Abstract
The dissertation focuses on the development of connections between mathematics and visual arts in education within the daily school teaching context. Its goal is to create a community of practice aiming at the integration of mathematics and the visual arts in teaching and learning through the interaction of two communities: the mathematical education community and the visual arts education community. Specifically, it deals with exploring the relationships between mathematics and visual arts as they manifest in the typical school framework, as well as the collaboration of teachers from both fields. A key element in this collaboration is the barriers, or boundaries, that exist between the two communities, and how teachers can overcome them while creating a practice that integrates both fields into teaching and learning. The theoretical background defines the terms: a) integration of art into mathematical education, b) collaboration of teachers from the perspective of communities of pract ...
The dissertation focuses on the development of connections between mathematics and visual arts in education within the daily school teaching context. Its goal is to create a community of practice aiming at the integration of mathematics and the visual arts in teaching and learning through the interaction of two communities: the mathematical education community and the visual arts education community. Specifically, it deals with exploring the relationships between mathematics and visual arts as they manifest in the typical school framework, as well as the collaboration of teachers from both fields. A key element in this collaboration is the barriers, or boundaries, that exist between the two communities, and how teachers can overcome them while creating a practice that integrates both fields into teaching and learning. The theoretical background defines the terms: a) integration of art into mathematical education, b) collaboration of teachers from the perspective of communities of practice, c) boundaries and boundary crossing, and d) the practice of integration based on a), b), and c).Regarding the research methodology, ethnographic approaches were initially used during the course of a school year in two art schools with the aim of: a) familiarizing the researcher with the research context, b) identifying connections and tensions between mathematics and visual arts in relation to how they develop in art classes and how they appear in mathematics classes (e.g., informal mathematical practices, informal tools, informal language, different goals of teachers). The author analyzed data from this initial study and identified mathematical practices used in visual arts classes as well as ways in which these differ from the corresponding mathematical practices in mathematics classes. Later, using data from the initial study, the author selected and developed material that incorporates mathematics with visual arts (e.g., tessellations, linear perspective, costume design) and supported a group of teachers in mathematics and visual arts in each school (due to COVID-19, data collection in one school was interrupted, so only one collaboration group coming from the other school was analyzed). Teachers were asked to go through a phase of familiarization between the two fields, then to design and implement integration activities in their classes, and finally, to reflect on their teaching experiments. Data analysis was conducted through grounded theory methods in combination with the analytical/theoretical framework of the community of practice and boundary crossing. Specifically, three levels of analysis were performed. The first level of analysis produced four basic processes of collaboration among members: facilitating collaboration regarding the cultivation of the community and the regulation of discussion, engaging in the negotiation process with explanations, clarifications, and the expression of positive and negative attitudes and tensions, engaging with resources related to mathematics, art, and their connection, and negotiating of connections between mathematics and art in education, including tensions between them. Within these four basic processes, the author focused on the connections and tensions that arose between the two fields. Subsequently, at the second level, these connections and tensions were analyzed for each mechanism. This analysis revealed a range of connections and tensions related to epistemological dimensions, content and tools of the two fields, teaching, and its transformation, as well as institutional issues such as collaboration among teachers and the importance of the school in supporting integration. Finally, in combination with grounded theory and the theoretical framework, the boundaries indicated by these connections and tensions were analyzed. These boundaries seem to focus on mathematical practices, tools (language and materials), and the curricula of the two fields. At the third level of analysis, the ways in which the members of the collaboration group managed the three central boundaries (analytical or visual thinking, mathematical or aesthetic dimensions, perceptual content gap) were analyzed.The results highlight that the collaboration between mathematics teachers and visual arts teachers, within the context of creating a community of practice, appears to be effective for the integration of mathematics and visual arts in teaching and learning. Regarding the crossing of boundaries and mechanisms of learning, it seems that the key mechanism for teachers is the coordination of ways of thinking and of dimensions (mathematical, aesthetic), as well as bridging the content concerning how one relates to the other. Recognizing whether the two fields are similar or different, coordination, and reflection on the members' perception of each of the two practices, all seem to enhance the transformation of teaching. The creation of integrated practice seems to rely on the process and outcome of teachers becoming familiar with both content areas through negotiating resources, designing integrated tasks, and reflecting on the integration and either reifying it or suggesting ways to improve it. Furthermore, the effectiveness of this integration appears to be linked to facilitating collaboration, maintaining positive attitudes, addressing tensions, becoming familiar with the other practice, sharing resources, recognizing connections and differences, recognizing boundaries, and handling them among group members so they can be transcended.The contribution of the thesis lies in identifying the connections and divergences between the two communities and, more specifically, the boundaries between them. It indicates how managing these boundaries can create learning opportunities for teachers. Thus, it provides a case study of what can happen within such collaboration and presents potential forms and benefits of this integration. Additionally, it combines theoretical perspectives in developing a data analysis tool that allows for the study of the development of the collaboration and the integration, as well as its outcomes. The thesis contributes to the understanding of how mathematics and visual arts teachers can integrate their teaching through collaboration, establishing connections, and overcoming obstacles.
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