La formazione degli insegnanti di matematica e le valutazioni standardizzate: primi risultati di un progetto di ricerca nazionale interdisciplinare

The contribution shows the first results of an interdisciplinary research project conducted by the INVALSI Group -Didattiche Disciplinari, an Osservatorio of the S.I.R.D. - Società Italiana di Ricerca Didattica, constituted by experts in mathematics and computer science education, pedagogists and in-service mathematics teachers. The Osservatorio of the SIRD (https://www.sird.it/osservatorio-didattica-e-saperi/ ) arise from a need for cohesion that has emerged from the experience conducted in recent years by the various Italian universities in the field of pre- and in-service teacher professional development programs, which has highlighted with increasing force, how the professionalism of teachers is based on the coherent, intelligent integration of pedagogical-didactic knowledge with that of the various disciplinary sectors. The aim of the Osservatorio is to promote dialogue between the field of didactic research and the field of disciplinary didactics at all school levels. More specifically, the objectives are to make a scientific contribution to the ongoing debate in the institutional and political world; to plan training/confrontation initiatives on the subject; to launch research projects in which researchers from the teaching filed and from the various subject areas collaborate jointly. The research project that emerged from the Research Group that is the subject of this contribution is aimed at investigating the link between the INVALSI Mathematics tests and the processes of teaching and learning Mathematics, in particular with teaching practices. The interdisciplinary work consisted in the construction of a tool for surveying teachers' attitudes towards INVALSI, both in INVALSI as an institute, with its aims and working methods, and towards the INVALSI Mathematics tests and their effects on teaching. The aim of the research is to identify professional development teachers’ needs at national level within schools and to propose guidelines for improving practices regarding the use of INVALSI surveys. To answer the research hypotheses, a questionnaire was designed and administered to investigate teachers’ beliefs regarding the knowledge and skills investigated by the INVALSI tests, their closeness to teaching practices in Mathematics and the role that they assume within the context school. In detail, the questionnaire consists of two areas of variables, one specifically for Mathematics Education and one relating to the aspects of Education. In detail Mathematics Education variables are aimed at investigating how much the Mathematical contents and abilities detected with the INVALSI tests are - more or less close to daily personal teaching practices; - lived as coherent/ inconsistent with the national guidelines and are recognized or not consistent with the intentions of INVALSI - considered useful for influencing/innovating personal teaching practice. Questions about teachers’ ability to read INVALSI data were in the questionnaire; these variables represent the focus of the survey and they are the dependent variables. The independent variables are those related to the aspects of Education and Didactics that refer to constructs aimed at detecting the attitudes of teachers and all scholastic subjects. The first results have been the subject of several publications at national and international level (see, for example, Arzarello & Ferretti, 2021, Faggiano, Ferretti, & Arzarello, 2022, Rizzo, Faggiano, Monaco, & Vaccaro, 2021, Vaccaro, Faggiano & Ferretti, 2021,). In this contribution, we will present what Arzarello and Ferretti have denoted as a "three-fold meta-didactical conflict" (Arzarello & Ferretti, 2021, Ferretti, & Arzarello, under review), which emerged from the analysis of the answers provided by 504 primary school teachers nationwide. To discuss what we have found until now, we make an analogy between the small context of an usual mathematics classroom and the general national school context, which our research is considering. In the analysis of classroom interactions it is common to see what Anna Sfard calls an ‘incommensurable discourse’ (Sfard, 2008) between the teacher and the students: they use the same words but with a different meaning and moreover are not aware of the difference; a conflict is generated, which, if not overcome, can have serious consequences for successful teaching/learning processes in the classroom. Something similar happened to us when we analyzed the answers to our questionnaire: also here we found incommensurable languages. They are the sign of what we call a three-fold meta-didactical conflict: it has been possible to realize its existence thanks to the questionnaire. As its name suggests, this conflict has three components and is meta-didactic since it concerns discourses about didactic processes like assessment, students’ competencies and mistakes, etc., and not about the thought mathematics concepts themselves. A first component of the conflict concerns the fact that many teachers perceive the difficulty of a question from the INVALSI survey very differently from the national trend. A second component concerns the fact that many teachers interpret the difficulties of students or evaluate their answers to the INVALSI tests in a way that is completely different from what unquestionably appears from the data of the survey. A third component is a consequence of the previous two and concerns the contradictory way according to which teachers interpret the rationale of the INVALSI tests. Of course, it is possible that the three components may be only the epiphenomenon of a deeper conflict, whose nature at the moment we have not yet understood, but until now we can speak only of a three-fold conflict, since its three components in any case appear deeply intertwined. We think that our current hypothesis about this conflict will be confirmed or refuted through the administration of the questionnaire to a wider court of subjects and a deep analysis of the related data. In case of confirmation, it will be possible to refine the same analysis of the conflict, deciding about its three-fold or different nature, and also clarifying its deep structure and nature, e.g. with respect the knowledge and beliefs of teachers. Basing on the analogy from the conflicts in the classroom, for which a successful strategy for overcoming them is generated by a clear understanding of their nature, it will be precisely from a clean picture of the structure and dynamics of our conflict that it will be possible to design suitable guidelines for getting rid of it and obtaining a real improvement of practices regarding the use of INVALSI tests in the school.