A partir d’un dispositif eTandem chinois-français initié et développé par l’Université de Genève (Suisse) et l’Université du Hubei (Chine) sur cinq années, cette thèse aborde deux problématiques : l’ingénierie pédagogique du dispositif et la co-construction des compétences via la réalisation des rôles d’expert et d’apprenant entre les locuteurs natifs et non natifs. D’une part, nous montrons que la conception du dispositif doit prendre en compte l’influence des exigences institutionnelles, des pédagogies et des cultures éducatives sur la motivation, les stratégies et les performances des apprenants. D’autre part, nous analysons de manière fine des interactions au sein de binômes dont les styles d’organisation peuvent varier. Le « projet didactique » sous-jacent à leurs échanges, grâce notamment à son caractère institutionnalisé, mobilise des ressources technologiques et interculturelles en lien avec le processus d’apprentissage. Nous montrons en particulier comment les stratégies de résolution de problèmes (négociation du sens et de la forme) sont prolongées et enrichies par les outils informatiques. / Based on a Chinese-French eTandem course initiated and developed by the University of Geneva (Switzerland) and the University of Hubei (China) over five years, this thesis tackles two issues: instructional design of the course and co-construction of competences through the realization of the roles of expert (native speaker) and learner (non-native speaker). On the one hand, our research shows that the course design should take into account the influence of the institutional requirements, teaching methods and the educational cultures on students’ motivation, strategies, and performance. On the other hand, we analyse interactions between learners, which present varying organisational styles. Thanks to the institutionalisation of the eTandem course, the « didactical characteristics » identified in their interaction mobilizes technological and intercultural resources related to the learning process. We show particularly how problem-solving strategies (negotiation of meaning and form) are extended and enriched by new technologies.

Syftet med studien var att ta reda på vilka strategier elever väljer när de ska lösa ett matematiskt problem. Vi genomförde en observation och nio individuella intervjuer med elever i årskurs 3. De fick lösa ett matematiskt problem som observerades. Utifrån elevernas lösningar genomförde vi sedan intervjuer för att ta reda på vilka strategier de valt att använda för att lösa problemet. Resultatet av elevernas lösningar visade på flera olika lösningsstrategier. Dessa delades in i yttre och inre representationer. Strategier som bilder, grafiska framställningar och matematiska symboler (siffror) hör till de yttre representationerna, då de består av konkreta bilder som eleverna måste se framför sig på papper när de löser matematiska problem. Huvudräkning, automatiserad kunskap och ”tänkande” är samtliga strategier som tillhör de inre representationsformerna. Med inre representationer menar vi det som sker i huvudet, det eleverna inte behöver se framför sig för att kunna lösa problemet. Vi fann att elevlösningarna innehöll kombinationer av flera olika strategier. Vilken eller vilka strategier eleven än väljer till sin problemlösning är det oundvikligt att använda sig av någon form av inre representationsform, för att tänka måste alla göra oberoende av vilken lösningsstrategi som väljs och hur duktiga problemlösare eleverna än är. När eleverna är unga kan det vara svårt och ovant för dem att skriftligt redovisa hur lösningsprocessen gått till. Därför måste vi lärare ha tid att sätta oss in i hur eleven tänker för att kunna bygga vidare undervisningen utifrån den enskilde individens behov. / The purpose of the study was to discern which strategies pupils employ when they solve a mathematical problem. We carried through one observation and nine individual interviews with pupils in school year 3. They were asked to solve a mathematical problem, which was observed. On the basis of the pupils’ solutions, we carried out interviews in order to determine which strategies they chose to employ. The outcome of the pupils’ solutions showed several problem solving strategies. These were divided into external and internal representations. Strategies such as pictures, graphs and mathematical symbols (numerals) are external representations, as they consist of concrete pictures that the pupils must see in front of them on a paper when solving mathematical problems. Mental arithmetic, automated knowledge and “thinking” are all strategies that belong to internal modes of representation. With internal representations, we mean what happens inside our heads – what pupils need not see in front of them in order to solve a problem. We found that the pupils’ solutions contained combinations of several different strategies. Irrespective of which strategy or strategies the pupil choose in his or her problem solving, it is inevitable to use some variety of internal representations; everyone has to think, regardless of the strategy chosen and the problem solving skills of the pupil. When pupils are young, it may be difficult for them to present the flow of their problem solving processes in writing. Consequently, as teachers we must have time to familiarize ourselves with how the pupil thinks in order to develop our teaching on the basis of the needs of the individual pupil.

