Mooney, Claire

Spatial reasoning and spatial structures are relatively new areas of research in mathematics education. In this study of children exploring spatial conceptions of grid structures, twenty-one children (ages 4-9) were given a series of tasks involving square grids during virtual interviews. As a result of an ideal-type analysis of the qualitative data, a typology of conceptions of grids emerged showing five distinct categories sequenced from very early conceptions of square grids (as a series of isolated cells) to more coordinated structuring (as related and intersecting rows and columns). The five categories - Single Cell Structuring, Partial Unit Building, Whole Figure and Parts-of-Figure Noticing, Composite Unit Structuring and Coordinated Structuring - are described through illustrative examples. Students' gestures, language and diagrams were considered together when constructing the types. Interestingly, the spatial structure of grids was not readily apparent to many students and in fact was found to be complex for students to conceptualize. With minimal research on grids as a spatial structure in the mathematics education research field, there is strong potential for further investigation in this area.

Author Keywords: Grids, Mathematics, Spatial reasoning, Young Children

This study investigates the potential for a responsive model of professional development in mathematics education which acknowledges how teachers perceive the value of professional learning, and examines how those perceptions are connected to teacher efficacy. Three fields of educational research ground this study: (i) professional development strategies in mathematics education, (ii) teacher efficacy, and (iii) self-determination theory and andragogy. Data collection and analysis involved four detailed case studies and a cross-case analysis of similarities and distinctions among the cases, in an instrumental-multiple-case study design. Results suggest: (1) some characteristics of professional development were consistently designated as high or low value, independent of efficacy ratings, (2) other professional learning experiences were valued relative to the participants' sense of efficacy at different times in their careers, and (3) characteristics of professional development designated as high value during periods of low efficacy were fundamentally teacher-centric, but during periods of high efficacy, they were fundamentally student-centric.

Author Keywords: efficacy, mathematics education, mathematics teachers, professional development, professional learning, teacher efficacy

Through narrative/life story research this study explores the educational experiences of six individuals identified as Deaf or hard-of-hearing. The research presented will be conveyed in the form of an autoethnography, an approach to research and writing that seeks to describe and analyze personal experience to understand cultural experience. I will combine the views of participants who have been part of the Ontario Public School System within the last 10-15 years (2004-2019), with my own educational experience, learning with hearing loss. In this study, three interrelated concepts—student engagement, motivation, and resilience—are examined through the lens of "mindsets." Mindsets are "assumptions that we possess about ourselves and others that guide our behaviour" (Brooks, 2012, p. 1). The research reviewed in this paper, shows that students' beliefs about their academic ability can influence their academic tenacity. Academic tenacity refers to the mindsets and skills that enable students to: establish long-term goals and persevere in the face of adversity. I illuminate some of the systemic factors which impact the mindsets of students who are Deaf and hard-of-hearing. The design lies within the qualitative spectrum; data were gathered and analyzed from open-ended interviews conducted with purposively selected participants.

Author Keywords: Academic Tenacity, Autoethnography, Deaf, Education, Hard-of-Hearing, Mindsets

This thesis reports the outcomes of a mixed methods exploratory study on young children's spatial reasoning and mathematics involving unplugged (offline) coding with young children (JK-Grade 2). Intrigued by the increased push for coding in schools, teachers and researchers worked together in a collaborative research process to design a sequence of unplugged coding activities and document student thinking. Qualitative results include the mapping of a hypothetical learning trajectory for unplugged coding focused on location and movement, as well as an analysis of the computational, spatial and mathematical thinking in unplugged coding. The grid was found to be a fundamental spatial structure that supported student thinking across all domains. Quantitative data included a range of spatial and mathematics measures that were administered pre-post with a subsample of 55 students. Findings showed strongest gains in mental rotations/visualization and magnitude comparison, suggesting this as a promising area for further study.

Author Keywords: Early Years, Learning Trajectories, Spatial Reasoning, Unplugged Coding, Young Children