Spatial reasoning in context : spatial‐mathematical relations and implications for problem solving

  • Danielle Harris

    Student thesis: Doctoral Thesis

    Abstract

    Spatial reasoning is ingrained in our daily lives, such as when we need to locate our keys or park our car. Spatial reasoning is a sweeping term that encompasses a wide range of different, though often related, skills. At a broad level, spatial reasoning describes the ability to mentally represent and transform objects and their relations. Many spatial reasoning skills have strong links with mathematics performance. Subsequently, understanding the ways spatial reasoning connects with mathematics has the potential to support achievement in school. The growing body of research across development, cognition, and mathematics education has resulted in spatial reasoning being considered so closely connected to mathematics it is no longer a question of whether the two are related, but how. However, current research practices fail to account for the contextualised nature of spatial skills; that is, that they are learned and developed in real-world, spatially demanding activities. To date, research has often focused on abstract spatial skills, measured by psychometric tests, to generalise about broader models of spatial reasoning (e.g., through psychological test batteries). However, spatial reasoning goes beyond performance on tests and because spatial skills are naturally learned and applied within context, theories devoid of context can be impoverished. I have sought to find the points of connection between the fields of cognitive psychology, often based in the lab, and mathematics education, situated in classrooms, to address the question: “how does student performance on psychometric measures of spatial skills translate to problem-solving contexts: in the classroom and beyond?”.
    This thesis is comprised of five published works, with each focusing on the application of spatial skills in different contexts (i.e., mathematics assessment, instruction, and in large-scale representations of space). The first paper presents a literature review which reflects on the current state of the field and identifies gaps in research. The second paper explores the nature of spatial-mathematical relations by examining connections between specific spatial skills and mathematics content, using traditional spatial measures that include object-based spatial tasks as well as larger-scale reasoning. Large-scale spatial skills are often overlooked in studies of spatial-mathematical relations as they do not have the intrinsic connections found with object-based skills. The third paper drills down at an item level to examine relations in the rapidly changing field of digital testing. In the fourth paper, the thesis moves away from testing to explore the role of spatial skills in mathematics instruction. In the fifth and final paper, I consider spatial skills beyond the classroom in the application of perspective-taking in local environments. Each of these papers presents insights into the unique role of spatial skills in real-world contexts with bridging chapters steering the thesis narrative.
    Several implications emerged from the research: 1) large-scale spatial skills have a unique and critical role in spatial-mathematical relations; 2) a disconnect exists between spatial skills measured by cognitive tests and their applications in mathematics assessment, the classroom and beyond; and 3) the presence of spatial skills does not guarantee their application. This thesis contributes to the growing body of work that spatial skills are necessary but not sufficient for success in mathematics. Recommendations are presented for how we these findings may be adopted in educational practice.
    Date of Award2023
    Original languageEnglish
    SupervisorTom Lowrie (Supervisor) & Ilyse Resnick (Supervisor)

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