<p>Syftet med studien var att ta reda på vilka strategier elever väljer när de ska lösa</p><p>ett matematiskt problem. Vi genomförde en observation och nio individuella</p><p>intervjuer med elever i årskurs 3. De fick lösa ett matematiskt problem som</p><p>observerades. Utifrån elevernas lösningar genomförde vi sedan intervjuer för att</p><p>ta reda på vilka strategier de valt att använda för att lösa problemet. Resultatet av</p><p>elevernas lösningar visade på flera olika lösningsstrategier. Dessa delades in i</p><p>yttre och inre representationer. Strategier som bilder, grafiska framställningar och</p><p>matematiska symboler (siffror) hör till de yttre representationerna, då de består av</p><p>konkreta bilder som eleverna måste se framför sig på papper när de löser</p><p>matematiska problem. Huvudräkning, automatiserad kunskap och ”tänkande” är</p><p>samtliga strategier som tillhör de inre representationsformerna. Med inre</p><p>representationer menar vi det som sker i huvudet, det eleverna inte behöver se</p><p>framför sig för att kunna lösa problemet. Vi fann att elevlösningarna innehöll</p><p>kombinationer av flera olika strategier. Vilken eller vilka strategier eleven än</p><p>väljer till sin problemlösning är det oundvikligt att använda sig av någon form av</p><p>inre representationsform, för att tänka måste alla göra oberoende av vilken</p><p>lösningsstrategi som väljs och hur duktiga problemlösare eleverna än är. När</p><p>eleverna är unga kan det vara svårt och ovant för dem att skriftligt redovisa hur</p><p>lösningsprocessen gått till. Därför måste vi lärare ha tid att sätta oss in i hur</p><p>eleven tänker för att kunna bygga vidare undervisningen utifrån den enskilde</p><p>individens behov.</p> / <p>The purpose of the study was to discern which strategies pupils employ when they solve</p><p>a mathematical problem. We carried through one observation and nine individual</p><p>interviews with pupils in school year 3. They were asked to solve a mathematical</p><p>problem, which was observed. On the basis of the pupils’ solutions, we carried out</p><p>interviews in order to determine which strategies they chose to employ. The outcome of</p><p>the pupils’ solutions showed several problem solving strategies. These were divided</p><p>into external and internal representations. Strategies such as pictures, graphs and</p><p>mathematical symbols (numerals) are external representations, as they consist of</p><p>concrete pictures that the pupils must see in front of them on a paper when solving</p><p>mathematical problems. Mental arithmetic, automated knowledge and “thinking” are all</p><p>strategies that belong to internal modes of representation. With internal representations,</p><p>we mean what happens inside our heads – what pupils need not see in front of them in</p><p>order to solve a problem. We found that the pupils’ solutions contained combinations of</p><p>several different strategies. Irrespective of which strategy or strategies the pupil choose</p><p>in his or her problem solving, it is inevitable to use some variety of internal</p><p>representations; everyone has to think, regardless of the strategy chosen and the</p><p>problem solving skills of the pupil. When pupils are young, it may be difficult for them</p><p>to present the flow of their problem solving processes in writing. Consequently, as</p><p>teachers we must have time to familiarize ourselves with how the pupil thinks in order</p><p>to develop our teaching on the basis of the needs of the individual pupil.</p>

En dépit de ses qualités, le Rorschach en Système Intégré présente des problèmes psychométriques substantiels que le nouveau système Rorschach Performance Assessment System (R-PAS) ne permet pas de résoudre. Aussi, l’objectif principal de la thèse que nous défendons est de développer une approche psychométrique du Rorschach qui soit satisfaisante sur les plans statistique et clinique. Une Analyse Parallèle et Une Analyse en Composantes Principales réalisée sur un échantillon normatif de 695 participants Belges, Français et Finlandais permet de définir un modèle du Rorschach en 12 Composantes. Si ces dimensions sont cohérentes avec les principes de cotation et les connaissances empiriques sur le Rorschach, elles font également apparaître certaines difficultés de cotation, des aspects du Rorschach qui ont été négligés dans la recherche, de même