1,720,970 research outputs found
Representations and invariants of links in lens spaces
No full textWe analyze different representations of knots and links in lens spaces, as disk diagrams, grid diagrams, mixed diagrams;
together with the associated moves describing the knot/link equivalence.
Using such representations we study some invariants of these type of knots/links, as fundamental group of the complement,
Alexander polynomial, twisted Alexander polynomial, HOMFLY-PT polynomial and lifting in the 3-sphere.
Some of these results are previously unpublished
TEACHING MATHEMATICS IN TIMES OF CRISIS. A CASE STUDY ABOUT DISTANCE LEARNING AT ALMA MATER STUDIORUM - UNIVERSITÀ DI BOLOGNA
No full textIn this article we analyze the strengths and weaknesses of mathematics teaching through Distance Learning in three mathematics courses of the University of Bologna aimed at students of Mathematics, Educational Sciences and Engineering. We interviewed the teachers and invited the students to fill in a questionnaire we wrote. We also compared the final marks of the same three courses in the academic years 2018-2019 (traditional classroom teaching) and 2019-2020 (Distance Learning). Finally, we compared the teacher evaluation questionnaires that the students fill out during the year, always in the two cases in question.
Distance Learning brings greater transparency in learning processes than in the classroom. The teachers recognize that they have dedicated more work to preparing the lessons that they can no longer "improvise" on the blackboard. The relationship with formalism also changes, which can no longer be so exasperated and which must be dosed to correspond to different levels of attention. In fact, the students probably have less attention even if they exercise it in greater numbers than in the classroom.
Teachers perception about students is of a greater and more widespread involvement, with more students asking questions and participating (especially among those in some sense weak). In the lessons in which participation tools were offered (chat), there was a more intense and prolonged dialogue over time, even beyond the official lesson time. Conversely, lessons that are totally focused on presentations are more sterile and less profitable: in the face of a top-down approach, students tend to isolate themselves and be passive. An engagement-centred approach instead leads to their unusual participation.
The students for their part declare that they felt more comfortable in a 1-to-1 relationship and that they were more involved and pushed to an active job: distance learning has for some reason increased their sense of responsibility (even if this could be the result of the climate of crisis due to COVID19 and the social distancing that ensued). This has an objective counterpart in the final marks, significantly greater than the previous year.
In the three courses there were cases of students who got involved by proposing exercises and mathematical reflections to the teacher (something particularly exceptional especially in the course of Education), as if the remote context had pushed them to be more involved. Our conjecture is that there is group pressure in the classroom that hinders the expression of some "categories" of students.
Even if we are aware that the results of our investigation cannot be automatically extended to any academic context (not even within the University of Bologna alone), we believe that they can contribute to a reflection on the academic teaching of mathematics both in the remote and in the in the classroom
On the complexity of non-orientable Seifert fibre spaces
Full text linkIn this paper we deal with Seifert bre spaces, which are compact 3-manifolds admitting a foliation by circles. We give a combinatorial
description for these manifolds in all the possible cases: orientable, non-orientable, closed, with boundary. Moreover, we compute a potentially sharp upper bound for their complexity in terms of the invariants of the combinatorial description, extending to the non-orientable case results by Fominykh and Wiest for the orientable case with boundary and by Martelli and Petronio for the closed orientable case. Our upper bound is indeed sharp for all Seifert bre spaces contained in the census of non-orientable closed 3-manifolds classied with respect to
complexity
PLS per la formazione di futuri docenti e docenti in servizio: le esperienze del Dipartimento di Matematica dell'Università di Bologna
No full textVerranno presentate le esperienze di formazione del PLS Matematica di Bologna ponendo l’attenzione su due aspetti: l’interazione tra futuri docenti e docenti
in servizio e le tematiche proposte. La presenza di un curriculum didattico nella Laurea Magistrale in Matematica, appositamente progettato per la formazione dei futuri insegnanti, crea occasioni di collaborazione tra studenti e docenti, sotto forma di tirocinio o tesi, svolti presso scuole secondarie. Queste occasioni curriculari negli ultimi anni sono state affiancate dalla partecipazione attiva degli studenti del curriculum didattico alle iniziative PLS di formazione insegnanti: durante i corsi intensivi (16 ore concentrate in un week end) o i laboratori tradizionali (10 ore di coprogettazione e successiva realizzazione nelle scuole) è stato possibile instaurare un’interessante dialettica tra futuri docenti e docenti in servizio su tematiche disciplinari e nodi didattici. Le tematiche partono sempre dalle richieste provenienti dagli insegnanti stessi: è interessante quindi riflettere su quali esse siano, perché evidenzia i bisogni e gli interessi dei docenti. Nell’ambito disciplinare la richiesta più forte è relativa alla Probabilità (su cui sono stati realizzati due corsi di formazione). Molto interesse c’è anche per le tematiche interdisciplinari, in particolare legate alla Statistica e alla Fisica, su cui sono stati proposti diversi corsi in collaborazione con altre aree PLS. Le tematiche dei corsi di formazione del 2020 sono la comunicazione della matematica e la presentazione, in chiave storico-didattica, di tematiche di ricerca attuali per combattere nei giovani il pregiudizio che la Matematica sia una disciplina in cui non c’è più nulla da scoprire
TRAINING SECONDARY SCHOOL TEACHERS TO DEAL WITH INTERDISCIPLINARITY BETWEEN PHYSICS AND MATHEMATICS: THE CASE OF THE BLACK BODY MODEL
Full text linkBoth the most recent EU trends and the current Italian reform advocate for new interdisciplinary
approaches that integrate the STEM disciplines. In this talk we report the results of a research concerning
the "interdisciplinary skills" necessary for secondary school teachers to implement didactical activities that
authentically integrate mathematics and physics. The empirical results that will support our argumentations
have been collected in three experimentations: a pilot study with 5 mathematics and physics studentteachers
and two experiences in in-service training courses (44 teachers). In this work we consider the case
of the blackbody model, since mathematics is particularly relevant, the logic underlying the process of
modeling is complex but, at the same time, the search for "oversimplification" usually leads authors of
textbooks to reproduce rituals that mortify any intellectually satisfaction (Viennot, 2006). We firstly carried
out an educational reconstruction (Duit et al., 2012) of the historical path that led Planck to “open the
secret door” of the new quantum world, starting from a mathematical conjecture. Then, we developed a
tutorial, where teams of teachers are asked to fill-in some missing steps in the reconstruction of Planck’s
modeling and to recognize where and how discreteness was introduced in physics to interpret the modeling
process of interaction between matter and radiation (as an exchange of discrete packets of energy). In this
paper we focus on teachers’ difficulties with the different uses of mathematics in modeling blackbody, in
particular in “zooming in and out” and keeping control on the whole process
Continuity and rupture between argumentation and proof in historical texts and physics textbooks on parabolic motion
Full text linkInternational audienceIn this paper, we analyze different presentations in a historical text by Galilei and a textbook for high school of the parabolic motion of a projectile with a lens developed within Mathematics education research on argumentation and proof (cognitive unity; Mariotti et al., 1997; Pedemonte, 2005). The analysis highlights possibilities and problematic issues, with particular attention to the aspects related to continuity and rupture between argumentation and proof in textbooks and the different interdisciplinary relationships between mathematics and physics mirrored by historical sources and textbooks. We discuss how a comparison between them can be exploited to develop a discourse about interdisciplinary that can enlarge the view of the relationship between the two disciplines and didactical implications that can be inferred from this comparison
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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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