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In questo lavoro si presenta un modulo didattico dal titolo La Lingua Matematica, rivolto a studenti del primo anno di scuola secondaria di secondo grado.Il modulo è stato presentato in classi di Liceo Matematico, ma può essere proposto anche in altri contesti. Esso ha un duplice obiettivo: introdurre questioni relative a matematica e linguaggio da un lato e introdurre i concetti di teorema e dimostrazione dall’altro. Il percorso ha permesso di introdurre nozioni di aritmetica modulare e ha condotto gli studenti a confrontarsi, elaborare ipotesi, produrre argomentazioni e generare nuovi teoremi.

The COVID-19-induced distance education was perceived as highly challenging by teachers and students. A cross-national comparison of five European countries identified several challenges occurred during the distance learning period. On this basis, the article aims to develop a theoretical framework and design requirements for distance and online learning tools. As one example for online learning in mathematics education, the ASYMPTOTE system is introduced. It will be freely available by May 2022. ASYMPTOTE is aimed at the adaptive and synchronous delivery of online education by taking a mobile learning approach. Its core is the so-called digital classroom, which not only allows students to interact with each other or with the teacher but also enables teachers to monitor their students’ work progress in real time. With respect to the theoretical framework, this article analyses to what extent the ASYMPTOTE system meets the requirements of online learning. Overall, the digital classroom can be seen as a promising tool for teachers to carry out appropriate formative assessment and—partly—to maintain personal and content-related interaction at a distance. Moreover, we highlight the availability of this tool. Due to its mobile learning approach, almost all students will be able to participate in lessons conducted with ASYMPTOTE.

In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers’ professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool MathCityMap and professional development to be accomplished using MOOCs. By taking into account the MOOC “Task Design for Math Trails”, with 93 finalists, we analyze the learning progress of 19 selected case studies from different nations and learning levels by taking into account their answers in a pre- and post-questionnaire and their posts on a specific communication message board, with a special focus on the MOOC’s topics’ task design for outdoor mathematics and the digital tool MathCityMap. The analysis is performed using different quantitative and qualitative approaches. The results show that the teachers studied have benefited from professional development, which is evident in the expansion/evolution of their knowledge from a content, pedagogical, and technological perspective. Finally, we formulate consequences for professional development in STEM education, and conclude the paper with limitations to be drawn and a perspective for further research.

The focus of this research is how Sicilian state university mathematics professors faced the challenge of teaching via distance education during the first wave of the COVID-19 pandemic. Since the pandemic entered our lives suddenly, the professors found themselves having to lecture using an e-learning platform that they had never used before, and for which they could not receive training due to the health emergency. In addition to the emotional aspects related to the particular situation of the pandemic, there are two aspects to consider when teaching mathematics at a distance. The first is related to the fact that at university level, lecturers generally teach mathematics in a formal way, using many symbols and formulas that they are used to writing. The second aspect is that the way mathematics is taught is also related to the students to whom the teaching is addressed. In fact, not only online, but also in face-to-face modality, the teaching of mathematics to students on the mathematics degree course involves a different approach to lessons (as well as to the choice of topics to explain) than teaching mathematics in another degree course. In order to investigate how the Sicilian State university mathematics professors taught mathematics at distance, a questionnaire was prepared and administered one month after the beginning of the lockdown in Italy. Both quantitative and qualitative analyses were made, which allowed us to observe the way that university professors have adapted to the new teaching modality: they started to appropriate new artifacts (writing tablets, mathematical software, e-learning platform) to replicate their face-to-face teaching modality, mostly maintaining their blackboard teacher status. Their answers also reveal their beliefs related to teaching mathematics at university level, noting what has been an advantageous or disadvantageous for them in distance teaching.

In this paper we present an experimental teaching activity conduced in some primary, middle and high schools in Sicily. The activity concerned several topics of graph theory. Here we highlight, in particular, the approach to teaching Eulerian graphs. The aim of the whole project was to present a fun, easy approach to mathematics in order to promote a good attitude towards mathematics in primary school children and to improve it in middle school kids and in high school young people. This goal is pursued also by showing some connections of mathematics with real life, making mathematics less abstract than the topics too often taught in school. Through this activity we also reach mathematical knowledge and practical abilities (related to graph theory), and above all mathematical competencies related to reasoning and mathematization, in particular by the use of graphs in mathematical models to solve problems. The teaching experiments were different, according to the different school level, but unified by the method, based on laboratorial activities, by presenting a problem to be solved together with classmates, by manipulating objects and guided by the teacher. These activities were realized by the use of artefacts: in the sense of Vygotskijan semiotic mediation, we used signs, symbols, maps, language and, in many cases, new technology’s artefacts, to mediate mathematical concepts. Lessons involved also the body as a mean to learning, especially with children, according to embodied cognition theory.