qu’elles remettent en question certains indices du Système Intégré. Ce modèle est appliqué à deux problèmes empiriques : l’expression de particularités culturelles au Rorschach et la capacité du test à identifier des stratégies de résolution de problème (qui est un aspect central du Système Intégré). Les normes américaines du Système Intégré ainsi que les normes internationales du R-PAS ne peuvent s’appliquer de manière universelle et il faut donc recourir à des valeurs de références nationales. De plus, le Rorschach ne permet pas d’identifier des stratégies de résolution de problème de manière fiable. Ces études montrent que certains principes fondamentaux du Système Intégré et du R-PAS sont à remettre en question et qu’il est nécessaire de développer un nouveau système d’interprétation du Rorschach selon une approche psychométrique. / In spite of its quailties, the Rorschach Comprehensive System (RCS) presents substantial psychometric issues which are not solved by the new Rorschach Performance Assessment System (R-PAS). Thus, the main objective of this dissertation is to develop a satisfying psychometrical approach of the Rorschach test. A Parallel Analysis and a Principal Component Analysis performed on a normative sample of 695 Belgian, French and Fins participants define a 12 Components model of the Rorschach. If these dimensions are coherent with scoring principles and empirical evidences for the Rorschach they also reveal some scoring issues, neglected aspects of the Rorschach in the research field as well as they question the validity of some indices of the RCS. This model was applied to two empirical problems : the cross-cultural study of the Rorschach and its ability to assess problem solving strategies (which is a key feature of the RCS). The american norms of the RCS and the international reference values of the R-PAS cannot be used universally and it is necessary to use national norms. Moreover, the Rorschach does not assess problem solving strategies in a satisfying manner. These studies demonstrate that some fondamental principles of the RCS and the R-PAS must be questionned and the necessity to develop a new interpretation system for the Rorschach based on a psychometrical approach.

A partir d’un dispositif eTandem chinois-français initié et développé par l’Université de Genève (Suisse) et l’Université du Hubei (Chine) sur cinq années, cette thèse aborde deux problématiques : l’ingénierie pédagogique du dispositif et la co-construction des compétences via la réalisation des rôles d’expert et d’apprenant entre les locuteurs natifs et non natifs. D’une part, nous montrons que la conception du dispositif doit prendre en compte l’influence des exigences institutionnelles, des pédagogies et des cultures éducatives sur la motivation, les stratégies et les performances des apprenants. D’autre part, nous analysons de manière fine des interactions au sein de binômes dont les styles d’organisation peuvent varier. Le « projet didactique » sous-jacent à leurs échanges, grâce notamment à son caractère institutionnalisé, mobilise des ressources technologiques et interculturelles en lien avec le processus d’apprentissage. Nous montrons en particulier comment les stratégies de résolution de problèmes (négociation du sens et de la forme) sont prolongées et enrichies par les outils informatiques. / Based on a Chinese-French eTandem course initiated and developed by the University of Geneva (Switzerland) and the University of Hubei (China) over five years, this thesis tackles two issues: instructional design of the course and co-construction of competences through the realization of the roles of expert (native speaker) and learner (non-native speaker). On the one hand, our research shows that the course design should take into account the influence of the institutional requirements, teaching methods and the educational cultures on students’ motivation, strategies, and performance. On the other hand, we analyse interactions between learners, which present varying organisational styles. Thanks to the institutionalisation of the eTandem course, the « didactical characteristics » identified in their interaction mobilizes technological and intercultural resources related to the learning process. We show particularly how problem-solving strategies (negotiation of meaning and form) are extended and enriched by new technologies.

