We use eye-tracking as a method to examine how different mathematical representations of the same mathematical object are attended to by students. The results show that there is a meaningful difference in the eye movements between formulas and graphs. This difference can be understood in terms of the cultural and social shaping of human perception, as well as in terms of differences between the symbolic and the graphical registers, as they have been examined in literature. The results are also discussed in terms of didactic implications to support teachers in helping students to both deal with and to integrate multiple mathematical representations as well as acknowledge their own specificity.

We present a new measure for evaluating focused versus overview eye movement behavior in a stimulus divided by areas of interest. The measure can be used for overall data, as well as data over time. Using data from an ongoing project with mathematical problem solving, we describe how to calculate the measure and how to carry out a statistical evaluation of the results.

In the spring of 2020, schools and universities around the world were closed because of the COVID-19 pandemic. The relative lockdown affected more than 1.5 billion learners as teachers and students sheltered at home for several weeks. As schooling moved online, teachers were forced to change how they taught. In the research presented here, we focus on university mathematics professors, and we analyze how their practice, knowledge, and beliefs intertwine and change under these circumstances. More specifically, the context of the pandemic and the relative lockdown provides us with the experimental basis to argue that the new practice affected both knowledge and beliefs of mathematics teachers and that practice, knowledge, and beliefs form a system. Being part of a system, the reactions to change in practice can be of two types, namely, the system as a whole tries to resist change, or the system as a whole changes — and it changes significantly. The research presented here proposes a model for describing and analyzing what we called a teaching system and examines three cases that help to better depict the systemic nature of teaching.

We consider a sample of about 700 people, interviewed on the streets, who are sorted into two groups by a self-report, screening questionnaire: namely, non-problematic gamblers/non-gamblers and problematic gamblers. Within each group, we compare both social (perceived) stigma and self-perceived (experienced) stigma, measured by means of other two self-report questionnaires, and we seek for relations between stigma and socio-demographic variables that can help targeting possible interventions to reduce gambling-related stigma. We, then, compare stigma between the two groups of non-(problematic) gamblers and problematic ones, and we also check the hypothesis that higher social stigma is related to higher self-perceived stigma, as well as higher stigma is related to lesser help-seeking. The latter hypothesis is of utmost importance, given that stigma is recognised to be one of the major causes for hindering help-seeking by problematic gamblers. The research is carried out in Italy, one of the first countries in the world for the money spent per capita in gambling activity every year.

Stemming from an interest in developing suitable didactical tasks to prevent gambling abuse during the school years, this article explores the use of an Android app that simulates the outcomes of a well-known Italian instant lottery. Some features that characterize the phenomenon of gambling abuse are sketchily recalled, the Android app is presented and an example from a classroom task is discussed. We conclude that the simulator contributes to developing statistical literacy, as traditional random generators do, and also exploits emotional reactions, such as shock, which allow curiosity to emerge and pave the way towards deeper understanding.

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