Mathematics classroom with Italian and Chinese students: Metacognitive experiences in an intercultural perspective

MaT²SMC: materials for teaching together: science andmMathematics teachers collaborating for better results

Let us start with an important statement: Mathematics and Science teachers do a good, and often an outstanding, job in teaching young people the basic knowledge of their respective fields! It is not the intent of this book to criticize what they do or how they do it. Keeping that in mind, and noting the fact that the teaching content of these fields intersects and overlaps, we observed – and this took us by surprise – that there is hardly any collaboration or consultancy between mathematics and science teachers (or textbook authors). Mathematics teachers often use science contexts in tasks, and science teachers often use mathematics, however they are usually working independently. Science c…

Una investigatión sobre las habilitades de formalizatión de los alumnos sobre un problema de teoria de los numeros

I libri di matematica che circolano nella scuola italiana e non: ricadute nella pratica d’aula

Perché gli studenti cinesi risolvono più facilmente i problemi di Matematica?

Graphical perception: a case study at the university level

The Socrates Comenius project between School, University and Research

Matematica in sezione: tradizioni culturali, pedagogiche e didattiche vicine e lontane

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.

Collaborative Teaching in the Italian "Liceo Matematico": A Case Study of Co-Planning and Co-Teaching

This contribution is centred on a case study of collaborative teaching, carried out among Upper Secondary School Math teachers. Here we present the context, the forms of the implemented collaboration and the effects that derived from the collaborative teaching. The used investigation tool was the semi-structured interview aimed to induce teachers to gradually reflect on their self and their teaching modus operandi. From the qualitative analysis emerged that collaborative teaching integrated different ways of teaching; it has been a stimulus for a etching “revision” and the possibility to improve the didactic-educational practice. For all teachers this way to define the teaching activities w…

Processi cognitivi e soluzioni di problemi matematici con studenti italiani e cinesi

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.

L’aula in classi multiculturali: approcci di Trasposizione Culturale tra pratica quotidiana e prospettive future sulla formazione matematica

Il fenomeno didattico della multiculturalità è un tema in molti casi discusso, vissuto però sovente in ambito scolastico come problema, non come risorsa. Parecchi sono infatti gli insegnanti che, sperimentando quotidianamente la realtà multiculturale nelle loro classi, manifestano un disagio, spesso associato ad una successiva richiesta di formazione; in molti casi disattesa o non adeguata ai loro bisogni. La ricerca nazionale in campo educativo, rivolta allo studio di questi fenomeni, è infatti a uno stadio quasi embrionale: non molte sono le riflessioni pedagogico-didattiche dirette ad insegnanti e formatori che operano in contesti complessi come quelli qui presi in esame, ancor meno le i…

La Geometria, una guida ai suoi contenuti e alla sua didattica

European and Chinese Cognitive Styles and their impact on Teaching/Learning Mathematics

Discrete Mathematics in Lower School Grades? Situation and Possibilities in Italy

This paper presents an overview of the Italian situation in teaching discrete mathematics in primary and middle school, taking into account the national teaching guidelines and their connection with the subject. We describe research conducted with about 150 teachers, interviewed in a preliminary questionnaire. The data collected shows, for all teaching grades, interest in having more discrete mathematics in the school curriculum even if there are some difficulties in teaching it and in inserting it in the usual mathematical activities at school, mostly related to teachers’ knowledge and self-confidence about the subject. We also discuss results and future plans for a continuing research pro…

La argumentaciòn y la demostraciòn en un context multicultural

Gli insegnati si raccontano … Matematica in Sezione

La lingua nell'apprendimento della Matematica da parte dei ragazzi cinesi. Una ricerca di didattica della Matematica

Il presente contributo discute alcune delle problematiche affrontate dal G.R.I.M. di Palermo sull'insegnamento/apprendimento delle matematiche in situazione di multiculturalità ed in particolare affronta lo studio della disciplina attraverso considerazioni di carattere sociale, culturale, antropologico, geografico etc. Si focalizza l’attenzione sulle relazioni (analizzate anche attraverso un continuo riferimento alla storia della Matematica), tra lingua naturale e forme argomentative rilevanti per l’apprendimento della disciplina nella cultura orientale (cinese) ed occidentale (europea). Vengono presentati i risultati di ricerca ottenuti dalla fine degli anni ’90 sino alla pubblicazione del…

