The Didactic Contract to Interpret Some Statistical Evidence in Mathematics Standardized Assessment Tests
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Free University of Bolzano-Bozen, Bolzano, ITALY
University of Bologna, Bologna, ITALY
I.C. Bassa Anaunia- Duenno, Trento, ITALY
Online publish date: 2018-05-11
Publish date: 2018-05-11
EURASIA J. Math., Sci Tech. Ed 2018;14(7):2895–2906
In this study we analyse results of Italian standardized tests in mathematics integrating quantitative analysis based on the Rasch Model and didactical interpretation. We use specific graphs to analyse the trend of each answer as function of the students’ math ability. This approach led us to focus on specific items in which a wrong answer results particularly popular among medium/high level students and analyse this particular trend with the lenses of math education theories. The study reveals that these phenomena are particularly related to implicit and explicit rules governing classroom practices exist at all school levels and regard different mathematical content and skills.
Anderson, J. O., Lin, H. S., Treagust, D. F., Ross, S. P., & Yore, L. D. (2007). Using large-scale assessment datasets for research in science and mathematics education: Programme for International Student Assessment (PISA). International Journal of Science and Mathematics Education, 5(4), 591-614.
Arzarello, F., Garuti, R., & Ricci, R. (2015). The impact of PISA studies on the Italian national assessment system. In Assessing Mathematical Literacy (pp. 249-260). Springer, Cham.
Barbaranelli, C., & Natali, E. (2005). I test psicologici: teorie e modelli psicometrici. Carocci.
Bolondi, G., Branchetti, L., Ferretti, F., Lemmo, A., Maffia, A., Martignone, F., Matteucci, M., Mignani, S., & Santi, G. (2016). Un approccio longitudinale per l’analisi delle prove INVALSI di matematica: cosa ci può dire sugli studenti in difficoltà? Report concorso idee per la ricerca, pp. 81-102. Roma: INVALSI.
Bolondi, G., Cascella, C., & Giberti, C. (2017). Highlights on gender gap from Italian standardized assessment in mathematics. Universita Karlova Press.
Branchetti, L., Ferretti, F., Lemmo, A., Maffia, A., Martignone, F., Matteucci, M., & Mignani, S. (2015). A longitudinal analysis of the Italian national standardized mathematics tests. Proceedings of the 9th Conference of European Research in Mathematics Education, (pp. 1695-1701) Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME.
Brousseau, G. (1980). L’échec et le contrat. Recherches, n.41, 177-182.
Brousseau, G. (1988). Le contrat didactique: le milieu. Recherches en Didactique des Mathématiques, 9(3), 309-336.
D’Amore, B. (2008). Epistemology, didactics of mathematics and teaching practices. Mediterranean Journal of Research in Mathematics Education, 7(1).
Di Tommaso, M. L., Mendolia, S., & Contini, D. (2016). The Gender Gap in Mathematics Achievement: Evidence from Italian Data. IZA Discussion paper, n.10053, Bonn.
EMS-EC (Education Committee of the EMS) (2012). What are the Reciprocal Expectations between Teacher and Students? Solid Findings in Mathematics Education on Didactical Contract. Newsletter of the European Mathematical Society, 84, 53-55.
Ferretti, F. (2015). L’effetto “età della Terra”. Contratto didattico e principi regolativi dell’azione degli studenti in matematica (Doctoral thesis), Alma Mater Studiorum Università di Bologna. Retrieved from
Ferretti, F., & Gambini, A. (2017). A vertical analysis of difficulties in mathematics by secondary school to level; some evidences stems from standardized assessment. Proceedings of the 10th Conference of European Research in Mathematics Education, Dublin (Ireland).
Gestinv 2.0. (07.01.2018). Archivio interattivo delle prove Invalsi. Retrieved from
Giberti, C., Zivelonghi, A., & Bolondi, G. (2016). Gender differences and didactis contract: analysis of two Inalsi tasks on power properties. 40th PME proceedings, 275.
Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory (Vol. 2). Sage.
INVALSI. (2017). Rilevazione nazionale degli apprendimenti 2016-2017. Rapporto tecnico. Retrieved on March 2018 from
Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come, Educational Researcher, 33(7), 14-26.
Leder, G., & Lubienski, S. (2015). Large-Scale Test Data: Making the Invisible Visible. In Diversity in Mathematics Education (pp. 17-40). Springer International Publishing.
Looney, J. W. (2011). Integrating formative and summative assessment: progress toward a seamless system? OECD Education Working Paper 58. OECD Publishing.
Mellone, M., Romano, P., Tortora, R., Statale, L. S., Mangino, M. B., & Pagani, S. I. (2013). Different ways of grasping structure in arithmetical tasks, as steps toward algebra. In Proceedings of CERME (Vol. 8, pp. 480-489).
Middleton, J. A., Cai, J., & Hwang, S. (2015). Why mathematics education needs large-scale research. In Large-scale studies in mathematics education (pp. 1-13). Springer International Publishing.
Rasch G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests, Danmarks Paedagogiske Institut, Copenhagen.
Sfard, A. (2005). What could be More Practical than Good Research? Educational Studies in Mathematics, 58(3), 393-413.