Currently, Information and Communication Technology (ICT) is available to almosteveryone. In the last few decades its impact has widely expanded in all fieldsincluding the educational one. There are important attitudinal factors affecting theusage of learning technology successfully. Information system researchers haveidentified the importance of personal factors, such as attitudes, beliefs, culture andbehaviours in technology acceptance (Davis, Bagozzi, & Warshaw, 1992). Previousresearch has analysed these factors in the acceptance of educational technology inhigher education (Liu, Liao, & Pratt, 2009), (Teo, 2009), (Terzis & Economides, 2011),(Cheung & Vogel, 2013). However, the factors playing a role in a mathematicalcontext have not been fully analysed. This research explores the role of several attitudinal factors in the acceptance ofeducational technology for the assessment process in mathematics in a highereducation setting. We examine the effects of formative on-line feedback on theadoption of educational technology by analysing both teachers' and students'opinions regarding enriched formative on-line assessment for mathematics. Ourresults suggest that UK students find on-line feedback is more enjoyable and usefulthan traditional feedback. Attitude and enjoyment are two important factorsinfluencing usage intentions. Results also show that two influential factors to facilitateusing the on-line testing environment are that feeling confident about computers andthe availability of information technology services. In Mexico, findings reveal thatstudents' attitude has the strongest influence on usage intentions which means thattheir feelings and opinions are important. They also think that on-line feedback ismore enjoyable than face-to-face feedback. Students who are proficient in on-linetesting are more likely to find it easy to use. Students also agree that when an on-lineenvironment is easy to use, it is also more likely that they consider it as useful andenjoyable. Taking into account these results can be the best way to design amathematics e-assessment activity for UK and Mexican students. UK instructors agreethat on-line assessments are useful tools to enrich instructional strategies. Teachersin Mexico have a similar opinion. Both results show that they really value providingon-line feedback.

The exploratory study sought to elicit and document mathematics teachers‟ views on how they enacted the process of transition between contexts and mathematics. The study pursued to understand teachers‟ beliefs and knowledge of mathematics. A mixed methods sequential explanatory research design was employed where a quantitative phase was followed by the connecting phase and concluded through a qualitative phase involving three case studies. A purposive sample of 165 practicing teachers who had registered for a professional advancement developmental course at a university participated in the study by voluntarily completing a survey questionnaire. From this sample, three cases of individual teachers were pursued. The first two cases involved conducting in-depth interviews with the teacher who had rated sentences in the questionnaire differently while the last case involved the recording of an interview of one individual using field notes. The questionnaire sought teachers‟ biographical details (section A), their views on contexts and mathematics (section B) and their rating of sentences in a passage with regard to the mathematics embedded in the sentences (section C). Semi-structured interviews were conducted in the qualitative phase to elicit in-depth views of the teachers‟ regarding the research problem. All the instruments were tested for validity and reliability. Quantitative data gathered was analysed using frequencies, percentages, cross tabulations, bar charts and pie charts as well as the calculation of Pearson chi-square tests (Cohen, Manion & Morrison, 2011). Descriptive and inferential statistics were used to collate teachers‟ views from which themes were drawn and related to make inferences. It was found that teachers‟ positive views about contexts and mathematics did not translate into them recognising mathematics in some mathematics potent contexts as captured in their ratings in section C of the questionnaire. Statistically significant associations were recorded to support this. The study also conceptualised a mathematical participation model (MP-model) as a tool to describe and analyse participation that involves the use of real world data in the teaching and learning of mathematics. The MP-model involves four components, viz. the community of practice (CoP), real world data, mathematics and a model in which members of the CoP tap into the real world data and mathematics to model their participation. The study recommends the MP-model as tool for description and enactment of full mathematical participation. / Mathematical Sciences / D.Litt.et. Phil. (Mathematics Education)

