Papers by Giorgos Psycharis
New ICMI studies series, 2024
This subsection identifies the research aims and questions described in the Discussion Document a... more This subsection identifies the research aims and questions described in the Discussion Document and references the other chapters, or the Themes and the Plenaries, organised within the conference. This chapter is the result of the work and paper presentations that took place both in person and remotely-before, during and after the conference-and of participants from the Theme D group. This chapter (Theme D) is focused on tools and resources for teacher collaboration and from teacher collaboration: "Resources for and from teacher collaboration can be considered as two ingredients of continuous processes: adopting a resource leads always to adapting it, and that is more the case in the context of teacher collaboration" (Borko & Potari, 2019, p. 9; italics in original). The research questions addressed in the call for contribution are: What resources are available to support teacher collaboration? With what effects, both on the collaboration and on the resources themselves? What resources are missing for supporting teacher collaboration? How and to what extent can teachers overcome these missing resources? To what extent and under what conditions do digital environments (e.g., mobile devices, platforms, applications) constitute opportunities for teacher collaboration? How have these resources been used to support teacher collaboration? Which resources can be used (and how) to sustain and scale up collaboration over time? How are teachers engaged in the design of resources in collaboration? What are the outcomes of these collaborations? (Borko & Potari, 2019, p. 9; italics in original) This chapter presents a new way to speak of tools and resources: seeing them as products of teachers' collaborative work or means to support teachers' collaboration and their possible evolution in various settings. The papers submitted examined
HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022
This paper proposes an analytical tool for the evaluation of prospective mathematics teachers' (P... more This paper proposes an analytical tool for the evaluation of prospective mathematics teachers' (PTs) diagnostic competencies through noticing critical incidents in hypothetical classroom situations (mathtasks). Data were collected from nineteen PTs attending an undergraduate course for one semester. Data analysis highlighted variations within the four characteristics of teachers' diagnostic competencies that are described by four internal levels inspired by how teachers notice. This analysis resulted to the analytical rubric we present and exemplify in this paper. We see the potential of the proposed rubric in research and mathematics teacher professional development.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 4, 2015
This paper proposes "formalising functional dependencies" as an approach to address critical aspe... more This paper proposes "formalising functional dependencies" as an approach to address critical aspects of the potential of digital technologies for the teaching and learning of functions. This approach focuses on the role of the available tools in supporting students' transition from experiencing dependencies in terms of non-algebraic digital representations to expressing these dependencies formally. To illustrate the approach, data from two studies based on the use of two distinct computational systems are analysed. Key aspects of their potential include: work with dependencies at the level of magnitudes, specially designed functionalities and dynamic interplay between symbolic and non-symbolic representations of functions.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 6, 2019
In this paper we investigate how a group of six mathematics teachers in Greece deals with the nee... more In this paper we investigate how a group of six mathematics teachers in Greece deals with the need to balance work on mathematically demanding tasks and differentiation in lesson planning and enactment. Videotaped lessons and pre and post reflection interviews were analysed with a specific focus on whole class discussion. The findings show certain teaching practices that appear to promote both mathematical challenge and differentiation and emerging patterns of actions that make the challenge accessible to students.
Constructivist Foundations, 2015
Brennan describes ways by which teachers can be supported to bypass a technocentric view of learn... more Brennan describes ways by which teachers can be supported to bypass a technocentric view of learning with technology in the classroom, from a constructionist perspective. She reports on the …
Journal of Mathematics Teacher Education
We study the interactions over 22 years between one mathematics teacher and his resources for tea... more We study the interactions over 22 years between one mathematics teacher and his resources for teaching, especially digital ones, with a dual focus on the teacher’s documentational and identity trajectories and professional development. We combined a theoretical framework on teachers’ work with resources—documentational approach to didactics (DAD)—with a framework based on social practice theory—patterns of participation (PoP). The DAD analysis provided rich descriptions of which digital resources the teacher interacted with and of the transformative evolution of these interactions over time. The PoP analysis offered explanations of how and why the teacher transformed his interactions with the resources through foregrounding affective and contextual factors as significant for the teacher’s formation of identity. We conclude that the combination of the two frameworks provided deeper and complementary insights into the teacher’s long-term professional development with digital resources...