Argumentation and Proving in Multicultural Classes: A didactical experience with Chinese and Italian students

Introduction of the JME Special Issue: Research on Classroom Practice at Primary Level

In July 2021, the ICME 14 took place in Shanghai, China, as a hybrid event; a thematic focus of this international conference was the TSG 36 Research on Classroom Practice at Primary Level under the leadership of Shuhua An. The aim of this TSG is to share and discuss, at an international level, a wide variety of experiences of teaching and learning mathematics in the classroom (An et al., 2022). According to this aim the TSG 36 explored state-of-the-art strategies and approaches to address the concerns and problems, and advance the research on classroom practice with an ultimate goal of supporting it.

The concept of operator in the numerical extensions: a theoretical base.

Dialogo sulla matematica nella scuola dell’infanzia

La storia della Matematica come chiave per l’inclusione interculturale nella pratica d’aula attuale

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…

On the formalization of a number theory problem by pupils

Processi cognitivi e soluzioni dei problemi: studenti italiani e studenti cinesi

Obiettivo primario della ricerca sulla quale ho lavorato negli ultimi quattro anni è stato quello di riflettere sulle questioni riguardanti le Matematiche Elementari in una visione quanto più ampia possibile, alla luce di una scuola sempre più “diversificata”, multiculturale e globalizzata, trattando in maniera diretta non soltanto le problematiche strettamente riferite ai contenuti disciplinari relativi specificatamente al pensiero algebrico e geometrico per la scuola Primaria e Secondaria, ma anche quelli che in molti casi possono definirsi come gli aspetti storico-epistemologici della disciplina discussa in aula con gli allievi. Quale didattica disciplinare nella classe del terzo millenn…

Indeterminate systems in the “Nine Chapters” by Liu Hui. The role of “context” for determining the “fundamental algorithm” as an argumentative tool

Italian Primary School prospective teachers beliefs about knowledge construction: a case study about models

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 qu…

Reasoning and proving in Algebra. Examples from 8th grade school mathematics textbooks in Italy

Some research studies concerning the didactics of Algebra discuss how learning to solve problems using symbolic algebraic language can be hard for students (Bohlmann et al., 2014; Palm, 2009). Students, in fact, have often difficulty to learn the ways in which the sym- bols should be manipulated to argue or to prove an assertion in order to reach a problem solu- tions. Although many studies conducted by mathematics educators discussed important contri- butions to this subject (e.g. Arzarello, Robutti & Bazzini, 2005; Boero, 2001; Carraher, Schliemann, Brizuela & Earnest, 2006; Lins & Kaput, 2004; Ursini & Trigueros, 2001), not many analysis were conducted on the role of the …

A New Approach to Investigate Students’ Behavior by Using Cluster Analysis as an Unsupervised Methodology in the Field of Education

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 need…

A phenomenological study about the effect of Covid-19 pandemic on teachers' use of teaching resources about reasoning & proving in mathematics

If we study the history of societies, we can find several pandemic events such as smallpox, cholera, plague, and SARS [1, 2]. Each one of these pandemics events af fected human life in many aspects from health to the economic sphere [3], education is one of these aspects. The SARS-CoV-2 pandemic (Covid-19) has had a massive impact on Education: many students of different countries have been affected by school and university closures due to the Covid-19. Italy was the first Western coun try to suffer a coronavirus emergency

Se e quando si arriva al pensiero algebrico

TAKING A LOOK AT CHINESE PEDAGOGY IN SHUXUE [MATHEMATICS]: A DIALOGUE BETWEEN CULTURES TO APPROACH ARITHMETIC AT FIRST AND SECOND ITALIAN PRIMARY CLASSES

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

Medida y premedida: una experiencia lúdica en la escuela primaria

An experience of game in a multicultural milieu at infancy and elementary school

European and Chinese Cognitive Styles and Their Impact on Teaching Mathematics

A General Framework and Theoretical References.- The Chinese Written Language as Tool for a Possible Historical and Epistemological Reflections on the Mathematics and the Impact of Teaching/Learning of Mathematics.- The Meta-rules between Natural Language and History of Mathematics.- Common Sense and Fuzzy Logic.- The Experimental Epistemology as a Tool to Observe and Preview Teaching/Learning Phenomena.- Strategy and Tactics in the Chinese and European Culture: Chess and Weich'i.- Rhythm and Natural Language in the Chinese and European Culture.- Conclusions.