Mathematics has been singled out as a challenging discipline to teach fully online (FO). Yet both the demand for and development of FO mathematics courses is increasing with little known about the quality of these courses and many calling for research. Whereas most research has investigated the nature of these courses by examining instructional outputs such as student grades this research seeks the same insight but by examining instructional inputs. Specifically, it seeks to investigate the nature of current assessment practice in FO mathematics courses. To conduct this investigation, deep learning (Marton & S??lj??, 1976a, 1976b) is used as the principle theoretical framework. From the growing body of literature associated with deep learning, two studies are selected to investigate current FO mathematics instructors assessment practices. An additional framework based on empirical findings related to the use of different kinds of feedback is also used. In total, six study measures are used to conduct a mixed methods study in two parts. The target demographic and course context are tertiary instructors from Western nations that teach introductory level mathematics (particularly statistics and calculus). The first study explores current FO mathematics assessment practices using an online survey (n=70) where the majority of participants originate from US higher education institutions. In the second study six of the US survey participants are interviewed about how their assessment practices and approaches used in their FO mathematics courses differ from those used in their face-to-face (F2F) mathematics courses. This study represents the first known attempt to investigate the nature of tertiary FO mathematics instructors assessment practices using appropriate theoretical frameworks. In particular, it investigates mathematics instructors experiences of the affordances and constraints of the FO course context when adapting their F2F practice to this new environment. Findings suggest the FO course context is a challenging environment for instructors to orient their teaching and assessment practice in a way that helps develop students understanding of mathematics. Analysis of interview responses suggests the problem lies with the nature of interactivity provided in the FO course context.

Cette thèse, qui s'inscrit dans une démarche clinique d'orientation psychanalytique en sciences de l'éducation, porte sur le devenir enseignant de mathématiques. Des recherches antérieures ont conduit des chercheurs s'inscrivant dans une telle démarche à qualifier d'« adolescence professionnelle » (Bossard, 2004) le moment du passage d'étudiant à enseignant et à proposer (Blanchard-Laville, 1997) et à mettre au travail (Chaussecourte, 2003, 2014) la notion de transfert didactique pour appréhender des modalités du rapport au savoir dans l'espace de la classe. Dans la lignée de ces travaux, cette thèse se propose de mettre au travail la notion de transfert didactique à travers deux modalités méthodologiques à la conjugaison desquelles elle réfléchit. Il s'agit d'une part d'entretiens cliniques de recherche et d'autre part d'observations cliniques. Ces dernières sont déclinées selon deux formes, l'une « ultra clinique » (Chaussecourte, 2003) et l'autre plus instrumentée (Blanchard-Laville, 1997). Le couplage observation et entretien fait l'objet d'une interrogation méthodologique. Dans cette thèse, les mathématiques sont considérées à la fois comme objet d'enseignement, mais également comme objet potentiellement structurant de l'économie psychique des sujets enseignants de mathématiques. Dans cette optique, la thèse pose la question de la place de la didactique des mathématiques dans une recherche clinique d'orientation psychanalytique. L'étude clinique du matériel nous conduit à proposer et à mobiliser la notion de parentalité psychique interne qui pourraient s'avérer pertinente pour appréhender des modalités du transfert didactique de l'enseignant notamment lors de moments d'insécurité professionnelle (début de carrière, changement d'affectation...). Enfin la sensibilité à ces questions nous semble pouvoir être une piste à prendre en compte en formation d'enseignant notamment par l'intermédiaire de dispositifs d'analyse des pratiques professionnelles. / This thesis, which take place in a clinical approach with a psychoanalytic orientation in the sciences of education, focuses on the future mathematics teacher. Previous research in such an approach has led researchers to describe the time of transfer from student to teacher, as "professional adolescence" (Bossard, 2004) and to propose (Blanchard-Laville, 1997) (Chaussecourte, 2003, 2014) the notion of transfert didactique to apprehend modalities of the relation to knowledge in the space of the class. In line with this work, this thesis proposes to put to work the notion of transfert didactique through two methodological modalities to the conjugation of which it reflects. It is firstly, clinical interviews of research and on the other hand clinical observations. The latter are declined in two forms, one "ultra-clinical" (Chaussecourte, 2003) and the other more instrumented (Blanchard-Laville, 1997). The coupling observation and interview is the subject of a methodological interrogation. In this thesis, mathematics is considered both as an object of instruction and as a potentially structuring object of the psychic economy of mathematics teachers. From this perspective, the thesis raises the question of the place of the didactics of mathematics in a clinical research with a psychoanalytic orientation. The clinical study of the material leads us to propose and to mobilize the notion of parentalité psychique interne professionnelle which could be relevant to apprehend modalities of the didactic transfer of the teacher especially during moments of professional insecurity (Beginning of career, change of assignment'). Finally, the sensitivity to these questions seems to us to be a way to be taken into account in teacher training, in particular through the use of devices for analyzing professional practices.

