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Le but de cette thèse était d’étudier le développement de la catégorisation des expressions faciales émotionnelles chez les enfants francophones à l’aide de deux tâches de jugement: l’étiquetage verbal (étude 1) et le jugement à choix forcés (étude 2). Le modèle théorique ayant guidé les études était celui proposé par Widen et Russell (2003, 2010). Les résultats de la première étude ont montré une très forte correspondance entre la séquence d’utilisation des catégories émotionnelles et celle prédite par le modèle de Widen et Russell. De plus, les résultats ont généralement appuyé les prédictions du modèle en ce qui concerne les profils de développement se rapportant à l’exactitude des jugements et à la fréquence d’utilisation et l’extension des catégories émotionnelles. Enfin, la première étude a permis de recueillir des informations sur le lexique émotionnel des enfants francophones, ce qu’aucune étude antérieure n’avait fait à notre connaissance. La deuxième étude visait à vérifier si le modèle de Widen et Russell décrivait bien l’utilisation des catégories émotionnelles dans la tâche de jugement à choix forcés. Les résultats ont montré que la performance des participants était supérieure au hasard dès 3 ans et, que conformément aux prédictions, elle augmentait pour chacune des six expressions entre 3 et 8 ans. Comme le prévoyait le modèle, le nombre de catégories émotionnelles utilisées par les enfants a augmenté en fonction de l’âge. L’utilisation des catégories de joie, tristesse et colère a diminué en fonction de l’âge alors que l’utilisation des catégories de peur, surprise et tristesse a augmenté. Cependant, les prédictions du modèle en rapport avec l’extension des catégories émotionnelles n’ont été que partiellement appuyées, puisque l’extension des catégories avait tendance à diminuer entre 3 et 8 ans seulement dans le cas de la joie et de la colère. Enfin, les résultats de la deuxième étude n’ont pas appuyé la séquence d’utilisation des catégories émotionnelles prédite par le modèle.

Bien que de nombreuses études aient examiné le décodage des expressions faciales émotionnelles, un débat subsiste toujours concernant la nature de l’information véhiculée par le visage. Parmi les approches théoriques qui se démarquent actuellement, figure le modèle des processus composants (MPC) élaboré par Scherer (1984, 1992, 2001). Ce chercheur soutient que les expressions faciales transmettent de l’information allant au-delà d’une simple catégorie émotionnelle et que les décodeurs seraient en mesure d’interpréter celles-ci en termes d’évaluations cognitives. D’après ce qui a été observé dans l’étude de Scherer et Grandjean (2008), les inférences basées sur les évaluations cognitives mèneraient à une reconnaissance se comparant en exactitude à celle obtenue avec les catégories émotionnelles. Néanmoins, il existe encore peu de données empiriques offrant un appui à ces conclusions. Cette thèse a donc comme objectif d’examiner les propositions théoriques de Scherer relativement au décodage du comportement expressif facial. Pour ce faire, nous proposons une série de trois études menées à l’aide d’une tâche de jugement et utilisant des photographies d’expressions faciales. Dans la première étude, nous avons répliqué une partie de celle de Scherer et Grandjean en y apportant certaines améliorations méthodologiques. Les pourcentages d’exactitude élevés obtenus valident ceux de l’étude originale et confirment la capacité des décodeurs à inférer les évaluations cognitives à partir du visage. Certaines divergences, en ce qui a trait à la justesse du jugement en fonction du type d’émotion, ont toutefois été observées. Lors de la seconde étude, nous avons repris la même tâche en créant deux conditions distinctes permettant d’évaluer l’impact du niveau d’abstraction des évaluations proposées sur la performance. Les résultats indiquent que les participants sont en mesure d’inférer l’évaluation cognitive avec un taux de réussite élevé, et ce, peu importe le niveau d’abstraction, offrant ainsi un appui additionnel au MPC. En outre, cette étude nous a également permis d’observer des patrons de reconnaissance similaires à ceux de l’étude 1 relativement aux types d’émotions présentées. Dans le cadre de la troisième et dernière étude, nous avons poussé plus loin la validation des prédictions du MPC en examinant spécifiquement si le décodeur est en mesure de reconnaitre les évaluations cognitives communiquées par diverses unités d’action faciales individuelles, et si certaines d’entre elles semblent posséder une valeur signalétique plus puissante ou distincte. Une tâche de jugement dans laquelle les participants ont évalué, sur une échelle d’intensité, l’adéquation entre l’unité d’action observée dans l’image et les cinq énoncés représentant les critères d’évaluation majeurs du MPC, a finalement été utilisée pour tester cet objectif. Nous avons ainsi pu constater l’aptitude du décodeur à identifier de l’information relevant de la composante cognitive sur la base de certains mouvements faciaux pris isolément, attestant de la valeur signalétique intrinsèque des unités d’action dans le processus d’interprétation des visages telle que postulée au sein du modèle de Scherer.