The Journal of Mathematical Behavior
Mathematics Education in the Digital Era
Dynamic manipulation schemes of geometrical constructions: Instrumental genesis as an abstraction... more Dynamic manipulation schemes of geometrical constructions: Instrumental genesis as an abstraction process
Technology, Knowledge and Learning, 2013
The general goal of this paper is to explore the potential of computer environments for the teach... more The general goal of this paper is to explore the potential of computer environments for the teaching and learning of functions. To address this, different theoretical frameworks and corresponding research traditions are available. In this study, we aim to network different frameworks by following a 'double analysis' method to analyse two empirical studies based on the use of computational environments offering integrated geometrical and algebraic representations. The studies took place in different national and didactic contexts and constitute cases of Constructionism and Theory of Didactical Situations. The analysis indicates that 'double analysis' resulted in a deepened and more balanced understanding about knowledge emerging from empirical studies as regards the nature of learning situations for functions with computers and the process of conceptualisation of functions by students. Main issues around the potential of computer environments for the teaching and learning of functions concern the use of integrated representations of functions linking geometry and algebra, the need to address epistemological and cognitive aspects of the constructed knowledge and the critical role of teachers in the design and evolution of students' activity. We also reflect on how the networking of theories influences theoretical advancement and the followed research approaches.
In this paper we aim to address the potential of computational environments offering integrated g... more In this paper we aim to address the potential of computational environments offering integrated geometrical and algebraic representations for the teaching and learning of functions. double learning situations of an experiment that took place in the French context through the lens of the original research tradition (Theory of Didactical Situations) and (Constructionism). The analysis indicates that this method enhances our efficiency to capture aspects of research traditions which influence knowledge concerning the nature of learning situations for functions with computers.
Μeτάφραση στα eλληνικά: Γιώργος Ψυχάρης Κριτική θeώρηση: Χρόνης Κυνηγός Πeρίληψη Η 'Θeωρία Δι... more Μeτάφραση στα eλληνικά: Γιώργος Ψυχάρης Κριτική θeώρηση: Χρόνης Κυνηγός Πeρίληψη Η 'Θeωρία Διδακτικής Τeκµηρίωσης' αποτeλeί άρθρο που γράφτηκe για να πeριληφθeί στον τόµο Encyclopedia of Mathematics Education (Trouche, Gueudet & Pepin 2018). Το παρόν άρθρο αποτeλeί eνηµέρωση της αρχικής έκδοσης που έγινe το 2020 (Trouche, Gueudet & Pepin 2020) και σe αυτό βασίζeται η παρούσα µeτάφραση στα eλληνικά. Η µeτάφραση αυτή αποτeλeί µέρος µιας συλλογής µeταφράσeων του άρθρου σe 14 γλώσσeς (https://hal.archives-ouvertes.fr/DAD-MULTILINGUAL). Η θeωρία διδακτικής τeκµηρίωσης eίναι µια eκ των θeωριών της διδακτικής των µαθηµατικών. Ο κύριος στόχος της eίναι η κατανόηση της eπαγγeλµατικής ανάπτυξης των eκπαιδeυτικών µέσα από τη µeλέτη των αλληλeπιδράσeών τους µe τους πόρους που σχeδιάζουν και χρησιµοποιούν για/στη διδασκαλία τους. Στο παρόν κeίµeνο πeριγράφονται µe συντοµία η δηµιουργία της θeωρίας και κύριeς πτυχές της: θeωρητικές αρχές, βασικές έννοιeς και σχeτική µeθοδολογία. Η πeριγρα...
International Perspectives on the Teaching and Learning of Mathematical Modelling
This chapter describes how novice and experienced mathematics teachers integrate authentic workpl... more This chapter describes how novice and experienced mathematics teachers integrate authentic workplace contexts into mathematics teaching. This goal was inspired by the European MaSciL project and introduced to the teachers in the context of a masters programme in mathematics education. Under an Activity Theory perspective, we use the notions of activity system and boundary crossing to study the process of teachers’ professional learning. In particular, we analyse teachers’ boundary crossings between two activity systems: mathematics teaching and workplace. Results indicate that collaborative task design and reflection made teachers combine elements from the workplace into mathematics teaching. Different ways of linking reality and mathematics teaching were identified in the modelling process in which the students were asked to be engaged.
