Chapter 2: Transformation Geometry From An Embodied Perspective

The theory of embodied cognition is utilized to interpret results from a series of studies of students interacting with a computer microworld for transformation geometry. Participants from three different groups (middle school, high school and undergraduate students) demonstrated very similar naive interpretations and “misinterpretations” of Euclidean transformations when they used the microworld. The theory of embodied cognition and the related field of cognitive linguistics are used to interpret these results and to contrast the students’ understandings with how geometry is construed in contemporary mathematics.

During its existence as a formal discipline, the field of mathematics education has drawn from different theoretical schools and core disciplines in order to carry out its investigations of mathematical thinking and learning, and has also generated new theories and explanatory paradigms of its own. There have been analyses of children’s mathematical activity from the perspective of information processing psychology and Piagetian constructivism. Mathematicians and philosophers have examined the nature of mathematics itself, whether considered as a transcendental domain or a human creation. During the past decade, a “turn to the social” within mathematics education has taken place, as researchers seek to understand how individual knowledge is related to the fundamentally social nature of human beings, and how mathematics itself can be viewed as a specialized form of social discourse. In general, one can perceive an overall broadening of boundaries within the field, from an early focus on individual cognition and problem solving to growing perspective that sees cognition as a phenomenon that is situated in specific contexts and distributed across people and artifacts.