This study is an investigation into school students' productive struggles in the simplification of trigonometric expressions and proving of trigonometric identities. Although studies have been published on the teaching and learning of trigonometrical concepts in schools and teacher education, there is a lack of published research into students' productive struggles in the simplification of trigonometric expressions and proving of trigonometric identities. To fill this gap in the literature, this study used a sample of 16- and 17-year-old students at a rural high school in South Carolina in the United States of America to conduct a study on the use of productive struggles in the simplification of trigonometric expressions and the proving of trigonometric identities. The study used the Anthropological Theory of the Didactic by Chevallard (1992) as the main theoretical framework. However, this main framework was supported by other frameworks. The Anthropological Theory of the Didactic contends that mathematical activities such as simplifying trigonometric expressions and proving trigonometric identities must be interpreted as a human activity rather than seeing these mathematical activities as a language, the creation of concepts (for example, “simplification” or “proof”) or a cognitive process. A praxeology consists of two parts, namely (in Greek) the praxis, or “know how”, and the logos, or “know why”. The praxis is commonly known as the practical block, and the logos the theoretical block. This means that the Anthropological Theory of the Didactic can be used to describe how certain actions regarding the simplification of trigonometric expressions and proving of trigonometric identities take place, and why these actions take place. The exercises in the activities were obtained and adapted from the students' prescribed textbook. These activity questions were sequenced using the Development Cognitive Abilities Test (DCAT). The DCAT reflects Bloom's (1956) hierarchy of cognitive abilities. This means that the exercises were organised in three groups of increasing complexity, i.e., easy, medium, and difficult. The easy exercises related to the DCAT's Basic Cognitive Abilities, referred to as DCAT 1; the medium exercises related to Application Abilities, referred to as DCAT 2; and the difficult exercises related to Critical Thinking Abilities, referred to as DCAT 3. The data in this study consists of video recordings from classroom observations in real time transcribed verbatim, documentary analysis of students' assessments, and audio-recorded focus group interviews. The focus group interviews were also transcribed verbatim. Each transcription focused on a different aspect of the students' productive struggles in the simplification of trigonometric expression and the proving of trigonometric identities. Errors made by the students in written assessments were analysed using the Newman Error Analysis framework. By using Newman Error Analysis, this study could investigate and compare how the errors on the assessments were related to the students' struggles as observed during the teaching and learning of the activity questions. Due to Co-Vid 19 restrictions that resulted in logistical difficulties, only one class of 15 students participated in this study. After listening to the focus group recordings numerous times and reading the transcripts, common patterns were noted that had emerged, either from paraphrasing or from direct quotes. The primary research question is: What is the nature of the productive struggles experienced by high-school students during the simplification of trigonometric expressions and proving of trigonometric identities and how do these productive struggles influence the learning and teaching of trigonometry? The study findings were that the students struggled with “carrying out known mathematical processes” such as manipulating equations, knowing under what conditions cancellation of terms can be applied, adding and subtracting algebraic fractions involving trigonometric expressions, and factorisation of trigonometric expressions. In addition, there were misconceptions about the concept of “simplification”. Delayed impasse struggles occurred; this is when a student does not initially struggle to get started with a question, but the struggling becomes apparent as the student progresses with the question. The students committed fewer Newman errors in proving trigonometric identities than in the simplification of trigonometric expressions. Subsequently, students performed better at proving trigonometric identities than at simplifying trigonometric expressions. It could well be that through productive struggles, the students developed some of their own strategies from the simplification of trigonometric expressions. Alternatively, proving identities could be seen as “easier”, since the students already know what the “answer” should be. Nonetheless, students still struggled to carry out common mathematical processes such as factorisation and the manipulation of algebraic fractions. Regarding factorisation and manipulation of algebraic fractions, students compartmentalised knowledge. For example, most students knew how to factorise algebraic expressions, but failed to see the resemblance between algebraic expressions and trigonometric expressions (and consequently, how to factorise trigonometric expressions). Although there was a decrease in the number of Newman errors from the simplification of trigonometric expressions to the proving of trigonometric identities, there was an increase at the comprehension hierarchy, which may be attributed to the fact that the students might have struggled with the concept of “proof”. Additionally, students in this study struggled with the concept of “simpler”. Some students thought that the solution to a simplification question should be more complex than the original question. Nonetheless, with both the simplification of trigonometric expressions and the proving of trigonometric identities it remained a challenge for the students to apply prior knowledge in a new mathematical context such as trigonometry. The significance of the study's findings is that they suggest that teachers re-evaluate how to instruct known mathematical processes and procedures, so as not to compartmentalise mathematical knowledge. Productive struggles may not always produce correct answers; but given sufficient time and appropriate intervention by their teacher, students can build their own knowledge and become independent thinkers who can apply prior knowledge in new contexts such as the simplification of trigonometric expressions and the proving of trigonometric identities. In future research, productive struggles in the simplification of trigonometric expressions and the proving of trigonometric identities should be explored with a bigger, more diverse group of students, taught by more than one teacher at more than one school. In addition, to investigate the long-term effects of productive struggles a study lasting more than six months could be carried out.