The study was an investigation into the teaching decisions that mathematics teachers make over time. I view a mathematics classroom as a didactical system of teacher, learners and content within an educational institution, where content is the material that brings teachers and learners together. Within such a system I view the teacher's role as making content available to learners. Prior research has often investigated the teacher's role by comparing teaching practices nationally or internationally, but these comparisons have tended to use the lesson as the unit of analysis. I propose that how teachers make content available can change over the course of a series of lessons and so my study used the lesson series as the unit of analysis. I purposefully designed the study so that it involved four cases, which allowed me to explore the role of the teacher and the topic in how content was made available. To investigate how teachers made content available to learners in each case, I developed an analytical approach from which I could study the modes of teacher interaction that featured across the lesson series, the forms of mathematical content made available and the sequencing of these forms. Attending to forms of content - rather than content itself - allowed for comparison of teaching of different topics. This original analytical approach represents a contribution to both mathematics education and mixed methods research. Within this small sample of cases, quantifiable differences were identified in how content was made available between classwork and seatwork, from lesson to lesson and between cases. Between-case differences in the nature of teaching 'between-the-desks' during seatwork were also identified. These differences illuminated teaching decisions to which teachers and classroom researchers may not routinely attend. The findings therefore contribute - and identify additional lines of enquiry that might contribute further - to a more extensive understanding of teaching practices.

Text in Afrikaans / A study of the philosophical and historical foundations of infinity highlights the problematic development of infinity. Aristotle distinguished between potential and actual infinity, but rejected the latter. Indeed, the interpretation of actual infinity leads to contradictions as seen in the paradoxes of Zeno. It is difficult for a human being to understand actual infinity. Our logical schemes are adapted to finite objects and events. Research shows that students focus primarily on infinity as a dynamic or neverending process. Individuals may have contradictory intuitive thoughts at different times without being aware of cognitive conflict. The intuitive thoughts of students about both the actual (at once) infinite and potential (successive) infinity are very complex. The problematic nature of actual infinity and the contradictory intuitive cognition should be the starting point in the teaching of the concept infinity. / Educational Studies / M.Ed. (Mathematic Education)

L'utilisation du jeu pour les apprentissages n'est pas une idée nouvelle. Cependant, l'étude de jeux à but éducatif montre que les concepteurs de jeux éprouvent des difficultés pour articuler didactique et ludique. C'est à ce niveau que se porte notre réflexion, particulièrement sur les conditions d'une articulation du ludique et du didactique lors du processus de conception d'une ressource. La prise en compte de cette articulation nous a conduit à introduire un nouveau terme jeu-situation désignant cet objet situé entre une situation didactique où les apprentissages sont prioritaires et un jeu où le ludique est prédominant. Notre travail se décompose en deux temps : la conception d'un jeu-situation numérique pour l'apprentissage de l'énumération à l'école maternelle d'une part et l'appropriation de cette ressource par des professeurs d'école maternelle d'autre part.La conception de la ressource repose sur différents cadres théoriques, notamment sur la théorie des situations didactiques. De plus, la conception associe la méthodologie d'ingénierie didactique et de Design-Based Research. Notre étude se poursuit par l'élaboration d'un modèle de conception d'un jeu-situation élaboré autour d'un processus fondamental qu'est l'intégration. Ce modèle est mis à l'épreuve lors de la conception du jeu-situation numérique " A la ferme " pour l'apprentissage de l'énumération à l'école maternelle.Nous abordons, dans un deuxième temps, l'appropriation de ce jeu-situation par des professeurs d'école maternelle. La conceptualisation de la notion d'appropriation s'appuie sur plusieurs domaines : celui de la psychologie de l'environnement et de gestion, celui de la didactique en convoquant notamment l'approche documentaire du didactique. Nous accordons aussi une place importante aux connaissances professionnelles des professeurs qui impactent les processus d'appropriation de ressources. Nous pouvons ainsi présenter un modèle théorique général du concept d'appropriation d'une nouvelle ressource que nous instancions à l'école maternelle et au numérique avec l'outil tablette tactile. L'appropriation est observée à travers trois regards : l'instrumentation, l'instrumentalisation et les orchestrations que nous lions aux connaissances professionnelles / The use of the game for learning is not a new idea. However, the study of educational purpose games shows that game designers have difficulty articulating didactic and ludic. It is at this level that our thinking is focused, especially on the conditions of articulating ludic and didactic during the process of designing a resource. Taking into account this articulation led us to introduce a new term game-situation for this object between a didactic situation where learning is a priority and a game where the ludic is predominant. Our work is divided into two stages: the conception of a digital game-situation for the learning of enumeration skills in the kindergarten on the one hand and the appropriation of this resource by kindergarten teachers, on the other hand. The design of the resource is based on various theoretical frameworks, notably on the theory of didactic situations. In addition, the design combines didactic engineering methodology with Design-Based Research. Our study continues with the development of a model of a game-situation concept based on a fundamental process of integration. This model is tested in the design of the digital game-situation "On the farm" for the learning of enumeration skills in kindergarten. In a second step, we deal with the appropriation of this game-situation by kindergarten teachers. The conceptualisation of the appropriation notion is based on several domains: social and management sciences, didactics by convening in particular the documentary approach to didactics. We also place an emphasis on the professional knowledge of teachers who impact on the processes of resource appropriation. We can thus present a general theoretical model of the concept of appropriation of a new resource that we instantiate in the kindergarten and the digital with the tactile tablet tool. The appropriation is observed through three perspectives: instrumentation, instrumentalization and orchestrations that we link to professional knowledge

