Data Structures and Algorithms (DSA) courses are critical for any computer science curriculum. DSA courses emphasize concepts related to procedural dynamics and Algorithm Analysis (AA). These concepts are hard for students to grasp when conveyed using traditional textbook material relying on text and static images. Algorithm Visualizations (AVs) emerged as a technique for conveying DSA concepts using interactive visual representations. Historically, AVs have dealt with portraying algorithm dynamics, and the AV developer community has decades of successful experience with this. But there exist few visualizations to present algorithm analysis concepts. This content is typically still conveyed using text and static images. We have devised an approach that we term Algorithm Analysis Visualizations (AAVs), capable of conveying AA concepts visually. In AAVs, analysis is presented as a series of slides where each statement of the explanation is connected to visuals that support the sentence. We developed a pool of AAVs targeting the basic concepts of AA. We also developed AAVs for basic sorting algorithms, providing a concrete depiction about how the running time analysis of these algorithms can be calculated. To evaluate AAVs, we conducted a quasi-experiment across two offerings of CS3114 at Virginia Tech. By analyzing OpenDSA student interaction logs, we found that intervention group students spent significantly more time viewing the material as compared to control group students who used traditional textual content. Intervention group students gave positive feedback regarding the usefulness of AAVs to help them understand the AA concepts presented in the course. In addition, intervention group students demonstrated better performance than control group students on the AA part of the final exam. The final exam taken by both the control and intervention groups was based on a pilot version of the Algorithm Analysis Concept Inventory (AACI) that was developed to target fundamental AA concepts and probe students' misconceptions about these concepts. The pilot AACI was developed using a Delphi process involving a group of DSA instructors, and was shown to be a valid and reliable instrument to gauge students' understanding of the basic AA topics. / Ph. D. / Data Structures and Algorithms (DSA) courses are critical for any computer science curriculum. DSA courses emphasize concepts related to how an algorithm works and the time and space needed by the algorithm, also known as Algorithm Analysis (AA). These concepts are hard for students to grasp when conveyed using traditional textbook material relying on text and static images. Algorithm Visualizations (AVs) emerged as a technique for conveying DSA concepts using interactive visual representations. Historically, AVs have dealt with portraying how an algorithm works, and the AV developer community has decades of successful experience with this. But there exist few visualizations to present concepts related to algorithm efficiency. This content is typically still conveyed using text and static images. We have devised an approach that we term Algorithm Analysis Visualizations (AAVs), capable of conveying efficiency analysis concepts visually. In AAVs, analysis is presented as a series of slides where each statement of the explanation is connected to visuals that support the sentence. AAVs were tested through a study across two offerings of CS3114 at Virginia Tech. We found that students using AAVs spent significantly more time viewing the material as compared to students who used traditional textual content. Students gave positive feedback regarding the usefulness of AAVs to help them understand the efficiency concepts presented in the course. In addition, students using AAVs demonstrated better performance than students using text on the efficiency part of the final exam. The final exam was based on a pilot version of the Algorithm Analysis Concept Inventory (AACI) that was developed to target fundamental efficiency concepts and probe students’ misconceptions about these concepts. The pilot AACI was developed through a decision making technique involving a group of DSA instructors, and was shown to be a valid and reliable instrument to gauge students’ understanding of the basic efficiency topics.

La thèse met en lumière les conditions d’enseignement et d’apprentissage des mathématiques en langue seconde en étudiant avec précision l’articulation des savoirs mathématiques et des savoirs linguistiques. Elle traite le cas spécifique de l’enseignement des mathématiques en anglais dans un contexte CLIL et les séances expérimentales ont lieu en classes européennes de lycée. Le thème commun à ces séances est celui des preuves visuelles et multimodales. La Théorie des Situations Didactiques (TSD) offre un cadre théorique privilégié – notamment pour la construction des situations expérimentales - cadre qu’il a fallu compléter par des approches théoriques sémiotiques et linguistiques. Ainsi l’approche adoptée s’est révélée en adéquation avec la perspective actionnelle et la phraséodidactique a apporté de nombreux éléments permettant de mettre en relief le rôle de la phraséologie dans un enseignement intégré. Une focalisation particulière a dû être opérée sur les objets mathématiques et les processus d’abstraction mais aussi sur certains faits de langue. Les investigations ont permis d’affiner les descriptions des raisonnements produits tout en conservant une référence aux niveaux de milieux, au sens de la TSD. L’étude a nécessité de développer le concept de représentation et de décliner les représentations produites dans le contexte de la L2. Ce sont ces concepts et celui d’adidacticité, central dans la TSD, qui ont permis d’organiser les séances de manière optimale, en faisant apparaître le rôle essentiel joué par la perception active dans les processus de conceptualisation. / The purpose of this thesis is to investigate learning and teaching conditions of mathematics in English as a second language by closely examining how mathematical and language knowledge can fit together. This study deals with the specific case of CLIL teaching and the related experimental situations are performed in European classes in a French high school. The situations have a common topic, namely that of visual and multimodal proof. The theory of Didactical Situations is the central theoretical framework but our study has proven to be compatible with task-based pedagogy. Besides, phraseodidactics provided a useful and adequate auxiliary framework by shedding some light onto the essential role played by4phraseology. We particularly kept focused on mathematical objects and processes of abstraction but also on some specific language features. The concept of representation is central in our research works and thus had to be precisely defined. The success of our experimental situations owes a lot to the use of adidacticity, a central concept in TSD, and our focusing on the crucial part played by active perception during processes of conceptualisation. The purpose of one of the experimental situations (conducted in a second language) was to ensure that pupils divised, by themselves, a visual proof of an arithmetic property previously conjectured, carried out on the very level of schematisation an explicit generalisation and used real cubes to perform another type of proof, thus making the inductive step of the induction explicit.

The dissertation is divided into two main parts. The first part defines the concept of dynamic visual proof and is placed in the context of proving in mathematics as a subject of science and in mathematics as a subject taught at school. The digital component of the dissertation is a collection of 19 applets with dynamic visual proofs created in the GeoGebra program and arranged in thematic chapters in the so-called GeoGebra-Book, available on-line on geogebra.org. In the second part of the work the research focused on the use of dynamic visual proofs in secondary school mathematics lessons and their influence on fulfilment of educational objectives is described. This a qualitative research where a case study focused on the detailed study of a mathematics teacher who uses dynamic visual proofs in her class. To identify educational objectives, a revised Bloom's taxonomy was chosen.