In our setting, verification is a process that checks whether a device's program (implementation) has been produced according to its corresponding requirements specification. Ideally a client builds the requirements specification of a program and asks a developer to produce the actual program according to the requirements specification it provides. After the program is built, a verifier is asked to verify the program. However, nowadays verification methods usually require good knowledge of the program to be verified and thus sensitive information about the program itself can be easily leaked during the process. In this thesis, we come up with the notion of secure and trusted verification which allows the developer to hide non-disclosed information about the program from the verifier during the verification process and a third party to check the correctness of the verification result. Moreover, we formally study the mutual trust between the verifier and the developer and define the above notion in the context of both an honest and a malicious developer. Besides, we implement the notion above both in the setting of an honest and a malicious developer using cryptographic primitives and tabular expressions. Our construction allows the developer to hide the modules of a program and the verifier to do some-what white box verification. The security properties of the implementation are also formally discussed and strong security results are proved to be achieved. / Thesis / Master of Science (MSc)

The interview is an important component of the selection process for employment and is one of the initial presentations of self by the applicant to the interviewer. As an extension of a study by Wilson, Aleman, and Leatham (1998), this study used politeness theory to investigate perception of face threat in the context of a job interview, specifically, when making requests and giving advice. This study predicted that jobseekers perceive an act as a greater threat to an interviewer’s negative face (appealing to interviewer’s autonomy) when making a request than when giving advice. Secondly, the study predicted that job seekers would perceive an act as greater threat to the interviewer’s positive face (appealing to the interviewer’s desire for approval) when giving advice or recommendations than when making a request. Both hypotheses were supported and other related interests such as acceptability of the act and likelihood of getting the job were also investigated. / text

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