PICTURES, GESTURES AND DISCOURSES: A CASE STUDY WITH KINDERGARTEN STUDENTS DISCOVERING LEGO BRICKS

The awareness of the importance to look, through a mathematical lens, to the children drawings, gestures and discourses, considering them as diagnostic tools for the mathematics competences, stays at the base of this contribution. It discusses a didactic experience conducted in a Kindergarten (students 5 or 6 years old) in which we asked children to represent and discus a Lego block with a drawing and speech, observed from different prospective. The discussed results seem to us interesting both for researchers in Mathematics Education and for Kindergarten teachers who want to deepen the role of drawing and gestures as an expressive and diagnostic forms to analyze students’ knowledge, abilit…

E questo dove lo metto? Esperienze geometriche in continuità tra la Scuola dell'Infanzia e la Scuola Primaria

I bambini si raccontano: soddisfazioni, paure e aspettative della loro scuola

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.

K-means Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman’s Unifying Approach

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 Cl…

Investigating the quality of mental models deployed by undergraduate engineering students in creating explanations: The case of thermally activated phenomena

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,'' ``descri…

Algebraic thinking and generalization of patterns: a didactical experience with Italian and Chinese students

Geometrical-mechanical artefacts for managing tangent concept

Unsupervised quantitative methods to analyze student reasoning lines: Theoretical aspects and examples

[This paper is part of the Focused Collection on Quantitative Methods in PER: A Critical Examination.] A relevant aim of research in education is to find and study the reasoning lines that students deploy when dealing with problematic situations. This can be done through an analysis of the answers students give to a questionnaire. In this paper, we discuss some methodological aspects involved in the quantitative analysis of a questionnaire by means of two different clustering methods, a hierarchical one and a nonhierarchical one. We start from the coding procedures needed to obtain analyzable data from the questionnaire and from a definition of a correlation coefficient suitable for measuri…

Why Asian children outperform students from other countries? Linguistic and parental influences comparing Chinese and Italian children in preschool education

This paper focusing on the complex situation of the Italian multiculturalism and trying to reply to why Asian children mathematically outperform students from other countries, discusses from the epistemological point of view, Chinese children’s skills before to start their formal education in Italian educational school context. A review of the literature, comparing pre-schoolers competences of Asian and Western students, reveals two important influenced factors: linguistic and parental stimuli. In particular many researchers showed that the structure of the Chinese language provides in children a head start in basic math skills, for example to discover, since preschool activities, a pre-alg…

Dalle classi multiculturali ad una didattica interculturale della matematica: verso una Smart Community di insegnanti in formazione

La presenza di alunni stranieri nelle nostre classi è ormai una realtà con cui i nostri insegnanti si devono confrontare ogni giorno. A partire dagli ’90 il Ministero ha cominciato a fornire indicazioni molto ampie, spesso volte a normare, gestire e sistematizzare l’iter scolastico, e non, degli studenti stranieri; per quel che riguarda gli insegnanti sovente si sono suggeriti atteggiamenti volti all’inclusione, poi integrati nelle proposte di educazione civica. Sono però insufficienti i richiami specificatamente disciplinari (in particolare sulla matematica) e più generalmente didattici (dal design alla trasposizione didattica), necessari ad intercettare, interpretare e rielaborare le diff…

Educazione musicale ed educazione matematica: contesti semiotici diversi tra loro interagenti

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

Problems with variation in teaching/learning Geometry: an example of Chinese Cultural Transposition

This paper discusses some theoretical/methodological observation and some qualitative results coming from a Cultural Transposition experience, implemented in the Italian school context (grade 8), according to the methodology of variation, as one of the most significant problem solving approach in Chinese schools. The framework of the Cultural Transposition and the methodology of variation are presented as an important condition for “decentralizing” the didactic practice from a specific social and cultural context. We argue that looking at different teaching/learning mathematics strategies coming from East-Asia cultures can favor some cultural contaminations at school and allow students to a…

Different procedures in argumentation and conjecturation in primary school:an experience with Chinese students