The purpose of this study was to determine the relationship between High School learners‟ mathematics-related belief systems and their approaches to mathematics non-routine problem-solving. A mixed methods approach was employed in the study. Survey questionnaires, mathematics problem solving test and interview schedules were the basic instruments used for data collection. The data was presented in form of tables, diagrams, figures, direct and indirect quotes of participants‟ responses and descriptions of learners‟ mathematics related belief systems and their approaches to mathematics problem solving. The basic methods used to analyze the data were thematic analysis (coding, organizing data into descriptive themes, and noting relations between variables), cluster analysis, factor analysis, regression analysis and methodological triangulation. Learners‟ mathematics-related beliefs were grouped into three Learners‟ mathematics-related beliefs were grouped into three categories, according to Daskalogianni and Simpson (2001a)‟s macro-belief systems: utilitarian, systematic and exploratory. A number of learners‟ problem solving strategies were identified, that include unsystematic guess, check and revise; systematic guess, check and revise; trial-and-error; logical reasoning; non-logical reasoning; systematic listing; looking for a pattern; making a model; considering a simple case; using a formula; numeric approach; piece-wise and holistic approaches. A weak positive linear relationship between learners‟ mathematics-related belief systems and their approaches to non-routine problem solving was discovered. It was, also, discovered that learners‟ mathematics-related belief systems could explain their approach to non-routine mathematics problem solving (and vice versa). / Mathematics Education / D.Phil. (Mathematics Education)

Η παρούσα διδακτορική διατριβή επικεντρώνεται σε δύο ερευνητικά προβλήματα που αποτελούν τα αντικείμενα δύο ερευνητικών φάσεων. Στην Α΄ ερευνητική φάση, διάρκειας ενός έτους, ασχολείται με τη διερεύνηση μαθηματικών πρακτικών σε τρεις ομάδες τεχνικών του Οργανισμού Τηλεπικοινωνιών Ελλάδας αναζητώντας παράλληλα την ύπαρξη αμετάβλητων στοιχείων της μαθηματικής επιστήμης τα οποία διαπερνούν την ακαδημαϊκή και την παρούσα εργασιακή κοινότητα. Στη Β΄ ερευνητική φάση, διάρκειας οκτώ μηνών, εξετάζει κάτω και υπό ποιες προϋποθέσεις πέντε σπουδαστές ενός Τεχνολογικού Εκπαιδευτικού Ιδρύματος που πραγματοποιούν την πρακτική τους άσκηση στον ίδιο Οργανισμό είναι σε θέση να αναγνωρίσουν τα αμετάβλητα αυτά στοιχεία. Στην Α΄ ερευνητική φάση η Θεωρία Δραστηριότητας των Vygotsky, Leont’ ev και των συνεχιστών του έργου τους, Engeström & Cole, αποτελεί τη θεωρητική βάση της εργασίας. Τα ερευνητικά δεδομένα προκύπτουν από εθνογραφικής φύσης παρατηρήσεις αλλά και συζητήσεις με τους συμμετέχοντες. Η μαθηματική δραστηριότητα που αναγνωρίσαμε στο χώρο εργασίας ήταν πολύπλοκη και πλούσια αλλά πλήρως ενταγμένη στο πλαίσιο αναφοράς της. Ειδικότερα, αναγνωρίσαμε και ταξινομήσαμε τα μαθηματικά εργαλεία τα οποία διαμεσολαβούσαν στις κεντρικές καθημερινές εργασιακές δραστηριότητες των τεχνικών και αναδείξαμε τους τρόπους με τους οποίους αυτά εμπλέκονταν με τα τεχνικής φύσης εργαλεία τους. Ταυτόχρονα αναγνωρίσαμε αμετάβλητα μαθηματικά στοιχεία στις μαθηματικές έννοιες, στο τρόπο κατανόησής τους από τους τεχνικούς και σε μαθηματικές διαδικασίες που οι ίδιοι χρησιμοποιούσαν για την επίτευξη των εργασιακών τους στόχων. Στην Β΄ ερευνητική φάση τα ερευνητικά δεδομένα προέρχονται από διερευνητικής και παρεμβατικής φύσης συνεντεύξεις με τους σπουδαστές και εθνογραφικές παρατηρήσεις. Μέσα από τις διερευνητικής φύσης συνεντεύξεις καταγράψαμε τις στάσεις των σπουδαστών ως μέλη της σπουδαστικής και της συγκεκριμένης εργασιακής κοινότητας και αναζητήσαμε μαθηματικές πρακτικές που ανέπτυξαν ως μαθητευόμενοι στην παρούσα εργασιακή τους κοινότητα. Οι μαθηματικές πρακτικές που ανέπτυξαν οι σπουδαστές, έστω και ασυνείδητα, είχαν άμεση εξάρτηση από τα εργαλεία και τους εργασιακούς στόχους της κάθε κοινότητας και αφορούσαν την ικανότητα οπτικοποίησης και την ανάγνωση και ερμηνεία σύνθετων οπτικών αναπαραστάσεων. Τέλος, μέσα από μια σειρά παρεμβατικής φύσης συνεντεύξεων αναλύσαμε με εργαλεία σημειωτικής τη δραστηριότητα που ανέπτυξαν οι ίδιοι σπουδαστές στην προσπάθεια ερμηνείας αυθεντικών αναπαραστάσεων με σκοπό τη σύνδεση κοινών μαθηματικών εννοιών που συναντώνται στην ακαδημαϊκή και στην παρούσα εργασιακή κοινότητα. Οι έννοιες αυτές αφορούσαν το θεσιακό σύστημα αρίθμησης και τη συναρτησιακή σχέση αντίστασης, μήκους, διαμέτρου χάλκινων καλωδίων. Καταλήγουμε, καταγράφοντας τα χαρακτηριστικά που προάγουν και αναστέλλουν, τη μεταφορά της γνώσης στο νέο κοινωνικό-πολιτισμικό πλαίσιο. Στο τέλος