C’est bien la thematique des ressources qui a assure, depuis leur origine, la continuite de ces j... more C’est bien la thematique des ressources qui a assure, depuis leur origine, la continuite de ces journees, un theme qui a ete approfondi de rencontre en rencontre, et a revele sa grande richesse scientifique. Les ressources pour faire, apprendre, enseigner les mathematiques, un enjeu de recherche majeur. Le choix d’orienter le regard sur les ressources pouvait apparaitre motive, lors des premieres journees de 2006, essentiellement par l’evolution des environnements technologiques (logiciels de calcul formel ou de geometrie dynamique ou ressources en ligne) qui bouleverse les conditions dans lesquelles un professeur concoit et realise son enseignement. C’est en effet pour cette prise en compte de nouveaux outils, complexes et puissants, que se sont developpes plusieurs dispositifs de recherche tres actifs, qui ont donne matiere a des collaborations avec plusieurs IREM, avant de deboucher sur un projet europeen, EdUmatics. C’est aussi pour questionner le foisonnement des ressources sur...
The chapter focuses on the attempts of a group of mathematics teacher educators (MTEs) to support... more The chapter focuses on the attempts of a group of mathematics teacher educators (MTEs) to support teachers in exploiting workplace situations in their mathematics teaching. We report on MTEs’ professional learning in the context of a European-funded project which brought together 18 partners from 13 countries. In Greece, 11 MTEs (academic researchers, teachers and mentors) with different research and teacher education experiences worked with thirteen groups of practising teachers who collaborated to plan, enact and reflect on lessons aligned to the aims of the project. The project provided substantial opportunities for challenging MTEs’ professional knowledge and teacher education practice. The analysis of the discussions during a series of meetings, where design and reflection on professional development activities took place, allowed for identifying and describing MTEs’ concerns and emerging tensions. Using the construct of boundary crossing we traced shifts in MTEs’ movements acr...
Dynamic manipulation of geometrical constructions enabled by a specially designed computational t... more Dynamic manipulation of geometrical constructions enabled by a specially designed computational tool, called variation tool, is studied during the implementation of proportional geometric tasks in the classroom. The analysis combined the use of two theoretical frameworks: instrumental genesis and situated abstraction. The Dynamic Manipulation Schemes (DMS) developed by 13-year-old students based on the use of the variation tool are reported in the paper. It is indicated that situated abstraction may complement instrumental genesis in analysing the links between student’s behaviors and expressions of mathematical ideas within particular computational settings.
The construction of meanings for the notion of angle in 3D geometrical space is studied during th... more The construction of meanings for the notion of angle in 3D geometrical space is studied during the implementation of specially designed geometrical tasks in the classroom. 13-year-old pupils were engaged in exploring the mathematical nature of angles while controlling and measuring the behaviours of geometrical objects in 3D simulations. Pupils worked in pairs using a specially designed computational environment that combines symbolic notation (by means of programming) and dynamic manipulation of graphically represented geometrical objects. The constructionist theoretical perspective of the present study is based on the assumption that programmable geometrical constructions designed to help children abstract the notion of turtle movement in the 3D space provide a useful environment for developing their conceptualizations of geometrical objects, like angles. In the findings it is reported the progressive conceptualization of angle as a dynamic entity interrelated with the recognition...
In this paper we describe the process of designing and implementing inquiry-based tasks relating ... more In this paper we describe the process of designing and implementing inquiry-based tasks relating mathematics and workplace context, through the collaboration of four teachers from different schools. Our focus is on the factors that influence the forms of inquiry integrated in community documentation. A common open task took different forms of inquiry during the implementation depending on factors such as the students’ mathematical abilities, the specificities of the different school contexts and the prerequisite mathematical knowledge. The process of teachers observing each other’s classroom implementations (hetero-observation) became the incentive for subsequent transformations of the shared resources, favoring the shifts from one form of inquiry to another.
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Papers by Giorgos Psycharis