Prospective elementary teachers’ perceptions of the processes of modeling: A case study

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…

A case stydy about the formalization by pupils of a number theory problem

A quantitative method to analyse an open-ended questionnaire: A case study about the Boltzmann Factor

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

Atti del SEMINARIO NAZIONALE SUL CURRICOLO VERTICALE

MOTIVATING AND EXCITING METHODS IN MATHEMATICS AND SCIENCE Plany vyucovacich hodin

Cultural transposition: Italian didactic experiences inspired by Chinese and Russian perspectives on whole number arithmetic

The paper presents some reflections and activities developed by researchers and teachers involved in teacher education programs on cultural transposition. The construct of cultural transposition is presented as a condition for decentralizing the didactic practice of a specific cultural context through contact with other didactic practices of different cultural contexts. We discuss the background theoretical issues of this approach and also give an analysis of two examples of cultural transposition experiences carried out in Italy. In particular, by means of qualitative analysis of some excerpts, discussions, and interviews, we show that the contact with different perspectives coming from Ch…

Il tango e la matematica: muoversi all’interno delle figure

A Phenomenological Study About the Effect of Covid-19 Pandemic on the Use of Teaching Resources in Mathematics

In this contribution, we discuss phenomenological research related to a pilot study carried out by the Consortium of the MaTeK Horizon 2020 project during the 2020–21 academic year. The research aims to analyse the effects of the Covid-19 pandemic on the use of teaching resources in mathematics in five coun- tries. A questionnaire made of seven questions was administered to a data sample made of teachers of all grades. The answers coming from the questionnaire were quantitatively and qualitatively analysed. Closed-ended questions were analysed by using a clustering methodology called k-means. Open-ended questions were qualitatively analysed. The results show that almost all the teachers are…

MOTIVATING AND EXCITING METHODS IN MATHEMATICS AND SCIENCE Unità di apprendimento

MOTIVATING AND EXCITING METHODS IN MATHEMATICS AND SCIENCE Stundenbilder

An example of developing a research program, together with a program of preparation of young researchers.

Aim of this short contribution is to briefly discuss our experience as young researchers in Math Education and give an example of developing a research program, together with a program of preparation of young researchers.

Pensiero aritmetico e pensiero algebrico in ambienti multiculturali: il caso cinese

Cultural diversity: how can it increases the complexity of teaching mathematics in multicultural class? The case of Chinese students

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

Esperienze con studenti italiani e cinesi: processi cognitivi e soluzioni di problemi matematici.

Uno dei problemi più interessanti che si pongono oggi è certamente quello di confrontarsi con la “diversabilità” in situazioni di multicultura, realtà ormai presente nella nostra società, in continuo mutamento socio-culturale, e quindi nodo centrale per la ricerca in didattica della Matematica e non solo. Se infatti i fenomeni di insegnamento/apprendimento delle discipline hanno già sistemi complessi di indagine, la “diversabilità multiculturale” ne aumenta notevolmente la complessità. Ogni persona, appartenente ad una stessa cultura, possiede differenze cognitive rispetto ai suoi simili; in ambienti multiculturali queste si sommano a quelle riscontrabili nei diversi saperi che interagiscon…

Analysing the conceptions on modelling of engineering undergraduate students: A case study using cluster analysis

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 st…

A study on science teaching efficacy beliefs during pre-service elementary training

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 ans…

Epistemic and didactic values of the demonstrative process in different cultures: a case study in Geometry with Chinese and Italian students

I sistemi indeterminati nei "Nove Capitoli" di Liu Hui. Il ruolo del "contesto" per determinare l'"algoritmo fondamentale" come strumento argomentativo

Integrazione e apprendimento: un’esperienza laboratoriale tra Lingua e Matematica alla Scuola dell’Infanzia

Cultural diversity as a resource or an obstacle for teaching practices in multicultural milieu: Experience of a training course for Italian teachers about Chinese Shuxue

This contribution, examining the increasing presence at school of East-Asian students (Chinese in particular) and the related didactical complexity rising from the contemporary presence of Western and non Western cultural heritages, discusses some historical, epistemological and linguistic aspects of Chinese culture and the related Shuxue (Mathematics) education. These were presented to Italian teachers and educators during a training course organized by the authors with the aim of answering teachers’ needs (K-12) for training about the didactical problematic of teaching in multicultural milieu (in particular with Chinese students). The laboratory activities designed and implemented in an a…