της διατριβής καταγράφονται και αναλύονται οι εκπαιδευτικές προεκτάσεις της έρευνας. / This dissertation thesis focuses on two different research problems carried out in two research phases. In the first research phase, lasting one year, it focuses on the exploration –identification of mathematical practices of three different groups of technicians of the Greek Telecommunication Organization. In parallel, it investigates the existence of invaried mathematical elements that are crossing the academic and the current workplace community. In the second research face, lasting eight months, it investigates how and whether five students of a Technological Educational Institute who were doing their practicum in this setting could recognize these invariant mathematical elements. In the first research phase, the theoretical framework is guided by Vygotsky and Leont’ev work on Activity theory and their followers, Engeström & Cole. Our data are coming from ethnographic observations and discussions with the participants. The mathematical activity we identified was complex and rich but completely contextual. Especially, we recognized and categorized the mediated mathematical tools in technicians’ central workplace activities and we were showing off how these are interrelated with their physical mediated tools. At the same time we recognized invariant mathematical elements in the category of mathematical concepts, the meanings the technicians attributed to these concepts and in the category of mathematical processes they were using in order to achieve their workplace goals. In the second research phase, our data are coming from eexploratory and intervention interviews with the students and ethnographic observations. In the exploratory interviews we recorded their experiences and their attitudes as members of the academic and the workplace community and we identified mathematical practices they developed as apprentice members of this community. Τhe main mathematical practices the students developed, mainly unconsciously, were attached to the tools and the goals of the workplace community and referring to visualization and reading and interpreting complex visual representations. Finally, through the intervention interviews, we analyzed with the help of semiotic tools the activity the same students developed in order to interpret mathematical objects that are common to the academic and workplace community. The mathematical objects were referring to the place value concept and the functional relation between the resistance, the length and the diameter of the copper wires. In the conclusion, we recorded the characteristics that support and block students’ transfer of knowledge in their new socio-cultural context. In the end of the thesis we discuss and analyze the educational implications of our findings.

The purpose of this study was to determine the relationship between High School learners‟ mathematics-related belief systems and their approaches to mathematics non-routine problem-solving. A mixed methods approach was employed in the study. Survey questionnaires, mathematics problem solving test and interview schedules were the basic instruments used for data collection. The data was presented in form of tables, diagrams, figures, direct and indirect quotes of participants‟ responses and descriptions of learners‟ mathematics related belief systems and their approaches to mathematics problem solving. The basic methods used to analyze the data were thematic analysis (coding, organizing data into descriptive themes, and noting relations between variables), cluster analysis, factor analysis, regression analysis and methodological triangulation. Learners‟ mathematics-related beliefs were grouped into three Learners‟ mathematics-related beliefs were grouped into three categories, according to Daskalogianni and Simpson (2001a)‟s macro-belief systems: utilitarian, systematic and exploratory. A number of learners‟ problem solving strategies were identified, that include unsystematic guess, check and revise; systematic guess, check and revise; trial-and-error; logical reasoning; non-logical reasoning; systematic listing; looking for a pattern; making a model; considering a simple case; using a formula; numeric approach; piece-wise and holistic approaches. A weak positive linear relationship between learners‟ mathematics-related belief systems and their approaches to non-routine problem solving was discovered. It was, also, discovered that learners‟ mathematics-related belief systems could explain their approach to non-routine mathematics problem solving (and vice versa). / Mathematics Education / D.Phil. (Mathematics Education)

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