Giulia Ferrari

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.

: In this article, we draw on assemblage theory to investigate how children aged 5 engage with different material surfaces to explore ordinal and relational aspects of number. The children participate in an activity in which they first interact with a strip on the floor, then with a multi-touch iPad application, to work with numbers in expressive ways. Focus is on the physicality and materiality of the activity and the provisional ways that children, surfaces, and number come together. While the notion of assemblage helps us see how movement animates the mathematical activity, we enrich our understanding of the entanglement of children, matter, and number as sustained by coordinated movements, from which numbers emerge as relations.

This work offers some insights coming from the use of the application Fractio Quest, which was developed in the Project Gamifying CLIL within a Mathematics Context, within the mathematics classroom. The app was conceptualized in principle for a CLIL approach to fraction learning. Focus is put on two complementary dimensions of usage: a pilot experiment conducted in Italy in 2020, which involved a grade 7 class and its mathematics teacher in using a preliminary English version of the app, and the development of supplementary materials for teachers. The chapter first discusses the challenges posed for teachers and students when the app is used in a foreign language and explores the language/content interplay fostered by the activity. Then, reflections on methodological aspects considered for the design of supplementary materials for teaching are presented. These aspects are framed into the CLIL framework and by following research trends in mathematics education.

This article relates a case study on how a conversation with materials and diagrams – the actual use of materials and diagrams to think, imagine, explain, collaborate, design and build – featured a certain kind of interplay between material and digital components. The physical components present in this setting included a water wheel, which is a wheel driven by flow of water whose rotational motion is a classic example of chaotic dynamics regulated by Lorenz equations. Digital components allowed for real-time graphical displays corresponding to the turning of the water wheel. We selected for this article a sequence of episodes from an interview with Jake, an undergraduate student majoring in engineering. Through a micro-ethnographic analysis, we reflect on how Jake combined the responsiveness of the digital displays with the tangibility of the water wheel to gain insight into some of the intricacies of oscillatory motion.

This paper focuses on the emergence of abstraction through the use of a new kind of motion detector—WiiGraph—with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their difference. They explored relationships that can be ascribed to an equation of the type A – B = C. We examine the notion of abstraction on its own, without assuming a dualism abstract-concrete according to which more of one is less of the other. We propose a distinct path for the attainment of abstraction, which involves navigating a surplus of sensible qualities. The work described in this paper belongs to early algebra, we suggest, because it involves the elementary symbolic treatment of unknowns and generals. More broadly, it advances a perspective on the nature of mathematical abstraction.

In this paper, we pursue a materialist approach to tool use to account for the material dimensions of learning mathematics with technology while decentralizing the human body from activity. We root this vision in theoretical advances on embodied mathematics learning and tool use that have been recently offered as alternatives to traditional theories of learning that draw attention only to the individual learner or the mind. Focus is on the ways that learners, tools and mathematics are entangled in provisional reconfigurations of the world and on how the tool partakes in this movement. Starting from our theoretical commitment, we discuss some episodes from a research study in which grade 9 students were introduced to function through a graphical approach. The study took advantage of graphing motion technology, which allows working with couples of position over time graphs, capturing spatio-temporal relationships. The episodes provide insight into the complex nature of learning in this context, valuing the mobile way that mathematics emerges from activity with the tool.