This study examines how undergraduate students use hand gestures to offload cognitive demands on their working memory (WM) when they are engaged in three major proving activities: reading, presenting, and constructing proofs of mathematical conjectures. Existing research literature on the role of gesturing in cognitive offloading has been limited to the context of elementary mathematics but has shown promise for extension to the college level. My framework weaves together theoretical constructs from mathematics education and cognitive psychology: gestures, WM, and mathematical proofs. Piagetian and embodied perspectives allow for the integration of these constructs through positioning bodily activity at the core of human cognition. This framework is operationalized through the methodology for measuring cognitive demands of proofs, which is used to identify the set of mental schemes that are activated simultaneously, as well as the places of potential cognitive overload. The data examined in this dissertation includes individual clinical interviews with six undergraduate students enrolled in different sections of the Introduction to Proofs course in Fall 2021 and Spring 2022. Each student participated in seven interviews: two WM assessments, three proofs-based interviews, a stimulated recall interview (SRI), and post-interview assessments. In total, 42 interviews were conducted. The participants' hand gesturing and mathematical reasoning were qualitatively analyzed. Ultimately, students' reflections during SRIs helped me triangulate the initial data findings. The findings suggest that, in absence of other forms of offloading, hand gesturing may become a convenient, powerful, although not an exclusive offloading mechanism: several participants employed alternative mental strategies in overcoming the cognitive overload they experienced. To better understand what constitutes the essence of cognitive offloading via hand gesturing, I propose a typology of offloading gestures. This typology differs from the existing classification schemes by capturing the cognitive nuances of hand gestures rather than reflecting their mechanical characteristics or the underlying mathematical content. Employing the emerged typology, I then show that cognitive offloading takes different forms when students read or construct proofs, and when they present proofs to the interviewer. Finally, I report on some WM-related issues in presenting and constructing proofs that can be attributed to the potential side effects of mathematical chunking. The dissertation concludes with a discussion of the limitations and practical implications of this project, as well as foreshadowing the avenues for future research. / Doctor of Philosophy / In this study, I examined how undergraduate students can rely on their hand gesturing to reduce the cognitive complexity of mathematical proofs. Specifically, I studied gestures produced by students when they are engaged in various kinds of proving activities: reading for comprehension, reading for validation, presenting, and constructing proofs of mathematical conjectures. During the experiments, the participants were not given pencils/paper, calculators, or any other and other figurative materials. Therefore, they had to rely on their imagination, working memory, and hand gestures to make progress on the tasks. Results suggest that students' hand gestures have a beneficial effect in navigating cognitive challenges associated with mathematical proofs. Moreover, I show that this effect takes different forms depending on the proving activity in which the student engages. Finally, I report on some memory-related issues in presenting and constructing proofs. The dissertation concludes with a discussion of the limitations and practical implications of this project, as well as foreshadowing the avenues for future research.

