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We present a methodological discussion of how to elaborate different scale epistemological reference models and in particular, present a large-scale model for the domain of arithmetic in Japanese primary school, based on the national program and selected textbooks. Our theoretical base is the Anthropological Theory of Didactic (ATD), specifically the notion of praxeology and the levels of didactic codetermination. We also briefly discuss our motivation for creating such models, namely to analyse how students experience shifts between mathematics in different school systems.

Questa tesi si propone di mettere in luce come l’analisi statistica di prove standardizzate di matematica possa avere importanti ricadute per lo studio di fenomeni didattici. In particolare, le ricerche presentate si riferiranno alle prove INVALSI studiate attraverso il modello di Rasch. Si mostrerà come questo approccio possa far emergere macro-fenomeni già osservati in didattica della matematica, studiandoli anche da un punto di vista quantitativo. In particolare verranno utilizzati per questi casi dei grafici, detti distractor plot, che mostrano l’andamento della risposta corretta e delle altre opzioni di risposta in funzione dell’abilità degli studenti. Questi grafici, applicati all’intera popolazione o a sottoinsiemi della stessa, permetteranno di evidenziare se una determinata risposta degli studenti, legata a un costrutto didattico, abbia una maggiore influenza su particolari livelli di abilità.

The purpose of this chapter is to present a systematic observational research on the math teachers' assessment practices in the classroom. This research is a specific phase of an international project (FAMT&L - Comenius Multilateral Project) and it is aimed to promote the use of formative assessment in teaching mathematics to students aged from 11 to 16. The observational study is carried out by a plan of systematic observations of teachers' behaviour in the classroom with the help of video recording. Thanks to a specific tool of video analysis (a structured grid), developed using indications from international literature and experiences of teacher training in the five Partner countries involved (Italy, France, Holland, Switzerland and Cyprus), we managed to gather many different indicators on good and bad practices for the formative assessment of mathematics teachers. Furthermore, the analysed video will be used in in-service teacher training courses in order to promote a correct use of formative assessment and to improve achievements in learning mathematics.

This paper reports on the development of a survey tool to investigate how programming and computational thinking (PCT) is implemented in Denmark, Sweden, and England. The survey is targeted at mathematics teachers and aims to understand their enactment of PCT in their field and their perceived attributes of the innovation. Developing this kind of survey is difficult as implementation strategies differ significantly. This paper argues that one way to build a foundation for comparison is to inform its focus by utilizing 1) implementation theory and 2) innovation-specific theory.

Over the last decades digital resources of various kinds have entered mathematics education including mathematical modelling. In this paper we present the a priori analysis of a modelling activity based on Study and Research Path using the notions of media-milieu dialectic and Herbartian schema from the Anthropological Theory of the Didactic. We use these notions to differ between resources: digital tools, textbooks, data and to differ between the pragmatic and epistemic value of the resources. Finally, we discuss how task design can benefit from addressing the potential roles resources can play in modelling processes.