Tiziana Pacelli

University of Naples Federico II | UNINA · Department of Mathematics and Applications "R.Caccioppoli"

We describe a didactic cycle involving the Napier bones algorithm, included in a wider research whose aim is to investigate whether and how the use of different kinds of artifacts can affect students' explanations, supporting the understanding of some aspects of the multiplication. We present and discuss some data regarding group and individual tas...

Relationship with mathematics strongly affects teachers’ practices. Specialist mathematics teachers’ positive relationship is often taken for granted, although recent studies suggest that this may not be the case. In this paper we present a narrative research aimed at investigating which events do prospective secondary teachers recognise as crucial...

This paper presents a research design carried out with fourth-grade class children. The study explores both an educational question and some theoretical considerations about the emergence of logical-mathematical modalities of thinking during activities involving collective linguistic handling. The activities are framed in an educational device whos...

Os estudos sobre o conhecimento do professor têm assumido, nos últimos 40 anos, um lugar de destaque e, mais recentemente, surgiram diversas conceitualizações do conhecimento do professor especificamente interessadas em discutir o conhecimento para a prática profissional do professor de matemática. Neste volume da Zetetiké, foi aberto um espaço esp...

In questo lavoro, in accordo con la prospettiva vygotskiana e focalizzando su alcuni aspetti della logica matematica, viene presentata una riflessione derivante da un insieme di ricerche che esplorano le relazioni tra linguaggio e sviluppo di abilità logiche. Si descrive la progettazione/implementazione di un dispositivo educativo, articolato in at...

This study concerns a professional development course designed and implemented for prospective teachers, centred on a teaching method regarding problem-solving activity, namely, the Thinking Classroom. The study is framed in the theory of cultural transposition, a perspective about the encounter with teaching practices from different cultural/schoo...

We start from the assumption that teachers need a deep and broad mathematical knowledge-called Interpretative Knowledge (IK)-that allows them to support students in building their mathematical knowledge from their own reasoning and productions. In the present study, we aimed to ascertain how collective discussions focusing on the interpretation of...

In this work, we examined mathematical knowledge mobilised by mathematics teachers while interpreting students’ answers, which we denote as Interpretative Knowledge (IK). In particular, we analysed the IK of prospective mathematics teachers (PTs), who were students of a Mathematics Education course for the Master’s Degree in Mathematics. In order t...

This paper presents a Vygotskian research device that focuses on collaborative activities based on the manipulation of linguistic objects in a primary school classroom, with 8–9-year-old children. Through social exchanges among the different points of view, the children were engaged in a dynamic process of building and negotiating mathematical mean...

In this chapter, we want to focus on the relationships between language and developmental processes of logical tools in “linguistic-manipulative” activities. A didactic path in a primary school classroom was designed based both on cooperation and meanings negotiation in interactional situations and on social-constructivist theories. The activities...

Relationship with mathematics is a crucial variable in the professional development of pre-service primary teachers: it can largely affect pre-service teachers’ reactions to educational prompts and also their future didactical choices in classroom. Many researches showed that pre-service primary teachers have often developed a negative relationship...

The work described in this paper is framed in a larger study focused on written argumentations produced by university students in tasks regarding graphs, conversions between graphs and their analytic properties and relations among different graphs. Using the functional linguistics framework, we analyse difficulties related to an examination task on...

The relationship with mathematics of future primary teachers is very often built on negative experiences with mathematics as students and characterized by strong negative emotions towards mathematics. This phenomenon is alarming because of its consequences on teachers’ development and practice. Nevertheless, many future primary teachers reveal a de...

Mathematics education is strongly interested in defining “what is necessary for teaching mathematics effectively”. The main directions of research emphasize the cognitive side of the answer to this question, trying to describe what kind of knowledge is needed in order to teach mathematics effectively. Starting from the point that teachers’ affect p...

As researches in mathematics education and also as teacher educators we are strongly interested in facing the question “what is necessary for teaching mathematics effectively”. The main directions of research emphasize the cognitive side of the answer to this question. In our view, attention from a purely cognitive dimension has to shift to a wider...

Una delle questioni di maggior rilievo nella ricerca in educazione ma-tematica riguarda il linguaggio. Il linguaggio, artefatto culturale per eccel-lenza (Vygotskij, 1934), gioca un ruolo fondamentale nei processi di ap-prendimento e nelle pratiche di classe, come ampiamente riconosciuto in letteratura (Sfard, 2001). Una gran parte dei fallimenti d...

In this paper we explore the relationship between language and developmental processes of logical tools through the analysis at different levels of some „linguistic- manipulative‟ activities in a primary school classroom. We believe that this kind of activities can spur in the children a reflection and a change in their language representation. Mat...

We analyze two episodes of a teaching experiment involving children of primary school. The children, handling a procedural language they previously constructed, single out equivalence rules. So they construct the concept of equivalence intuiting a semantic equivalence in the language. We adopt a qualitative approach mainly based on observational an...

Some attempts to establish a link between point-free geometry and the categorical approach to fuzzy set theory is exposed. In fact, it is possible to find functors between the category of fuzzy set as defined by Höhle in [4] and a category whose objects are the pointless ultrametric spaces.

A general approach to fixed point theory is proposed which is related to the notion of fuzzy ordering. This approach extends both the fixed point theorems in metric spaces and the ones in ordered sets.

As stressed in [1] and [12] an interesting question on philosophy of probability is to assign probabilistic valuations to individual phenomenon. In [10] such a question was discussed and a solution was proposed. In this chapter we start from the ideas in [10] to sketch a method to design expert systems, probabilistic in nature. Indeed, we assume th...

In this paper an abstract notion of approximate metric space is proposed by means of an interval-valued distance between regions. Regions are interpreted as pieces of information in a space. The resulting theory supports some promising applications to some topics of fuzzy set theory, rough set theory and clustering.

An effective menu organization is fundamental to obtain usable applications. A common practice to achieve this is to adopt empirical methods in the menu design phase, by requesting a number of intended final users to provide their ideal tasks arrangements. However, to improve the effectiveness of this approach, it is necessary to filter results, by...

In accordance with the ideas of Interval Analy- sis, a notion of interval-valued semimetric space is proposed. Also, the possibility of applying the resulting theory to some chapters of Computer Science is examined.

In accordance with an idea in (8), in this paper w e sketch a method to design expert systems, probabilistic in n ature. Indeed, we assume that the probability that an individual sati sfies a property is the percentage of similar individuals satisfying such a property. In turn, we call "similar" two individual satisfying the same observable prope r...

In this paper we explore the relationship between language and developmental processes of logical tools through the analysis at different levels of some "linguistic-manipulative" activities in a primary school classroom. We believe that this kind of activities can spur in the children a reflection and a change in their language representation. Math...