Corpographies en Danse est une recherche complexe et « indisciplinée ». Développée entre les domaines de la Science de l'information et des Sciences du langage,l'investigation se lie fortement aussi au terrain de la Danse et s'appuie, principalement,pour des fondements philosophiques, débordant et conjuguant donc, différentes frontières disciplinaires. Cette trame théorique est développée afin de rendre visible la présupposition qui déplace notre quête, que ce soit: l'hypothèse que le corps éprouve,sensiblement, l'information et qu’à travers la gestualité nous pouvons mettre en évidence cette relation sous-jacente. Ainsi le début de notre argumentation est orienté par une réflexion philosophique sur le corps, en vue de souligner la complexité de notre objet principal et également, de proposer une approche qui réfléchit ce corps en communion constante avec le monde. Nous nous référons à l´ontologie de la chair chez Merleau-Ponty, que nous plaçons à l’arrière-plan du jeu entre les éléments que nous avons mis en lumière afin d’intégrer et composer le tracé souhaité. Parmi ces éléments,l’information est le premier à être déployé, révélant ses aspects sensibles et qualitatifs qui seront appelés infosignes. Dans cette direction, l’information trouve son devant et son envers, son visible et son invisible, et avant tout elle devient puissance, qui doit être actualisée devant un corps qui est son dispositif. Ensuite, le geste est révisé dans une revue de littérature qui va de l’anthropologie et la philosophie à la perspective somatique et la danse. Face à ce qui est présenté, le geste est saisi en tant que médialité pure, ayant dans la gestualité son côté le plus apparent. Quant à l’approche sur le terrain de la danse, nous proposons un bref panorama historique qui inclut l’émergence de la danse moderne au tournant du XXe siècle. Partant du schéma de François Delsarte qui cherchait à indiquer les associations entre les gestes et les émotions humaines, nous avons examiné quelques réflexions artistiques parmi lesquelles on peut souligner les systèmes élaborés par Rudolf Laban, qui nous serviront partiellement dans les analyses.De ce point de vue nous appréhendons l’improvisation en danse comme un exercice créatif capable de provoquer l’agencement des altérités imaginaires qui peuvent pointer le caractère sensoriel et émotif de l’information. De là nous nous questionnons les spatialités, ici centrées sur le corps. Intervient alors la notion de corpographie, à partir du point de vue de Britto et Jacques, d’où est avancée une conception du lieu, de l’espace et de l’ambiance - à des fins analytiques – comme des temps distincts de l’expérience corporelle dans l’entité physique. A partir de cette cartographie théorique nous passons à l’analyse des corpographies en danse, qui constituent notre objet empirique. Pour cela nous avons créé une méthodologie de recherche dans laquelle desdanseurs volontaires de plusieurs parties de l’Amérique du Sud et de l’Europe ontenregistré des vidéos d’improvisation en danse, dans des espaces publics, avec des consignes données en préalable. Le travail développé comprend l’information, le geste et l’espace comme des éléments d’une seule chair qui opèrent en synergie et pour lesquels il faut déterminer un méta-point de vue, qui permet de les déployer et de les conjuguer.L’apport de notre recherche apparaît dans le traçage d’une ligne invisible de sens entre l’information et la gestualité, qui suscite déjà son désassemblage dans le corps, toujours en mouvement continu. / Bodygraphies in Dancing is a complex and “undisciplined” investigation. It has been developed in between the fields of Information Sciences and Language Sciences, and it hasbeen deeply rooted to the Dance Field and is essencially fundamented by philosophical grounds, conjugating therefore distinct disciplinary boundaries. Such theoretical weave isdeveloped in order to make visible the presumptions that move our issues, which are: the hypothesis that the body experiments information quite much, and that gestures make thissubjacent relation evident. The principle of our argumentation goes somewhat around the philosophical reflection about the body so as to point out the complexity of our main research object and to equally suggest an approach which considers it in constant communion with the world. This way we investigate the onthology of the flesh by Merleau-Ponty to make it the background for the game among the elements we point out to integrate and shape up the desired design. Among such elements, information is the fisrt one to be unfolded, unraveling its sensitive and qualitative aspects which will be named infosigns. In such verticalization, information gets its right side and its inside out, its visible and its invisible sides, and above all, it becomes potency, to be updated before a body which is its trigger. Further on, the gesture comes to be revised with views of a literature that ranges from antropology and philosophy to the somatic perspective and the dance. Due to what is presented, it is taken as pure mediality and has in gesturing its most aparent side. Concerning the dance field approach, we promote brief retrospective which compromises the urge of modern dance at the turn of the 19th to the 20th century. Having François Delsarte’s schematic as a starting point, who attempted to show associations between gestures and human emotions, we glide through some artistic reflections such as the systems elaborated by Rudolf Laban, the most outstanding ones, which are important references ground to our analysis demands. From that being done we could consolidate our understanding of improvisation in the dance, as a creative exercise able to provoke the acting of imaginary alterities which may point to the sensorial and emotional character of information. We have therefore dedicated ourselves to the debate over the spacialities which are here focused in the body. In such scope, the notion of bodygraphy has been included – under Jacques and Britto’s points of view – and from this notion, our conceptions of place, space and ambience – elaborated for analytical ends - have also been included, as distinct times of the bodily experience in the physical entity. Up to this point, we conclude our research cartography and go towards the analysis of our bodygraphs in dancing, which conform with our empiric objective. With that in mind, a research methodology was developed in which volunteer dancers from various parts of America and Europe made videos of dance improvisation in public spaces according to previous orientation. That way the elaborated work encompasses the information, the body, the gesture and the space as elements of the same flesh which operate in sinergy and demand a complex point of view that can unfold, tighten and conjugate them. Such efforts and contributions of this research design an invisible thread of sense between information and gesturing which untangles as it is built since the body is an ever moving (meaningful) entity.

There is an increase in Hispanic English Language Learners (ELL). Poverty levels and lack of teacher training can also be stacked against the ELL population. Gesturing is a teaching technique that is used in successful methods such as The Natural Approach (NA) and Total Physical Response (TPR) in helping ELL students in English comprehension and output. This study examined the effects that increased teacher gestures have on the number of words spoken by the child in multiple settings. Data were collected in the context of a multiple baseline design across three settings. The results indicate that there was an effect on the amount of words spoken in two out of three settings. Suggestions are presented to expand on this effect.

The purpose of this project is to argue that we possess a minimal self. It will demonstrate that minimal selfhood arrives early in our development and continues to remain and influence us throughout our entire life. There are two areas of research which shape my understanding of the minimal self: phenomenology and enactivism. Phenomenology emphasizes the sense of givenness, ownership, or mineness that accompanies all of our experiences. Enactivism says there is a sensorimotor coupling that occurs between us and the environment in a way which modulates the dynamic patterns of our self development; the laying down of these basic patterns helps make us who we are and gives rise to the phenomenological, experiential mineness. Drawing on these two core ideas, I will be arguing for a Phenomenological-Enactive Minimal Self (abbreviated PEMS). I will be emphasizing the role of the body and the role of affects (moods, feelings, and emotions) as the most important components relevant to understanding minimal selfhood. Put more concretely, the set of conditions which constitute the PEMS view are: (i) The minimal self is the experiential subject; the minimal sense of self is present whenever there is awareness. It is the subjectivity of experience, the sense of mineness, or givenness which our experiences contain. (ii) The phenomenological part of the PEMS view turns on the idea of a bodily and dynamic integration of sensorimotor coupling and affective experience. It is, ontologically speaking, the lived body in enactive engagement with the environment. It is this embodied subject which anchors and forms the foundation for the later ‘narrative' self, which emerges from it and which is continually influenced by it. It is the subject enactively engaged with others, dependent on sensorimotor processes and affects. We have an identity, but it emerges from relational and dynamic processes.