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Il presente contributo nasce da una ricerca/azione attualmente in corso relativa alla motivazione degli studenti coinvolti nell’iniziativa fiorente dei ‘Licei Matematici’ (‘LM’) in Italia. L’argomento che qui si vuole trattare riguarda una pratica d’insegnamento che rientra tra le forme del Collaborative Teaching. Nello specifico, si discute un esempio di co-planning tra docenti di matematica ed altre discipline di un Liceo Classico di Palermo, all’interno di un percorso interdisciplinare di una classe prima del LM. Sarà descritta tale forma di collaborazione in riferimento al modulo di “Matematica e Storia”, esplicitando come questa sia stata una sfida di insegnamento/apprendimento per i docenti coinvolti ma soprattutto per gli studenti.

Il contributo, evidenziando l’attuale proble- matica didattica relativa alla multiculturalità nel panorama scolastico nazionale, discute alcuni aspetti chiave della cultura cinese, uti- li ad interpretare il perché di particolari competenze algebriche, evidenziate negli allievi di area confuciana dagli insegnanti di tutti i gradi scolastici, coerenti con le valuta- zioni internazionali PISA e TIMMS. Con questo scopo, il lavoro propone nello specifico una riflessione epistemologica del rapporto tra lingua scritta cinese e avvia- mento informale al pensiero algebrico-rela- zionale e discute i dati sperimentali (di tipo implicativo) di una ricerca-azione condotta in classi di Scuola Primaria con un’alta inci- denza di studenti cinesi, in accordo con la Teoria delle Situazioni Didattiche di G. Brousseau. The paper, highlighting the didactical pro- blematic of multiculturalism in the national educational landscape, discusses some key aspects of Chinese culture. These should be useful to interpret the good algebraic skills highlighted by teachers in Confucian Area students of all school levels, consistent with the PISA and TIMSS feedback. With this purpose, the contribution specifi- cally proposes an epistemological treatise on the relationship between Chinese writ- ten language and the informal introduction to algebraic-relational thinking. It also di- scusses some experimental data (implicati- ve) of a research conducted in Primary School with a high incidence of Chinese stu- dents, with the use of the Theory of Didactic Situation of G. Brousseau, as framework.

Il contributo, evidenziando la problematica didattica relativa alla multiculturalità nel panorama scolastico nazionale, discute alcuni aspetti chiave della cultura cinese. Con l’obiettivo di analizzare il perché di particolari competenze algebriche, evidenziate negli allievi cinesi dagli insegnanti di tutti i gradi scolastici, coerenti con le valutazioni internazionali PISA TIMMS per l’area confuciana, si propone una riflessione teorica del rapporto lingua scritta cinese – approccio informale al pensiero algebrico e, in un’ottica di una futura formazione insegnanti secondo approcci di tipo multiculturale, si accenna alle ricerche innovative condotte in Italia sulla trasposizione culturale di artefatti provenienti dalla cultura cinese, utili ad un avviamento precoce al pensiero algebrico-relazionale.

La nostra ricerca vuole mostrare come lo studio di approcci sviluppati in diversi contesti culturali può essere importante per riflettere sulle nostre pratiche didattiche e per progettare nuove sperimentazioni nelle classi. In particolare abbiamo studiato le rappresentazioni grafiche usate per descrivere e risolvere problemi additivi nella scuola primaria in Russia e Cina. In questo articolo introdurremo l’idea di trasposizione culturale che sarà anche esemplificata attraverso la descrizione e analisi di due percorsi didattici realizzati in una II e in una V primaria italiane.

Questionnaires are perhaps the most widely used instruments to assess conceptual learning in physics as well as in mathematics. In the field of physics and mathematics education research it is surely interesting to be able to use a questionnaire as a “diagnostic instrument,” i.e., to know details about relationships among student answers to the different questions. In recent years several research works focused on this goal by using different quantitative methodologies, like Factor, Model and Cluster Analyses. However, very few research works deepened the theoretical aspects of the Cluster Analysis. In this contribution, we discuss two Cluster Analysis methods with respect to this issue. By means of an example of application on real data, groups of students homogeneous with respect to the ways students answer a questionnaire are identified. Each of these groups is identified without any prior knowledge of what form those groups would take (unsupervised classification) and can be characterised by means of the answering strategies the students deploy when facing the questionnaire. Each characterisation allowed us to infer the students’ lines of reasoning. Finally, we show to what extent the two clustering methods are coherent with each other.

