Eugenia Taranto

The concepts of variable and parameter are fundamental for mathematical activity but are also challenging to rigorously introduce at a didactic level. In this paper, we discuss findings from an 11th-grade class interdisciplinary project involving mathematics and linguistics, promoting a conceptual approach to the learning of variables and parameters through narratives. We analyze the written productions of 22 Italian students across two tasks: the first aimed at exploring differences in the meaning of variables and parameters while employing a logico–scientific or narrative mode of thinking; the second involved a meta-reflection on the methodological tools used in the disciplines involved. Students’ productions were qualitatively analyzed using content analysis and thematic analysis, respectively. The analysis enables an elaboration on students’ understanding of the different roles of variables and parameters and of their epistemic features. Students’ conceptualizations of variables and parameters went beyond formal description, drawing on a variety of real-world situations. Moreover, the meta-reflection on the methodological tools shows new awareness of students’ understanding of disciplinary concepts. These findings suggest that interdisciplinary approaches involving mathematics and linguistics can effectively support the conceptual understanding of algebraic notions in secondary school. We therefore recommend further research exploring the integration of narrative contexts and cross-disciplinary collaborations in mathematics teaching.

In this paper, we finish describing the project and the experimentation of Ricerca Operativa Applicazioni Reali (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools. ROAR is composed of three teaching units addressed to grades 10, 11, and 12, respectively. To improve students’ interest, motivation, and skills related to science, technology, engineering, and mathematics disciplines, ROAR integrates the teaching of mathematics and computer science through operations research. Its implementation started in 2021 in a grade 10 class at the scientific high school IIS Antonietti in Iseo (Brescia, Italy). We provided the details of the first two units in previous papers. Here, we focus on the third and last unit, carried out from October 2022 to January 2023, with the same students, then in a grade 12 class. Similarly to the first two units, we describe objectives, prerequisites, topics and methods, the organization of the lectures, digital technologies used, and a challenging final project that, this time, involved the manufacturer company Filtrec S.p.A. with a case. After analyzing the feedback from students, teachers, and practitioners engaged in the experimentation, we reflect on the entire experimentation and provide some insights to replicate a similar experience. Funding: G. Colajanni was partially supported by the research project Programma Ricerca di Ateneo UNICT 2020-22 linea 2, Ottimizzazione di Modelli di Network slIce 5G con UAV, the Italian Ministry of University and Research and the European Union for the Programma Operativo Nazionale project on Research and Innovation 2014-2020, D.M. 1062/2021, and the GNAMPA-INdAM Group. A. Raffaele was partially supported by the National Group for Scientific Computation. E. Taranto was partially supported by the National Group for Algebraic and Geometric Structures, and their Applications. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ited.2023.0065 .

We present the continuation of a study on an international MOOC for the training of mathematics teachers who were introduced to the methodology of outdoor mathematics through MathCityMap. Previously, we presented the immediate learning and professional development outcomes achieved by teachers who participated in the MOOC. Here, using the theoretical framework of Meta-Didactical Transposition and performing a mixed-type analysis, we investigate the long-term impact of the MOOC on these teachers to whom we administered a questionnaire one year after the end of the MOOC. We conclude that for these teachers, practising mathematics outdoors has become a consolidated teaching practice, but they still feel quite uncomfortable for structural reasons about using some pedagogical instruments they have learned in the MOOC.

In this paper, we continue describing the project and the experimentation of Ricerca Operativa Applicazioni Reali (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools, introduced. ROAR is composed of three teaching units, addressed to Grades 10, 11, and 12, respectively, having the main aim to improve students’ interest, motivation, and skills related to Science, Technology, Engineering, and Mathematics disciplines by integrating mathematics and computer science through operations research. In a previous paper, we reported on the design and implementation of the first unit, started in Spring 2021 at the scientific high school IIS Antonietti in Iseo (Brescia, Italy), in a Grade-10 class. Here, we focus on the second unit, carried out in Winter/Spring 2022 with the same students, now in a Grade-11 class. In particular, we describe objectives, prerequisites, topics and methods, the organization of the lectures, digital technologies used, and a challenging final project. Moreover, we analyze the feedback from students and teachers involved in the experimentation. Funding: G. Colajanni and E. Taranto were partially supported by the research projects Programma Ricerca di Ateneo UNICT 2020-22 linea 2, EEEP&DLaD, and OMNIA, respectively, of the University of Catania. The research of G. Colajanni was also partially supported by the Italian Ministry of University and Research and the European Union for the PON project on Research and Innovation 2014–2020 [Grant D.M. 1062/2021]. A. Raffaele was partially supported by the Gruppo Nazionale per il Calcolo Scientifico. These supports are gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ited.2023.0001 .

This article delves into the significance of bodily experiences in the context of outdoor STEAM activities. It features a case study involving three tenth-grade students who engage in outdoor tasks – which are part of an outdoor STEAM trail – using the MathCityMap app. The research focuses on the students’ emerging strategies when dealing with two modelling tasks by integrating the modelling cycle phases with a perspective on embodiment that encompasses learning as navigating mathematical places. By intertwining these theoretical stances, the analysis uncovers the students’ strategies and seeks to describe their orientations during the experience. Despite the students not reaching the expected solutions, they bodily engage with the modelling tasks in meaningful ways, employing an array of various strategies. Trying to overcome the separation between domains, classically emphasised in the modelling context, the authors show how bodily engagement operates at their intersection and discuss the relevance of their approach for STEAM activities.

Since teachers have the greatest impact on student learning, it is crucial to consider how professional development programs (PDP) for teachers can enhance their contribution, especially in designing mathematical tasks for teaching. This paper focuses on identifying patterns of practices of mathematics teacher educators related to crucial aspects of two teacher PDPs: one conducted face-to-face and the other using a Massive Open Online Course (MOOC). The Meta-Didactical Transposition is employed as the theoretical framework for comparing the two PDPs and for identifying patterns of practices. The findings suggest that educators, both in face-to-face and online settings, consider certain practices to guide teachers in designing mathematical tasks. This paper aims to share experiences of good practices that can be implemented by other researchers seeking to guide teachers in task design, either alone or in small groups.