Tangibility for Teaching, Learning and Communicating Mathematics

Finding new ways to teach powerful mathematical ideas is an urgent societal objective.

The mathematics of space and motion is a domain that has wide-ranging relevance for what children need to learn in school. This subject also presents particularly interesting challenges for a theory of embodied cognition.

This project aims to advance understanding of 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.

We ground this approach in empirical studies and aim to articulate useful perspectives on the nature of mathematical knowledge for the technical workplace, for teachers, and for curriculum designers.

A team of three university groups is conducting a coordinated series of empirical and design studies that focus on learning the mathematics of space and motion. This research employs design experiments in diverse settings. One such setting is an extended summer program for talented high school students that recruits from racially diverse and/or economically disadvantaged communities. Another environment is methods courses for secondary pre-service mathematics teachers.

Studies are conducted in professional workplaces and formal, academic settings where people learn and teach these subjects. This research involves professional mathematicians, graduate students in mathematics, professionals working with mapping and spatial analysis, pre-service high school mathematics teachers, high school students, pre-engineering vocational students, and talented middle and high school youth.

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 team 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.