Two 20-h modelling-based workshops focused on the explanation of ther- mally activated phenomena were held at the University of Palermo, Italy, during the Academic Year 2014–2015. One of them was conducted by applying an inquiry-based approach, while the other, still based on laboratory and modelling activities, was not focused on inquiry. Seventy-two students belonging to the Undergraduate Program for Chemical Engineering attended the two workshops. The related content was focused on an à la Feynman unifying approach to thermally activated phenomena. Question- naires were administered to the students of both groups, before and post instruction. Responses were analysed using k-means cluster analysis and students’ inferred lines of reasoning about the description and explanation of phenomena were studied in both groups. We find that both workshops can be considered effective in improving student’s reasoning skills. However, the inquiry-based approach revealed to be more effective than the traditional one in helping students to build mechanisms of func- tioning and explicative models and to identify common aspects in apparently different phenomena.

Two science teaching workshops for students of the elementary teacher education degree course at the University of Palermo, Italy are discussed, one based on inquiry-based methods and the other on "traditional" teaching methods. A questionnaire aimed to understand the teaching styles preferred by students, their reasons for learning/teaching science, and their beliefs about the difficulties a teacher faces when planning and trying out science teaching activities in the class were completed by the students before the first workshop, at its end, and the end of the second workshop. The answers given by the students were studied using cluster analysis methods. The results of the analysis of answers given to initial and intermediate questionnaires indicate that the students recognize the importance of teaching scientific subjects in elementary school. However, the self-perception of their abilities to effectively teach science is negative, both before and after attending the "traditional" type teaching workshop. After doing the inquiry-based teaching workshop and holding several days of a science fair, most of the students' negative beliefs have changed into positive ones. A better general understanding of the fundamental role played by the teacher in encouraging the natural curiosity of children and offering scientific activities based on everyday life experiences was observed.

The problem of taking a data set and separating it into subgroups, where the members of each subgroup are more similar to each other than they are to members outside the subgroup, has been extensively studied in science and mathematics education research. Student responses to written questions and multiple-choice tests have been characterised and studied using several qualitative and/or quantitative analysis methods. However, there are inherent difficulties in the categorisation of student responses in the case of open-ended questionnaires. Very often, researcher bias means that the categories picked out tend to find the groups of students that the researcher is seeking out. In this paper, we discuss an example of application of a quantitative, non-hierarchical analysis method to interpret the answers given by 118 Tenth Grade students in Palermo (Italy), to six open-ended questions about algebraic thinking. We show that the use of non-hierarchical analysis allows us to interpret the reasoning of students solving different mathematical problems using Algebra, and to separate them into different groups, that can be recognised and characterised by common traits in their answers, without any prior knowledge on the part of the researcher of what form those groups would take (unbiased classification). Keywords: algebraic thinking; cluster analysis; mathematics education; quantitative analysis

Noise-induced phenomena characterise the nonlinear relaxation of nonequilibrium physical systems towards equilibrium states. Often, this relaxation process proceeds through metastable states and the noise can give rise to resonant phenomena with an enhancement of lifetime of these states or some coherent state of the condensed matter system considered. In this paper three noise induced phenomena, namely the noise enhanced stability, the stochastic resonant activation and the noise-induced coherence of electron spin, are reviewed in the nonlinear relaxation dynamics of three different systems of condensed matter: (i) a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian, Levy distributed, noise sources; (ii) a graphene-based Josephson junction subject to thermal fluctuations; (iii) electrons in a n-type GaAs crystal driven by a fluctuating electric field. In the first system, we focus on the switching events from the superconducting metastable state to the resistive state, by solving the perturbed stochastic sine-Gordon equation. Nonmonotonic behaviours of the mean switching time versus the noise intensity, frequency of the external driving, and length of the junction are obtained. Moreover, the influence of the noise induced solitons on the mean switching time behaviour is shown. In the second system, noise induced phenomena are observed, such as noise enhanced stability (NES) and stochastic resonant activation (SRA). In the third system, the spin polarised transport in GaAs is explored in two different scenarios, i.e. in the presence of Gaussian correlated fluctuations or symmetric dichotomous noise. Numerical results indicate an increase of the electron spin lifetime by rising the strength of the random fluctuating component. Furthermore, our findings for the electron spin depolarization time as a function of the noise correlation time point out (i) a non-monotonic behaviour with a maximum in the case of Gaussian correlated fluctuations, (ii) an increase up to a plateau in the case of dichotomous noise. The noise enhances the coherence of the spin relaxation process.

