1,721,112 research outputs found
Teaching mathematics in today's society: Didactic paradigms, narratives and citizenship
Full text linkWhat is the paradigmatic direction of teaching and learning mathematics? According to Yves Chevallard, father of the anthropological theory of the didactic, the current paradigm is characterized by an obsolescent form of monumentalism. But is a new paradigm possibly on the rise? And what is the role of powerful organizations such as the OECD? We reflect on these and related questions in connection to issues of citizenship, democracy, inclusion and standardization
Inquiry activities are not for everyone: teachers’ beliefs and professional development
No full textThis study investigates teachers’ beliefs about the inquiry-based learning approach in mathematics. In particular, as the first research problem, it addresses teachers’ beliefs about the appropriateness of inquiry activities for all students, after three years of attendance in a professional development programme, focused on inquiry. As a second research problem, it studies the evolution of teachers’ beliefs and practices, during their fourth year of attendance of the programme. The results show that, at the beginning of the fourth year, the teachers, despite thinking that inquiry activities in mathematics have several valuable aspects, held the belief that they are not appropriate for all the students, but only for the high-achieving ones. The two case studies, analysed to address the second problem, refer to two teachers with different outcomes of their developmental paths. During the fourth year, in which the teachers have been invited to experiment with inquiry activities in their whole classes, one of them accepted the challenge and, as a consequence, had the opportunity to change both her practices and her beliefs. The second teacher, instead, continued to propose inquiry activities only to her high-achieving students and, consequently, showed no signs of change, either in her practices, nor in her beliefs
Evolution of Didacticians’ meta-didactical Praxeologies and Documentation Work
Full text linkThis study is aimed to understand the connections between didacticians’ meta-didactical praxeologies for the design and implementation of a teacher professional development program and their documentation work for the program itself. Didacticians are mathematics education researchers with the role of teacher educators. Data presents a case study, in which two didacticians (the authors) generate documents for the work with seventeen in-service mathematics teachers working at the lower secondary level, on inquiry mathematics tasks. The results reveal relationships, not yet fully addressed in research, between the intertwining evolution processes of the didacticians’ meta-didactical praxeologies and their documentation work, nurtured by the collaboration with the teachers. The whole process is led by the evolving goal of the professional development program, from the promotion of the classroom implementation of inquiry mathematics tasks to the broader goal of building an inquiry community with the teachers. This study could contribute to the introduction of an interpretative model for the didacticians’ work for the design and implementation of a teacher professional development program, based on the combination of Meta-Didactical Transposition and Documentational Approach to Didactics frameworks
Italian Research in Mathematics Education 2000-2003
No full textpubblicazione curata per l'ICME 10 del luglio 200
Time(s) in the Didactics of Mathematics: A Methodological Challenge
No full textWhen the focus of a research study is on the processes during classroom activity, time plays an essential function. It is trivial to observe that -every experiment has to match the time of the school (periods, weekly schedule, holidays); -the processes - either individual or social - develop over time; -observation is carried out over time. The above are three instances of ‘physical time’, the linear sequence of moments measured by the clock . This physical time, which the observer can read on his clock, is in recent videopapers emphasised by the timeline where different media such as video, text, graphics and audio files are synchronised. Yet, Varela himself calls our attention on the existence of an ‘inner time’, that gives rise to human temporality, centred on the present and manifesting as a threefold unity of the just-past and the about-to-occur. This inner time is mostly individual and unconscious. However its features may be inferred from external traces (linguistic expressions, gestures, metaphors). Moreover, it may be partially shaped from outside (e. g. by the teacher), so that the learner becomes conscious of the possibility of moulding it in problem solving. The main purpose of this paper is to show that:1)both kinds of time are relevant in the research in Mathematics Education, when the focus is on the processes of teaching and learning mathematics;2)a further finer specification of both is needed, that requires the introduction of several theoretical constructs related to human temporality and that introduces a lot of methodological problems concerning the relationships between them
Stories of devoted university students: the mathematical experience as a form of ascesis
Full text linkDrawing on autobiographical essays written by master's students in mathematics preparing to become teachers, we investigate what mathematical identity these students articulate and how. By means of a discursive thematic analysis centered on the notion of ascesis, we show that the participants' identity revolves around a characterization of mathematics as a challenging, useful, and comforting activity or knowledge, which is however regarded negatively by others. Indeed, mathematics is described as a uniquely challenging activity which requires an increasingly demanding self-discipline. Moreover, mathematics is depicted as a variously useful form of knowledge which is additionally capable to offer comfort to those who engage with it. However, the participants often remark that other people regard mathematics negatively, a fact explained by stressing others' inability or unwillingness to understand or appreciate mathematics' inherent positive features. This sets the boundary of an ideal club of math enthusiasts whose elitist membership is regulated in terms of acceptance or refusal of its constitutive values. Belonging to the club as well as proselytizing in order to recruit new members appears to be central to the participants' mathematical identity
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Meta-Didactical Transposition.2: The Evolution of a Framework to Analyse Teachers’ Collaborative Work with Researchers in Technological Settings
No full textMeta-Didactical Transposition is a framework created to interpret and analyse the interactions between teachers and researchers in the general context of teachers’ professional development. The use of this framework in specific contexts (not only professional development face-to-face courses, but also within MOOCs or collaborative research projects) triggered the need to develop the main ideas of the framework, intertwining them with ideas from other theoretical frameworks that analyse interactions between actors in education. In this chapter we present the evolution of the Meta-Didactical Transposition framework, focusing, in particular, on the integration of new theoretical elements with the aim to deepen the analysis and interpretation of the so-called phenomenon of “internalisation”, which allows teachers and researchers to introduce external components to their own praxeologies. Specifically, we show, by means of three examples in which digital technologies play complementary roles, how this theoretical integration has supported the investigation of the internalisation process from different perspectives, that is, “the where”, “the why” and “the how”
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