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Tangibility for the Teaching, Learning, and Communicating of Mathematics

Assessment Intervention Learning Policy Training

Abstract

We propose research that takes advantage of technical advances in multi-modal and spatial analysis to develop new theories of embodied mathematical cognition and learning. Three university groups will conduct a coordinated series of empirical and design studies that focus on learning the mathematics of space and motion which is a domain that has wide-ranging relevance for what children need to learn in school, and that presents particularly interesting challenges for a theory of embodied cognition. Studies will be conducted in professional workplaces and formal, academic settings where people learn and teach these subject matter areas; they will include professional mathematicians, graduate students in mathematics, professionals working with mapping and spatial analysis, pre-service high school mathematics teachers, high school students, re-engineering vocational students, and talented middle and high school youth.

Two major ideas from embodied cognition are especially relevant for the study of mathematical understanding: (1) Grounding of abstraction in perceptuo-motor activity. This conception shifts the locus of "thinking" from a central processor to a distributed web of perceptuo-motor activity situated within a physical and social setting; therefore, it suggests that to make meaning people ground seemingly abstract concepts in modality-specific, sensory-motor systems. (2) Cognition is for action. This tenet proposes that things, including mathematical symbols and representations, are understood by the actions we can perform with them, or by mentally simulating the actions that underlie or constitute them. The aim of our research is to advance understanding of basic questions about learning and teaching through the development of a theory of embodied mathematical cognition that can apply to a broad range of people, settings and activities. Such a theory, grounded in empirical studies, will help us to identify promising implications for mathematics teaching and learning as well as to articulate useful perspectives on the nature of mathematical knowledge for the technical workplace, for teachers, and for curriculum designers.

The research team spans a range of disciplines, including educational and developmental psychology, educational technology, teaching and teacher education, literacy, mathematics and mathematics education. The investigative team also brings together expertise from a range of research methodologies, including design based research, interactional analysis, ethnography, experimental design, qualitative and quantitative discourse analysis methods, gesture studies, protocol analysis, and curriculum design. The development of a theory of embodied mathematical cognition is consonant with the emergence of ideas across disciplinary fields and has the potential to play a transformative role in cognitive science, as well as mathematics, science, and engineering education.

A theory of embodied mathematical cognition empirically rooted in classroom learning and workplace practices will broaden the range of activities and emerging technologies that count as mathematical and help educators to envision alternative forms of bodily engagement with mathematical problems. This broadening is particularly important at a time in which our society faces persistent achievement gaps between groups of students from different cultural backgrounds or from families with different economic standing. Finding new ways to teach powerful mathematical ideas, including uses of these ideas that have engaging social relevance, is an urgent societal objective. This project addresses these needs, in part, by creating specific corridors for research findings to impact how the mathematics of space and motion is taught and learned, with design experiments conducted in diverse settings that range from an extended summer program for talented high school students that recruits from racially diverse and/or economically disadvantaged communities, to methods courses for secondary preservice mathematics teachers.