprendre dans l’interaction: analyse des médiations sémiotiques [Learning through interaction: analysis of semiotic mediations] (pp. 279–300). Nancy: Presses Universitaires.Google Scholar
  32. 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. 229–269). Charlotte: IAP: Information Age Publishing Inc.Google Scholar
  33. Sinclair, J., & Coultard, M. (1975). Toward an analysis of discourse: the English used by teachers and pupils. Oxford: Oxford University Press.Google Scholar
  34. Verschaffel, L., Greer, B., & de Corte, E. (2000). Making sense of word problems. Educational Studies in Mathematics, 42(2), 211–213.CrossRefGoogle Scholar
  35. Yildirim, H. H., & Berberoğlu, G. (2009). Judgmental and statistical DIF analyses of the PISA 2003 mathematics literacy items. International Journal of Testing, 9(2), 108–121.CrossRefGoogle Scholar

Copyright information

© Instituto Superior de Psicologia Aplicada, Lisboa, Portugal and Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PsychologyAlma Mater Studiorum University of BolognaBolognaItaly
  2. 2.Alma Mater Studiorum University of BolognaBolognaItaly

Personalised recommendations