Background:Research in Science Education has shown that often students need to learn how to identify differences and similarities between descriptive and explicative models. The development and use of explicative skills in the field of thermal science has always been a difficult objective to reach. A way to develop analogical reasoning is to use in Science Education unifying conceptual frameworks.Material and methods:A questionnaire containing six open-ended questions on thermally activated phenomena was administered to the students before instruction. A second one, similar but focused on different physical content was administered after instruction. Responses were analysed using k-means Cluster Analysis and students’ inferred lines of reasoning about the analysed phenomena were studied.Results:The pre-instruction results show that the students reasoning lines were mainly oriented to the use of lines of reasoning based on the use of memory of past studies and on an application of mathematics without a search for a proper mechanism of functioning. After instruction, these lines of reasoning seem to have clearly evolved to explicative ones.Conclusions:Students reasoning lines seem to have clearly evolved to explicative ones and it is reasonable to think that the Feynman Unifying Approach has favoured this change.

The problem of taking a set of data and separating it into subgroups where the elements of each subgroup are more similar to each other than they are to elements not in the subgroup has been extensively studied through the statistical method of Cluster Analysis . This method can be conveniently used to separate students into groups that can be recognized and characterized by common traits in their answers, without any prior knowledge of what form those groups would take (unsupervised classification). In the last years many studies examined the consistency of students’ answers in a variety of situations. Some of these papers have tried to develop more detailed models of the consistency of students’ reasoning, or to subdivide a sample of students into intellectually similar subgroups by using Cluster Analysis techniques. In this paper we start from a description of the data coding needed in Cluster Analysis, in order to discuss the meanings and the limits of the interpretation of quantitative results. Then a method commonly used in Cluster Analysis is described and the variables and parameters involved are outlined and criticized. Section 3 deals with the application of this method to the analysis of data from an open-ended questionnaire administered to a sample of university students, and discusses the quantitative results. Finally, some considerations about the relevance of this method in Physics Education Research are drawn.

The research on the intercultural phenomenon in Italy increased with the growing phenomenon of migration, highlighting the problem of cultural diversity and social policies. The school has, in this process, a key role. The goal of a good educational project is to understand that the intercultural requires continual reference to the concrete experiences of the people. Theoretical assumptions of our project are the concepts of “interaction”, “empathy”, “decentralization” and “cognitive transitivity" (Nanni 1998). In this theoretical direction, we present an experimental multidisciplinary mathematical laboratory where students and teachers can understand that a discipline that seems static and rigid is the result of an evolution involving different peoples, with very different, often conflicting, traditions and religions. Multi-ethnicity, which increasingly characterizes our society, is surely an important opportunity of growth and enrichment for people.

The problem of taking a set of data and separating it into subgroups where the ele- ments of each subgroup are more similar to each other than they are to elements not in the subgroup has been extensively studied through the statistical method of cluster analysis. In this paper we want to discuss the application of this method to the field of education: particularly, we want to present the use of cluster analysis to separate students into groups that can be recognized and characterized by common traits in their answers to a questionnaire, without any prior knowledge of what form those groups would take (unsupervised classification). We start from a detailed study of the data processing needed by cluster analysis. Then two methods commonly used in cluster analysis are before described only from a theoretical point a view and after in the Section 4 through an example of application to data coming from an open-ended questionnaire administered to a sample of university students. In particular we de- scribe and criticize the variables and parameters used to show the results of the clus- ter analysis methods.

In this contribution we discuss the application of a quantitative, non-hierarchical clustering method to make sense of the answers that 120 engineering undergraduates students at the University of Palermo, Italy, gave to four open-ended questions on the meaning of the modeling processes in Science. We will show that the use of non-hierarchical analysis allows us to easily separate students into groups that can be recognized and characterized by common traits in students’ answers without any prior knowledge on the part of the researcher of what form those groups would take (unbiased classification).

Il processo che porta alla formazione della conoscenza musicale è tutt’altro che semplice e consta di diversi elementi, apparentemente lontani tra loro. In primo luogo è opportuno evidenziare l’esistenza di una componente primitiva nell’ascolto della musica che lega sensazioni e reazioni emotive a specifiche gamme timbriche e tonali

Il presente contributo, attraverso delle riflessioni teorico/sperimentali, prova a mettere in luce atteggiamenti, soddisfazioni, aspettative e paure di bambini di Scuola Primaria e dell'Infanzia relative al loro mondo di vedere la Scuola. Attraverso le loro verbalizzazioni spontanee gli autori hanno cercato di definire un possibile framework teorico capace di teorizzare, seppur in una prima analisi, lo scollamento vissuto in alcuni casi dai bambini intervistati tra le attività di gioco della Scuola dell'infanzia e quelle più formalizzate della Scuola Primaria.