Geometrical-mechanical artefacts mediating tangent meaning: the Tangentograph

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 f…

Motivating and Exciting Methods in Mathematics and Science, IT Team

Glossary of Terms

Arithmetical and algebraical approach to the second degree equations (age: 15-19 years)

Argumentation and proving: a didactical experience with Chinese and Italian students

Il concetto di tempo e le sue misurazioni alla Scuola dell’Infanzia: dal calendario alla clessidra

Il contributo, affrontando, seppur in una prima approssimazione, la problematica epistemologica, psicologica e didattica legata alla scoperta del concetto di tempo da parte dei bambini e le relative misurazioni attraverso strumenti quali il calendario, l’orologio, la clessidra e il metronomo, presenta i risultati di un percorso sperimentale realizzato in una Sezione di SdI con bambini di 5 anni. The paper discussing, even if in a not exhaustive way, the epistemological problematic and the psychological and didactic ones related to the children discovery of the time’s concept and its measurements through artefacts such as a calendar, a clock, a hourglass and a metronome, presents the results…

Provide Motivation Through Exciting Materials in Mathematics and Science Lesson Plans

Using cluster analysis to study the modelling abilities of engineering undergraduate students: a case study

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).

Matematica e Musica: l’Apprendimento di base

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…

Mathematics and Music: a paradigmatic pair for basic learning

The aim of the trial path described in this article is to highlight the possibility to develop intuition, analysis and synthesis abilities, which are typical of the logical - deductive mathematical thought, in primary school children (2nd class), through a significant approach to musical education, meant as systematic analysis of the sound parameters, which characterize and qualify its language. The Vygotskijan theoretical framework, which leads and interprets the didactic engineering proposed in class, emphasizes how the Mathematics - Music pair has promoted the changeover among different semiotic registers (Duval 2002), referred to Natural, iconographic, musical, geometric and pre - algeb…

Exploring the Coherence of Student Reasoning when Responding to Questionnaires on Thermally Activated Phenomena

Many research results show that students often highlight “mixed-type” reasoning when tackling problematic situations and problems. This reasoning is based on the simultaneous use of common-sense and mere descriptions of facts, perceived as sufficient to build an “explanation” of observed or proposed situations and problems. This fact can be interpreted as a lack of coherence. In this paper, we study the coherence of responses that a sample of undergraduate chemical engineering student give when they are asked to face real-life situations, to create explanations, and to use models in different contexts. We administered open-ended questionnaires before and after a twenty-hour Inquiry-Based wo…

DEVELOPING AN INTEGRATED FRAMEWORK FOR ANALYZING WAYS OF REASONING IN MATHEMATICS

Mathematics education literature involves studies that sought a way of investigating the mode of reasoning in mathematics textbooks because textbooks are the main resource for teachers in planning their mathematics lessons. In this vein, this study aimed to analyze the ways of reasoning in mathematics textbooks that are currently used in five countries: Slovakia, Czech Republic, Italy, Norway, and Turkiye, as a part of a Horizon 2020 Project. We initially started with a framework that aimed to examine the effect of teachers’ participation in the lesson study on the improvement of students’ mathematical reasoning (Project LESSAM). However, as the textbook analysis of different countries proc…

I libri di testo come strumento per ripensare la formazione degli insegnati di Scuola Primaria e dell’infanzia di Matematica in un’ottica interculturale

SORTING ALGORITHMS FOR 5TH AND 6TH GRADE STUDENTS: GREEDY OR COOPERATIVE?

