2,249 research outputs found
Teaching mathematics in today's society: Didactic paradigms, narratives and citizenship
No full textWhat 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
Evolution of Didacticians’ meta-didactical Praxeologies and Documentation Work
No full textThis 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
Maths in the time of social media: conceptualizing the Internet phenomenon of mathematical memes
No full textMathematical memes are an Internet phenomenon with an epistemic potential noteworthy for the teaching and learning of mathematics. The aim of this paper is to conceptualize this phenomenon on an empirical base, elucidating its educational potential. To pursue this goal, a two-year ethnographic research study has been conducted in a selection of social media communities that exchange mathematical memes. In the paper, a twofold theoretical lens is used to investigate the phenomenon from a memetic perspective focused on the general characteristics of Internet memes, and from a cultural perspective considering the Web 2.0 environment. Analysis tools derived from the memetic and cultural theoretical background are applied to an instrumental case study, to reconstruct how mathematical memes activate the interaction among members of an online community. The investigation elicits key characteristics of the phenomenon, provides grounds to conceptualize mathematical memes as hybrid representations of mathematical statements, and sheds light on the traits of the epistemic culture they establish in the community
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
Stories of devoted university students: the mathematical experience as a form of ascesis
No full textDrawing 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
Meta-Didactical Transposition: A Theoretical Model for Teacher Education Programmes
No full textWe propose a new model for framing teacher education projects that takes both the research and the institutional dimensions into account. The model, which we call Meta-didactical Transposition, is based on Chevallard’s anthropo- logical theory and is complemented by relevant elements that focus on the specificity of both researchers’ and teachers’ roles, while enabling a description of the evolution of their praxeologies over time. The model is illustrated with examples from differ- ent Italian projects, and it is discussed in light of current major research studies in mathematics teacher education
Riflessioni su funzioni e variabili
No full textPresentiamo un progetto di studio sui modi con cui gli studenti concepiscono e trattano variabili e funzioni, in attività a livelli diversi di insegnamento. Il nostro progetto di ricerca si basa su un approccio trasversale, inteso come in tempi scolastici diversi e in contesti disciplinari diversi. L'obiettivo didattico consiste nell'utilizzare situazioni problematiche atte a favorire la costruzione di significati per variabili e funzioni, in cui entrino sia componenti locali che globali
Thinking inside the post: Investigating the didactic use of mathematical Internet memes
No full textWe venture in the almost unexplored field of mathematical Internet memes, with the aims of investigating their didactical features in a teaching and learning setting. The work is framed within the research field studying the links between emotions and mathematical
thinking and takes off with a schematization of the meanings carried by a meme, formulated through an a-priori analysis of spontaneous web productions and results of an exploratory experiment. The analysis is then compared to the data collected in a teaching experiment
conducted at high school level. Results sustain the conjectured meanings structure and elicit evidence of students’ emotions and of their role in the learning process initiated by the interaction with memes
Un dialogo fra analisi e algebra
No full textInvertibilita' globale di funzioni. Si puo' estendere il teorema di Cramer alle funzioni polinomiali? Non esistenza di prodotti commutativi in dimensione >2
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