H παρούσα εργασία , έγινε στα πλαίσια της Διπλωματικής εργασίας, με θέμα : «Aλγοριθμική επίλυση προβλήματος» Στην εργασία επιχειρείται, η κατάθεση εμπειριών, προβληματισμών και προτάσεων σχετικών με την εισαγωγή και αξιοποίηση Logo περιβάλλοντος στη διδακτική πράξη και συγκεκριμένα του Microworlds pro, με σκοπό την ανάδειξη σημαντικών πτυχών της σχεδίασης, ανάπτυξης, εφαρμογής και αξιολόγησης εκπαιδευτικών σεναρίων και δραστηριοτήτων, στο πλαίσιο της αποτελεσματικής ένταξης των εκπαιδευτικών λογισμικών, στη διδακτική της Πληροφορικής. Η διαδικασία που ακολουθεί περιλαμβάνει τρία βήματα: α) δημιουργία κινήτρου, β) οικοδόμηση της γνώσης μέσω της διερεύνησης και συνεργασίας, γ) εφαρμογή-αναδόμηση της γνώσης. Σκοπός των μαθημάτων, που πραγματοποιήθηκαν σε μαθητές της Γ΄ Γυμνασίου, ήταν να αποκτήσουν οι μαθητές ,ευχέρεια στη χρήση συμβολικών μέσων έκφρασης, για την αναπαράσταση της διαδικασίας επίλυσης προβλημάτων, να αναπτύξουν αναλυτική συνθετική σκέψη και να ασκηθούν στα βασικά δομικά στοιχεία και τις έννοιες του προγραμματισμού. Στόχος, δεν ήταν να μάθουν μια γλώσσα προγραμματισμού, αλλά να κατανοήσουν την έννοια του Αλγόριθμου, δηλαδή ,να μπορούν να αναλύσουν ένα απλό πρόβλημα σε ακολουθία σαφώς ορισμένων και πεπερασμένων βημάτων. / The present work , became in the frames of Diplomatic work, on the subject: " Algorithmic resolution of problem " In the work is attempted, the deposit of experiences, reflections and proposals relative with the import and exploitation Reason of environment in the instructive practice and concretely the Microworlds prο, aiming at the appointment of important aspects of designing, growth, application and evaluation of educational scripts and activities, in the frame of effective integration of educational softwares, in the didactics of Information technology. The process that follows includes three steps: a) creation of motive, v) construction of knowledge via the investigation and collaboration, c) application of knowledge. Aim of courses, that were realised in students of c class, of High school, was acquires the students, occasion in the use of symbolic means of expression, for the representation of process of resolution of problems, to develop analytic synthetic thought and to practise itself in the basic structural elements and the significances of planning. Objective, was not they learn a language of planning, but they comprehend the significance of Algorithm, that is to say, they can analyze a simple problem in sequence of course certain and finite steps.