The complexity of electron dynamics in low-doped n-type InP crystals operating under fluctuating electric fields is deeply explored and discussed. In this study, we employ a multi-particle Monte Carlo approach to simulate the non-linear transport of electrons inside the semiconductor bulk. All possible scattering events of hot electrons in the medium, the main details of the band structure, as well as the heating effects, are taken into account. The results presented in this study derive from numerical simulations of the electron dynamical response to the application of a sub-Thz electric field, fluctuating for the superimposition of an external source of Gaussian correlated noise. The electronic noise features are statistically investigated by computing the correlation function of the velocity fluctuations, its spectral density and the variance, i.e. the total noise power, for different values of amplitude and frequency of the driving field. Our results show the presence of a cooperative non-linear behavior of electrons, whose dynamics is strongly affected by the field fluctuations. Moreover, the electrons self-organize among different valleys, giving rise to the reduction of the intrinsic noise. This counterintuitive effect critically depends on the relationship among the characteristic times of the external fluctuations and the temporal scales of complex phenomena involved in the electron dynamical response. In particular, the correlation time of the electric field fluctuations appears to be crucial both for the noise reduction effect and the appearance of an anomalous diffusion effect.

The paper, examining the increasing presence of different culture students in Italy, discusses the didactical problematic of multiculturalism at School. In particular a possible “comparison” between East (China, Korea and Japan) and West mathematical epistemology is presented through a historical and linguistic cultural approaches. Some evidences of analogies and differences between the cognitive styles of Chinese and Italian learners in mathematics are presented as examples to show the complexity of teaching/learning mathematics in multicultural classroom

his paper describes a quantitative method to analyse an open- ended questionnaire. Student responses to a specially designed written questionnaire are quantitatively analysed by not hierarchical clustering called k-means method. Through this we can characterise behaviour students with respect their expertise to formulate explanations for phenomena or processes and/or use a given model in the different context. The physics topic is about the Boltzmann Factor, which allows the students to have a unifying view of different phenomena in different contexts

The Math Teaching at School means to reflect on the pedagogical and didactical traditions that are present in the classroom didactical practice; cultural references emerging since the first years of the kindergarden. This work claims to discuss a possible epistemic reflection on our way of working in School through a possible comparison with a didactic setting very different from ours, the Chinese one. We present the practice of variation, that can be found in textbooks as a significant methodology for the teaching/learning of the mathematical thought at Kindergarten and Primary School.

This paper describes a method aimed at pointing out the quality of the mental models undergraduate engineering students deploy when asked to create explanations for phenomena or processes and/or use a given model in the same context. Student responses to a specially designed written questionnaire are quantitatively analyzed using researcher-generated categories of reasoning, based on the physics education research literature on student understanding of the relevant physics content. The use of statistical implicative analysis tools allows us to successfully identify clusters of students with respect to the similarity to the reasoning categories, defined as ``practical or everyday,'' ``descriptive,'' or ``explicative.'' Through the use of similarity and implication indexes our method also enables us to study the consistency in students' deployment of mental models. A qualitative analysis of interviews conducted with students after they had completed the questionnaire is used to clarify some aspects which emerged from the quantitative analysis and validate the results obtained. Some implications of this joint use of quantitative and qualitative analysis for the design of a learning environment focused on the understanding of some aspects of the world at the level of causation and mechanisms of functioning are discussed.

The purpose of this paper is to analyze two cases of task design about straws and word problems in different cultural traditions (the Eastern and Western one). By means of two paradigmatic examples developed in Italy, we aim at showing, on the one hand, the effects and advantages of intercultural dialogue and, on the other hand, the need to take into account and to respect culturally rooted pedagogies, avoiding uncritical transfer from one culture to another. This perspective implies a reciprocal respect of the different approach modalities and hence a continuous back and forth between the practical and the deeply related theoretical dimension

In this paper we discuss a study on the approaches to modeling of students of the 4-year elementary school teacher program at the University of Palermo, Italy. The answers to a specially designed questionnaire are analyzed on the basis of an a priori analysis made using a general scheme of reference on the epistemology of mathematics and physics. The study is performed by using quantitative data analysis methods, i.e. factorial analysis of the correspondences and implicative analysis. A qualitative analysis of key words and terms used by students during interviews is also used to examine some aspects that emerged from the quantitative analysis. The students have been classified on the basis of their different epistemological approaches to knowledge construction, and implications between different conceptual strategies used to answer the questionnaire have been highlighted. The study's conclusions are consistent with previous research, but the use of quantitative data analysis allowed us to classify the students into three ``profiles'' related to different epistemological approaches to knowledge construction, and to show the implications of the different conceptual strategies used to answer the questionnaire, giving an estimation of the classification or implication ``strength.'' Some hints on how a course for elementary school physics and mathematics education can be planned to orient the future teachers to the construction of models of explanation are reported.