Our main research goal lies in a proposal to discuss the lack of, and improve, activities in the Italian school curriculum about discrete mathematics, computer algorithms and cryptography, especially for 3rd to 8th grade students. Activities of this kind are missing almost entirely, both in the school programs and in textbooks, despite many agree that they can be really useful to improve both general skills, such as reasoning and modeling, and skills particular to discrete mathematics, such as algorithmic and recursive thinking. A survey among various grades teachers confirmed this. The activity we are going to describe fits into a wider research project. Design research, chosen as the meth…

Multidimensional Scaling in Cluster Analysis: examples in Science and Mathematics Education

Several researches in STEM education research highlight the advantages of an inte- grated approach to these disciplines that relates knowledge and know-how, design and implementation, theoretical and practical problems [5, 4, 6]. In some researches, the effectiveness of these approaches on students conceptual understanding and motivation and has been studied through the use of quantitative analysis tools such as cluster analysis (CLA) [1, 7]. Through CLA it is possible to characterize students analyzing the strategies they deploy to tackle, for example, questionnaires built so as to investigate the lines of reasoning implemented by them when they are proposed with problematic situations. In…

Problems with variation: an educational experience of cultural transposition with prospective primary teachers

The paper presents some theoretical reflections and some methodological notes about a Professional Development (PD) path worked out during the last two years by Italian researchers for prospective Primary teachers. The theoretical construct of Cultural Transposition defines the framework of the PD path's activities and the related research. It was used to define an interesting cultural lent to delineate possible new approaches for effective pre-service teacher education programs, in particular for the Primary level. The defined methodology was based on the possibility to reflect about the decentralization of didactic practices based on a specific cultural context through one or more contact…

Drawings, Gestures and Discourses: A Case Study with Kindergarten Students Discovering Lego Bricks

This paper presents a study aimed at investigating the didactic potentiality of the use of an artefact, useful to construct mathematical meanings concerning the coordination of different points of view, in the observation of a real object/toy. In our view, the process of meaning construction can be fostered by the use of adequate artefacts, but it requires a teaching/learning model, which explicitly takes care of the evolution of meanings, from those personal, emerging through the activities, to the mathematical ones, aims of the teaching intervention. The main hypothesis of this study is that the alternation between different semiotic systems, graphical system, verbal system and system of …

Enhancing geometrical knowledge, metacognitive reasoning and visual spatial skills through a playing chess laboratory.

Il numero naturale nei suoi aspetti cardinale, ordinale e ricorsivo: giochi e artefatti in sinergia per la scuola primaria

Il presente lavoro di ricerca e sperimentazione riguarda l’introduzione del concetto di numero naturale e punta alla costruzione di una prima idea dei suoi diversi aspetti, in una prospettiva di curricolo verticale. Attraverso la sinergia di tre artefatti e con il gioco si è favorita la costruzione del ‘senso’ di numero naturale, nei suoi tre aspetti cardinale, ordinale e ricorsivo. Il presente percorso, progettato sulla base della teoria della Mediazione Semiotica e della sinergia tra artefatti, ha avuto come obiettivo principale quello di costruire il concetto in senso globale di numero naturale attraverso la realizzazione della linea dei numeri naturali passando da un’idea intuitiva leg…

To the beginnings of the XXI century, which possible use of neurosciences results in research in Mathematics Education ?

In the last 20 years we witnessed a development of research on "how" our brain works, how it processes the information, how it stores, how it links these, which are the areas appointed to a certain function and how these are interconnected with this each other etc. Then how it learn. Many people are interested to these results, first of all psychologists that are interested in the problems since long time, but also the neurophysiologists and the many categories of people who have intentions of speculative nature, but also with other kind of application. We can think to problems arising from situations of disability, related to brain injury to various types and more, etc ... In the study of …

A-Didactical Situation in Multicultural Primary School

On the formalization of a number theory problem by pupils

Teaching/learning mathematics in different cultural environments: some experimental considerations with Chinese and European students

Calculus Artefacts in Chinese Textbooks: Variational Approaches with Prospective Primary Teachers

The first part of the paper presents some theoretical reflections and some methodological notes about a Professional Development (PD) path worked out during the last two years by Italian researchers for prospective primary teachers. The theoretical construct of Cultural Transposition defines the framework of the PD path’s activities and the related research. It was used to define an interesting cultural lens to delineate possible new approaches for effective pre-service teacher education programs in particular for the primary level. The defined methodology was based on the possibility to reflect on the he decentralization of didactic practices based on a specific cultural context through on…

Il fumetto può aiutare nei processi di insegnamento/apprendimento delle Matematiche?

Matematica e musica: linguaggi ... in accordo!

Ontogenesis and phylogenesis in the passage from arithmetic to algebraic thought

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.

