1,721,251 research outputs found
Roleplaying to develop students’ awareness and robust learning of advanced mathematical concepts
No full textWe present a model for roleplaying (RP) for university students that
is aimed at fostering the interactions of each learner with the teacher
and coursemates, self- and peer-assessment, as well as an awareness
and meaningful learning of mathematics. Specific features of our
model are its focus on metacognition and individualized learning,
based on a careful distribution of the tasks according to the individ-
ual student’s profile. Within our model, the students play, alternately,
the role of the teacher and their own role: firstly they assign problems
to their peers, then they solve problems formulated by their peers,
and, finally, they assess their peers’ problem-solving processes. We
discuss an implementation of the RP within a teaching/learning path
regarding mathematical induction, aimed at promoting robust learn-
ing and use. We analyse the outcomes of a pilot study carried out
with engineering students and identify their common praxeologies
in solving the tasks. Moreover, the effects on students’ attitudes and
learning are highlighted at the linguistic, cognitive, metacognitive
and affective levels
Roleplaying to develop students’ awareness and robust learning of advanced mathematical concepts
No full textWe present a model for roleplaying (RP) for university students that is aimed at fostering the interactions of each learner with the teacher and coursemates, self- and peer-assessment, as well as an awareness and meaningful learning of mathematics. Specific features of our model are its focus on metacognition and individualized learning, based on a careful distribution of the tasks according to the individual student’s profile. Within our model, the students play, alternately, the role of the teacher and their own role: firstly they assign problems to their peers, then they solve problems formulated by their peers, and, finally, they assess their peers’ problem-solving processes. We discuss an implementation of the RP within a teaching/learning path regarding mathematical induction, aimed at promoting robust learning and use. We analyse the outcomes of a pilot study carried out with engineering students and identify their common praxeologies in solving the tasks. Moreover, the effects on students’ attitudes and learning are highlighted at the linguistic, cognitive, metacognitive and affective levels
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
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
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
Fostering Engineering freshmen’s shifts of attention by using Matlab LiveScript for solving mathematical tasks
No full textWe designed an experimental path including a summative assessment phase, where engineering freshmen are involved in solving mathematical tasks by using Matlab LiveScripts. We analyzed the students’ answers to a questionnaire about their perceived impact of the use of Matlab on their way to solve mathematical tasks. The main result is that students show shifts of attention from computations to other aspects of problem solving, moving from an operational to a structural view of mathematics
Platone e la matematica, parte I
No full textEsaminiamo e commentiamo la matematica presente nel pensiero e nell’opera di Platone, nella prospettiva di un laboratorio per docenti e studenti delle scuole superiori
Exceptional surgeries on certain (1,1)-knots
No full textWe determine certain exceptional surgeries on a 3--parametric family of hyperbolic 1--bridge genus one knots ((1,1)-knots, in short). In particular, we show that such knots admit two infinite series of lens space surgeries. Our work is related to a nice paper of Teragaito [16], since we represent his toroidal manifolds as 2--fold coverings of the 3-sphere branched over well--specified links
Studio fenologico delle allergofite urbane in relazione alle allergopatie nella popolazione umana di Macerata.
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
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