In this paper we discuss a study on the approaches to modeling of students of the 4-year Primary School Teacher program at the University of Palermo, Italy. The answers to a specially designed questionnaire are analyzed on the basis of an a-priori analysis made using a general scheme of reference on the epistemology of mathematics and physics. The study is performed by using quantitative data analysis methods, i.e. analysis of implicative and similarity trees. Dans ce papier, nous menons une étude relative à l’approche de la notion de modélisation par des étudiants de 4ème année de formation à la fonction de professeur d’école primaire à l’Université de Palerme, Italie. Les réponses à un questionnaire spécifique sont analysées sur la base d’une analyse a priori référencée par l’épistémologie des mathématiques et de la physique. L’étude est menée à l’aide de méthodes d’analyses de données, en l’occurrence ici les graphes d’implication et les arbres de similarité.

To compare cognitive processes adopted by students with different cultures in solving mathematical problems we have to focus on the Math epistemology through a cultural analysis concerning the fundamental elements of the students different cultural traditions and the philosophical, logic and linguistic bases subtended to the mathematical thought and its historical evolution. The paper describes this theoretical framework, emphasizing a possible comparison between different cognitive styles and mathematical problem solutions in the context of arithmetic and Algebraic thought of Italian and Chinese students in multicultural classes.

Il percorso sperimentale descritto nell’articolo4 vuol porre in evidenza come, attraverso un approccio significativo all’educazione musicale, intesa nello specifico come analisi sistematica degli indici di articolazione strutturale, che ne caratterizzano e qualificano il linguaggio, si possano sviluppare le capacità d’intuizione, analisi e sintesi tipiche del pensiero logico- deduttivo. Gli approfondimenti svolti in tale prospettiva, hanno permesso di evidenziare come un iter siffatto promuova in maniera evidente il passaggio tra registri semiotici diversi (Linguaggio Naturale, iconografico, musicale, geometrico e pre-algebrico), favorendo l’acquisizione di una buona competenza nell’analisi e nella produzione del linguaggio musicale e matematico. Inoltre l’isomorfismo che caratterizza i concetti di relazione, trasposizione strutturo-ritmica, classificazione e discriminazione, letti secondo questa duplice prospettiva, qualifica l’educazione musicale come strumento significativo per l’acquisizione di competenze interdisciplinari e transdisciplinari. La dicotomia che percorre l’intero progetto pone in evidenza come il parallelismo tra le due discipline, apparentemente molto distanti tra loro, sfoci in un sostanziale accordo tra due forme “linguistiche”, quella matematica e quella musicale, che si coadiuvano e si completano vicendevolmente in un rapporto dialettico proficuo. Scopo del percorso sperimentale è dunque fornire evidenza scientifica degli elementi di cui sopra, promuovendo una nuova prospettiva del far musica, che dismette i suoi panni di puro svago divenendo “analogica” espressione di stati interni logicamente e coerentemente comunicati.

This work deals with the didactical use of geometrical-mechanical artefacts to acquire tangent concept in vygotskian perspective. We adopt Rabardel’s theory on instru-mental approach to distinguish artefacts and instruments specially to evince the history-to-education ontogenesis-phylogenesis process. From this point of view we trace a historical-epistemological pathway for the tangent up to set an ad hoc didactical counterpart. Specifically in this paper we deepen the kinematical properties of the tangent (introducing the XVII century so called tractional motion) designing a laboratorial didactic pathway for 12th grade students with the use of a particular geometrical-mechanical artefact for mediating tangent meaning: the Tangentograph. The paper could be an interesting contribution on the study of the problems related to the tangent meaning and its properties. It can be a first step to the definition of an educational pathway related to the same mathematical content by the use of the tractional instruments that concretely manage it and thus could help the student to explore the tangent meaning.

With this work we retrace some of the fundamental historical and historical epistemological steps of the evolution of algebraic thought. Given the accepted parallelism between ontogenesis and phylogenesis we believe such a research to be a useful approach to the interpretation of obstacles and difficulties that students encounter during the acquisition of algebraic thought.