Text in Afrikaans / A study of the philosophical and historical foundations of infinity highlights the problematic development of infinity. Aristotle distinguished between potential and actual infinity, but rejected the latter. Indeed, the interpretation of actual infinity leads to contradictions as seen in the paradoxes of Zeno. It is difficult for a human being to understand actual infinity. Our logical schemes are adapted to finite objects and events. Research shows that students focus primarily on infinity as a dynamic or neverending process. Individuals may have contradictory intuitive thoughts at different times without being aware of cognitive conflict. The intuitive thoughts of students about both the actual (at once) infinite and potential (successive) infinity are very complex. The problematic nature of actual infinity and the contradictory intuitive cognition should be the starting point in the teaching of the concept infinity. / Educational Studies / M.Ed. (Mathematic Education)

L’objet de notre étude porte sur la logique et le langage à la transition entre le lycée et l’université dans le contexte camerounais. Au Cameroun, dans l’enseignement secondaire, les concepts de logique sont très peu explicités en classe de mathématiques, du fait que leur enseignement n’est pas prescrit par les nouveaux programmes1 officiels. Ce n’est pas le cas de l’enseignement supérieur où un cours de logique formelle sous forme de rappel, est souvent donné en début d’année. Ce cours n’est pas prescrit par les programmes, mais certains enseignants en voient la nécessité. Les résultats de plusieurs travaux ont montré que certaines des difficultés que les étudiants rencontrent dans la pratique des mathématiques proviennent d’une mauvaise maîtrise des concepts de logique. Nous faisons l’hypothèse qu’ils sont insuffisamment pris en charge pa rles enseignants dans la classe de mathématiques, qui pensent qu’ils sont disponibles chez les étudiants, du fait de leur utilisation dans la vie courante d’une part, et progressivement dans l’activité mathématique. La thèse que nous soutenons est que, pour rendre opératoire les concepts de logique chez lesétudiants nouvellement arrivés à l’université, un minimum d’explicitation de ces concepts en relation avec leur usage dans l’activité mathématique est nécessaire pour les apprentissages en mathématiques à tout le moins dans l’enseignement supérieur. Pour défendre notre thèse, nous avons divisé notre travail en deux parties. Dans la première partie, nous présentons des éléments théoriques et analytiques nécessaires à notre travail, et une revue des travaux antérieurs en relation avec notre problématique. La deuxième partie porte sur les résultats d’une expérimentation que nous avons menée avec des élèves de terminale C d’un lycée de Yaoundé 2, et des étudiants de première année de licence de mathématiques de l’Ecole Normale Supérieure de Yaoundé. Elle s’est déroulée en deux temps : nous avons fait passer un questionnaire portant sur la logique et le langage aux élèves et aux étudiants, et à la suite de ce questionnaire, nous avons organisé un module de suivi avec huit étudiants ayant passé ce questionnaire. Le questionnaire nous a permis de repérer certaines conceptions des élèves et des étudiants concernant les concepts de logique,et le module de suivi a permis de provoquer des débats qui permettaient dans certains cas d’affiner nos analyses et nous donnaient des éléments permettant d’identifier des occasions pour expliciter certaines notions. / Our study focuses on logic and language at the transition between high school and university in the Cameroonian context. In Cameroon secondary education, the concepts of logic are paid little attention in mathematics classes, due to the fact that their teaching is not prescribed in the new official syllabuses3. This is not the case of higher education, where a course on formal logic is oftengiven at the beginning of the year to first year university students, with a refreshing purpose. That course is not required in the syllabus, but some teachers see the need. Several scientific studies have shown that some of the difficulties encountered by studentswhile practicing mathematics come from their poor familiarity with concepts of logic. We assume that these students are insufficiently attended to by their teachers who think that the concepts are at their reach, since they are used in everyday life on the one hand, and they are gradually used in mathematical activities, on the other hand. In this thesis, we stand for the point that, for the concepts of logic to become real operational tools to a student who begins university studies, some teaching of these concepts which should address the connections with mathematical activities is necessary, at least as a starting point in higher education studies. To defend our thesis, we have divided our work into two parts which are as follows : In the first part, we present theoretical material necessary to our work as well as other technical tools that will be needed. We also provide a review of previous studies related to our issue. The second part is on an experiment we carried out with students from the Upper Sixth class - science option - of a high school in Yaoundé (Cameroon), and with first year university students of mathematics of the Yaoundé Higher Teachers’ Training College. This experiment had two stages : Firstly, the high school students and the university students filled out a questionnaire on logic and language. Following this, we organized a follow-up module involving 8 students purposely selected from their answers to the questionnaire. This questionnaire enabled us to detect meaningful points on how high school and university students grasp the concepts of logic, and the module helped to start debates which enabled in some cases to refine our analysis, and also provided us with strategic approaches forexplaining certain concepts of logic.