1,721,072 research outputs found
USE OF EXAMPLES IN CONJECTURING AND PROVING: AN EXPLORATORY STUDY
No full textIn this paper we report the first part of a study concerning the use of examples in conjecturing and proving, in Elementary Number Theory. The study was carried out on protocols of university students: we analyzed students' behaviours and we seized different uses of examples among the groups with different mathematical background and relationship with mathematics
TOWARDS A COMPREHENSIVE FRAME FOR THE USE OF ALGEBRAIC LANGUAGE IN MATHEMATICAL MODELLING AND PROVING
No full textIn this paper we consider the use of algebraic language in modelling and proving. We will show how a specific adaptation of Habermas' construct of rational behaviour allows to describe and interpret several kinds of students' difficulties and mistakes in a comprehensive way, provides the teacher with useful indications for the teaching of algebraic language and suggests further research developments
Conceptual Change in Group Discussion: An Exploratory Study
No full textIn this contribution, we discuss conceptual change in mathematics, as it takes place during
social interaction in group-work in the classroom. We rely on a socio-cultural perspective,
according to which the learning of mathematics takes place in a social context (Radford, 2006,
2011). We argue that conceptual change, as part of mathematics learning, may be a social act
deeply related to the subjectivities of students involved in group activity. Students’ interactions
are analyzed by means of an integrated frame, encompassing the construct of subjectification
(Radford, 2008), identity (Sfard & Prusak, 2005) and rational behavior (Boero & Morselli,
2009). The analysis shows that, during the group activity, there is a continuous interplay
between social interaction and individual identity; each student, by means of his rationality,
engages in the construction of coherent structures. Conversely, each individual contributes to
the construction of group coherent structures. Thus, a sort of “group-coherence” turns out to be
a necessity in the subjectification process. In both processes, (change at individual level and
construction of a group coherence) communicative rationality plays a key rol
PROVING AS A RATIONAL BEHAVIOUR: HABERMAS' CONSTRUCT OF RATIONALITY AS A COMPREHENSIVE FRAME FOR RESEARCH ON THE TEACHING AND LEARNING OF PROOF
No full textIn this paper we draw from Habermas' construct of rational behaviour a construct for rationality in proving that we propose as suitable to investigate the teaching and learning of proof and generate new research developments. At first, we discuss our conception of the proving process, where cognitive and cultural aspects are shown to play a crucial role, and we present our adaptation of Habermas' construct as a way of taking into account both cognitive and cultural aspects. The adapted construct is shown to be useful in the discussion of some examples at tertiary level; finally, drawing from the analysis of the examples, we indicate some research questions ( formulated in terms of the theoretical construct) that we feel worth to be explored
THE USE OF ALGEBRAIC LANGUAGE IN MATHEMATICAL MODELLING AND PROVING IN THE PERSPECTIVE OF HABERMAS' THEORY OF RATIONALITY
No full textIn this paper we consider the use of algebraic language in modelling and proving. We will show how a specific model of rational behaviour derived from Habermas' elaboration allows to describe and interpret several kinds of students' difficulties and mistakes in a comprehensive way, provides the teacher with useful indications for the teaching of algebraic language and suggests further research developments
MATHS AVOIDANCE AND THE CHOICE OF UNIVERSITY
No full textIn the last decade, in Europe, there has been a constant decrease of enrolment in university degrees with scientific orientation. In Italy, those degrees are characterised by at least one compulsory mathematics course. Our hypothesis is that a negative attitude towards mathematics (i.e. a negative emotional disposition towards mathematics) plays a role in the refusal to enrol in university scientific courses. After presenting arguments to maintain the existence of a link between attitude and university choice, it seems crucial from researchers' point of view to understand which kind of experiences with mathematics characterise a negative emotional dispositions towards the discipline. With these aims a study has been carried out within a national Project, using a purposefully), designed questionnaire. namely QCM (Questionnaire on the Characterization of Mathematics). This report discusses the main features of the QCM, describes some results of that study and suggests some implications for research on attitude
Accessing knowledge through narrative context
No full textIn this paper we discuss how narrative may contribute to create meaningful learning contexts. Starting from a socio-constructivist and situated learning perspective, we acknowledge the crucial role of context in accessing knowledge. Then we point out the potential of narrative in education and discuss the positive role it can play in the creation of meaningful learning contexts. To this end, we focus on different examples of narrative contexts within technology-enhanced learning environments, drawn from the literature. We analyze what kind of contexts raise from different ways to set up narrative activities. Our study points out that narrative can be a powerful tool for the creation of a variety of contexts Suitable for different learning situations, by stimulating learners' direct involvement and offering a concrete starting point for reflection
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
Indoor residual clutter characterization for UWB sensor radar networks
No full textSensor radar networks (SRNs) employing ultra-wideband (UWB) signals are a prominent solution for accurate localization and tracking in indoor environments. However, tracking device-free targets via SRNs is challenging, especially in environments heavily affected by clutter. Clutter characterization is vital to derive performance benchmarks as well as to design inference algorithms for SRNs. Examples of clutter statistical characterization have been provided in the literature for conventional SRNs employing narrowband signals in outdoor scenarios. However, considerably less effort has been devoted for SRNs employing UWB signals in indoor environments. This paper proposes an approach to characterize the clutter-plus-noise component after mitigation filtering in UWB SRNs. In particular, the statistical properties of the residual clutter-plus-noise are derived by applying statistical tests on measurements gathered in an indoor environment via UWB sensor radar networks
From Anecdotal Exchange to Critical Dialogue in Kindergarten: A Case Study in Italy Based on Habermas’ Construct of Rational Behavior
No full textThe objective of this study was to investigate preschool-aged children’s rational behavior and dialogical critical thinking and analyze different types of dialogical exchange about mathematics among 5-years-old children. Based on a two-part theoretical framework, one referred to Habermas’ construct of rational behavior and the second to Daniel’s model about typology of dialogical exchange among peers, the study shows that a dialogue containing all three components of the rational behavior can be reached by children just when the dialogue is a critical dialogical type. This happens when children show spontaneous and complete justifications, with a critic approach and this allows children to reach a modification of the initial idea as a common solution. Considerations about teacher’s role are presented
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