94 research outputs found
Knots with the Lens Space Surgery
No full textIn this paper we construct an infinite family of hyperbolic
(1, 1)–knots with two parameters, and show that some of them admit
exceptional Dehn surgery such as lens space surgery, Seifert surgery, and toroidal surgery. Furthermore, we give simple examples of hyperbolic (1, 1)–knots which admit two toroidal surgeries at distance four such that both toroidal surgeries do not create Klein bottles
IPSE: An Individualized Digital Environment for Strategic Planning at the University Level.
No full textThis study focuses on the design and the implementation of a digital environment aimed at fostering strategic planning competence in problem-solving through individualization features: the Individualized Planned Strategy Environment (IPSE). Within IPSE, students are engaged in a sequence of oriented activities, guiding them in constructing and following a theoretically justified plan for solving a mathematical problem, thus promoting a gradual integration between conceptual and procedural
knowledge. IPSE envisages also meta-level activities, aimed at fostering the
handling of multiple representations toward a unifying and structural view of the subject at stake. We discuss the results of a case study conducted with engineering freshmen at the University of Salerno, involved in problem-solving activities devoted to peer assessment. This led us to identify certain student profiles both theory-and data-driven, according to the students’ progress in using the components of Habermas’ rationality when solving a problem. We highlighted that some students show a full realization of the dynamic nature of Habermas’ model of rationality, where knowing, acting and communicating interact and intertwine
From traditional exams to closed-ended quizzes: an exploration towards an effective assessment in mathematics at university level
No full textThe pandemic emergency has almost forced the transition from face-to-face to remote evaluation. Starting from the results
of the research in Mathematics Education, this exploratory work focuses on how to design effective closed-ended questions
of different types, capable of reliably assessing mathematical learning outcomes, especially in terms of the involved
competencies. We also investigate how to aggregate the questions into Moodle quizzes able to effectively replace the
traditional open written exam. We propose a three-dimensional theoretical model, which takes into account the various
types of questions, expected learning outcomes, and mathematical arguments, to shed light on the problems of validity,
reliability, balance, and correctness of closed-ended quizzes. We discuss the results of the first implementation of the
model within a Linear Algebra course for engineering freshmen
Design e analisi di task per introdurre studenti di scuola secondaria di secondo grado alla ricorsione
No full textDesign of Individualized Digital Activities Fostering Strategic Planning in Linear Algebra
No full textIn this paper we present the design of the IPSE (Individualized Planned Strategy Environment), an online environment aimed at fostering the strategic planning competence for solving problems in linear algebra. The IPSE is composed by connected digital activities that guide university students in designing a plan and executing its phases by means of procedural steps theoretically justified. A peculiar feature of the IPSE is the individualization of teaching/learning, pursued by specific feedback provided within the activities and methodological choices left to the student. Moreover, we report the outcomes of a pilot study carried on with first year engineering students: relying on the notion of aletheic component of rational behavior [10], we classify some different expressions of it arisen in written problem solving processes by students who worked with the IPSE
Dostoevskij mathematician (Part I)
No full textThe image of mathematics in Fyodor Dostoyevsky’s
novels is clearly negative. Notes from Underground
contain several famous and violent pages against
Mathematics, and this criticism is also echoed in other
masterpieces, such as Crime and Punishment and The
Possessed. Dostoevsky explicitly accuses mathematical
determinism of being arrogant and oppressive. On the other
hand, some of his main characters, such as Kirillov in The
Possessed and Ivan in The Brothers Karamazov, seem to
disclose unexpected mathematical sympathies. Here, in
Part I of a two-part article, we discuss Dostoyevsky’s
opinion of mathematics and, more generally, of science. In
Part II we also compare truth and freedom in mathematics
and in the vision of the Russian writer
SOME HYPERBOLIC SPACE FORMS WITH FEW GENERATED FUNDAMENTAL GROUPS
No full textWe construct some hyperbolic hyperelliptic space forms
whose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extended Coxeter group generated by plane reflections and half-turns. Then we describe covering properties and determine the isometry groups of the
constructed manifolds. Furthermore, we give an explicit construction of space form of the second smallest volume nonorientable hyperbolic 3-manifold with one cusp
Promoting formative assessment in mathematics teacher education. An experience of distance teaching
No full textWe discuss a distance teaching-learning approach, developed within two courses for prospective mathematics teachers, exploiting digital technologies to activate formative assessment practices. In particular, we analyse excerpts, from synchronous and asynchronous activities within the courses, to highlight the formative assessment processes that were activated, the feedback provided by prospective teachers to each other and their meta-reflections that testify learning in the domain of teacher education
Promoting formative assessment in mathematics teacher education: An experience of distance teaching
No full textWe discuss a distance teaching-learning approach, developed within two courses for prospective mathematics teachers, exploiting digital technologies to activate formative assessment practices. In particular, we analyse excerpts, from synchronous and asynchronous activities within the courses, to highlight the formative assessment processes that were activated, the feedback provided by prospective teachers to each other and their meta-reflections that testify learning in the domain of teacher education
Promoting a meaningful learning of double integrals through routes of digital tasks
No full textWithin a wider project aimed at innovating the teaching of mathematics for
freshmen, in this study we describe the design and the implementation of two routes of
digital tasks aimed at fostering students’ approach to double integrals. The tasks are
built on a formative assessment frame and classical works on problem solving. They
provide facilitative and response-specific feedback and the possibility to request differ-
ent hints. In this way, students may be guided to the development of well-connected
knowledge, operative and decision-making skills. We investigated the effects of the inter-
action with the digital tasks on the learning of engineering freshmen, by comparing the
behaviours of students who worked with the digital tasks (experimental group, N=19)
and students who did not (control group, N=19). We detected that students in the ex-
perimental group showed more flexibility of thinking and obtained better results in the
final exam than students in the control group. The results confirmed the effectiveness
of the experimental educational path and offered us interesting indications for further
studies
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