La formazione degli insegnanti della scuola di base: considerazioni metodologiche ed esperienze specifiche nel Master dell’Università di Palermo

Arithmetical thought and algebraic thought in a multicultural milieu: the Chinese case

Atti GIORNATE DI STUDIO DELL'INSEGNANTE DI MATEMATICA (GIMat).Le mani, la parola, la testa: capire, argomentare, dimostrare in matematica

Nello spirito di sempre, gli atti del convegno, pubblicati prima del convegno stesso, vogliono offrire ai lettori, anche attraverso i 25 contributi scritti/presentati da insegnanti, insegnanti/ricercatori e ricercatori universitari intervenuti a GIMat 2022 e riportati di seguito, la possibilità di riflettere prima, durante e dopo le stesse GIMat su tante esperienze portate avanti sul territorio nazionale e internazionale, nell’ambito dell’Educazione matematica

Stili cognitivi nell’apprendimento/insegnamento delle matematiche nella cultura cinese ed europea

Tenuto conto del valore epistemologico della cultura cinese e di quella italiana con particolare riferimento all’analisi degli elementi cardine delle due tradizioni culturali come la filosofia, la logica, la lingua, la storia dello sviluppo del pensiero matematico etc., la ricerca condotta mira a comparare, in un’ottica interculturale, possibili schemi logico-argomentativi messi in atto da studenti italiani e cinesi, inseriti nelle classi italiane, evidenziandone analogie e differenze alla luce di analisi teorico/sperimentali condotte in Italia e direttamente in Cina.

La realtà multiculturale della scuola: comparazione di processi cognitivi tra studenti italiani e cinesi

Obiettivo primario della ricerca è quello di riflettere sulle questioni riguardanti le Matematiche Elementari in una visione quanto più ampia possibile, alla luce di una scuola sempre più “diversificata”, multiculturale e globalizzata, trattando in maniera diretta non soltanto le problematiche strettamente riferite ai contenuti disciplinari relativi specificatamente al pensiero algebrico e geometrico per la scuola Primaria e Secondaria, ma anche quelli che in molti casi possono definirsi come gli aspetti storico-epistemologici della disciplina discussa in aula con gli allievi. Quale didattica disciplinare nella classe del terzo millennio? Quale formazione matematica? Quali saperi? E quindi.…

Special issue BOOK OF ABSTRACT 2022 CTRAS CONFERENCE NEW AND OLD CHALLENGES TO SUPPORT ALL STUDENTS’ MATHEMATICS TEACHING AND LEARNING IN INCLUSIVE, FAIRLY AND MEANINGFUL WAY

Special issue BOOK OF ABSTRACT 2022 CTRAS CONFERENCE

Playing in Preschool Mathematics Education during SARS-CoV-2 pandemic: a phenomenological study with Italian teachers

This paper discusses the results coming from a phenomenological study implemented with a sample of 110 Italian preschool teachers about the impact of the Covid-19 on preschool education. We investigate in which way the related pandemic phenomenon changed and is still changing the preschool pedagogical/didactic scenario about Mathematics playing. Through a questionnaire we qualitatively analyze and classify teachers’ argumentations highlighting their teaching approaches, their attitudes, their expectations in playing Mathematics in Preschool Education.

MATHEMATICS EDUCATION IN A GLOBALIZED ENVIRONMENT - L’ENSEIGNEMENT DES MATHÉMATIQUES DANS UN ENVIRONNEMENT GLOBALISÉ. Actes/Proceedings CIEAEM 63

GIORNATE DI STUDIO DELL'INSEGNANTE DI MATEMATICA (GIMat). Insegnare Matematica Oggi - I EDIZIONE - 2016

La Sicilia nel secolo scorso crediamo si possa dire che sia stata uno dei poli più attivi per quanto riguarda la matematica sia dal punto di vista della ricerca scientifica che per quanto riguarda la didattica della matematica.
Si deve all'iniziativa individuale dello studioso Giovanni Battista Guccia, la fondazione a Palermo, il 2 marzo 1884, del Circolo Matematico. Lo statuto del Circolo permise l'associazione anche di membri stranieri e, grazie a ciò, il Circolo raggiunse ben presto il suo scopo, "diventando una società internazionale di altissima qualità con una prestigiosa pubblicazione matematica”, i Rendiconti del Circolo Matematico di Palermo. Il Circolo divenne così un punto di rif…