Papers by Ferdinando Arzarello
Research in Mathematics Education, 2010
Mitteilungen der Gesellschaft für Didaktik der Mathematik, Feb 1, 2016
Witwatersrand, Johannesburg, South Africa)-The Hans Freudenthal Medal for a major cumulative prog... more Witwatersrand, Johannesburg, South Africa)-The Hans Freudenthal Medal for a major cumulative programme of research Please join with us in congratulating both Alan and Jill, and acknowledging their fine contributions to mathematics education and therefore to the mathematics education community. We look forward to honouring them at ICME-13 in Hamburg in 2016.
Bollettino Della Unione Matematica Italiana, 1998
Two facts mark the emerging of the new status of mathematics education as a scientific discipline... more Two facts mark the emerging of the new status of mathematics education as a scientific discipline: the inauguration in 1969 of the tradition of International Congresses on Mathematical Education (ICMEs), and the contemporary launch of journals related to mathematics education research. The early ICMEs acted as catalysts for new ideas that have their roots in important events that took place in the 1950s and 1960s. As a consequence new issues found their place in the international discussion on mathematics education and opened new lines of research and forms of action inside ICMI, so that we may talk about a genuine ICMI Renaissance. In our contribution we examine the background and circumstances that fostered and shaped the emergence of the new issues that have developed in mathematics education up to the present day
New ICMI studies series, 2023
Each of the previous chapters in this section proposed research tools-methods, questions, theoret... more Each of the previous chapters in this section proposed research tools-methods, questions, theoretical lenses-that might help those engaged in mathematics curriculum reform to learn from other reform efforts through examination of different aspects of the systems and contexts in which they take place. The authors and theme E participants made these explorations because the study of curriculum reform is still in its infancy, and its foundations are in the early stages of being built. The papers should be read individually in order for the reader to make full use of their nuanced implications. However, several key considerations stand out across these chapters that we suggest should shape approaches to future curriculum reform and reform research efforts. Considering Curriculum Reform Contexts as Systems Can Make Important Choices Stand Out Curriculum reform is not carried out in the abstract but is always situated in a particular context at the jurisdiction level, and further instantiated within multiple local contexts like schools and training programmes. While these contexts are all unique,
Journal on Mathematics Education, Oct 10, 2022
Meaning-making in teaching-learning mathematical processes is a relevant issue analysed through d... more Meaning-making in teaching-learning mathematical processes is a relevant issue analysed through different philosophical and educational frames. In particular, the use of digital tools in mathematics education affects the meaning-making processes. This paper discusses meaning-making from a phenomenological standpoint, in which interpretative activities are relevant. This approach requires a careful analysis of the semiotic resources' evolution, including those related to the used digital tools. The paper aims to introduce an analytical tool, the Timeline. This tool is an elaboration on previous analysis tools, like the interaction flowchart and the semiotic bundle. Such a tool allows the analysis of relationship among interactions, semiotic resources, and meaningmaking. In this paper, the Timeline is used to analyze two episodes from two different learning experiments where GeoGebra and augmented reality are used. High school students from Italy and Israel participated in this study. Video recording has been used to document the entire learning experiments. The analysis provides evidence that the Timeline enables investigating the relationship between students-teacher-artifacts interactions and meaningmaking. Moreover, results may give teachers ideas for using digital tools to foster students' meaning-making.
On the Role of Gestures in Learning Mathematics.- A Semiotic Approach and Perspectives on Learnin... more On the Role of Gestures in Learning Mathematics.- A Semiotic Approach and Perspectives on Learning.- Extended Methods and Methodology.- Results on the Representational and the Epistemic Functions of Gestures.- Towards the Role of Gestures: A Comparison.- Reflections, Synopsis, Perspectives.
New ICMI Study Series
A broad perspective must be taken while discussing teachers, resources and assessment practices i... more A broad perspective must be taken while discussing teachers, resources and assessment practices in relation to reform and this is what we have attempted in the present chapter. We consider factors in curriculum implementation including physical materials, technologies, but also processes such as classroom and system assessment practices and, in a privileged way, the role of teachers. Curricular change can become just a proposal printed on an official paper if it does not actively involve teachers and their practices, and if it does not secure the needed resources for teachers. In focusing in this chapter on the implementation of curriculum reform,
HAL (Le Centre pour la Communication Scientifique Directe), Feb 4, 2015
Touchscreen dynamic environments user interfaces employ a specialized interaction model on screen... more Touchscreen dynamic environments user interfaces employ a specialized interaction model on screen. In this paper, we analyse students' manipulation to explore and justify their geometrical reasoning on a free online touch device: the Geometric Constructer (GC) software. We discuss data from a teaching experiment with Italian High School students. The experiment was videotaped. Based on this we observe two domains (constructive and relational) regarding the development of geometrical thinking on GC. Students' manipulation on constructive domain is basically done to make construction and it contributes to exploration and to arise conjecturing. Indeed, manipulation in relational domain can suitably support and improve students' justifying and proving performances.
The Journal of Mathematical Behavior
HAL (Le Centre pour la Communication Scientifique Directe), Sep 12, 2020
This paper focuses on the epistemic and cognitive characterization of backward reasoning in strat... more This paper focuses on the epistemic and cognitive characterization of backward reasoning in strategy games resolution. It explores the use of AiC (Abstraction in Context) as a tool for the analysis of the epistemic actions involved in these processes. It is reported a first analysis developed by the research team in order to be used as protocol-guide in the analysis of a study carried out with PhD students in Mathematics Degree in a Spanish and an Italian University, who face problem solving games. The case study shows the process of discovery that a PhD student makes to formulate a general recursive formula. It is a key for understanding the interaction between the AiC model and the characteristics of backward reasoning. The analysis allows to combine the two models-backward reasoning and AiC-in a unified framework that allows to focus both short-term and long-term processes in students' activities.
arXiv: History and Overview, 2016
The celebration of the Centennial of the International Commission on Mathematical Instruction off... more The celebration of the Centennial of the International Commission on Mathematical Instruction offered the occasion to look back at the history of ICMI and outline the evolution of mathematics education until it achieved its present status as an academic discipline. The years after WWII up to the late 1960s were crucial in this evolution for both the settlement of some institutional aspects, mainly concerning the relationship with mathematicians, and the establishment of new trends of the activities. In this paper we outline, on the basis of unpublished documents, the role of two important figures in those years: Heinrich Behnke and Hans Freudenthal.
Mathematics and Technology, 2017
In this chapter, we discuss the results of a research project which investigates aspects of stude... more In this chapter, we discuss the results of a research project which investigates aspects of students’ cognitions during the process of solving tasks dealing with a Dynamic Geometric Environment with touchscreen (DGEwT). In this chapter, we discuss data from two teaching experiments carried out with Brazilian and Italian high school students dealing with GeoGebraTouch (GT) and a Geometric Constructer (GC) software. With the focus on strategies used by students to solve the proposed tasks, we suggest two domains: Constructive and relational. Furthermore, we suggest the drag-approach as an important form of manipulation to improve geometrical thinking. Finally, we present a selected variety of representative examples of didactic, cognitive, and epistemological implications for learning and researching with the use of DGEwT.
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Papers by Ferdinando Arzarello