A Cultural-Historical Perspective on Mathematics Teaching and Learning

Abstract

Eighty years ago, L. S. Vygotsky complained that psychology was misled in studying thought independent of emotion. This situation has not significantly changed, as most learning scientists continue to study cognition independent of emotion. In this book, the authors use cultural-historical activity theory as a perspective to investigate cognition, emotion, learning, and teaching in mathematics. Drawing on data from a longitudinal research program about the teaching and learning of algebra in elementary schools, Roth and Radford show (a) how emotions are reproduced and transformed in and through activity and (b) that in assessments of students about their progress in the activity, cognitive and emotional dimensions cannot be separated. Three features are salient in the analyses: (a) the irreducible connection between emotion and cognition mediates teacher-student interactions; (b) the zone of proximal development is itself a historical and cultural emergent product of joint teacher-students activity; and (c) as an outcome of joint activity, the object/motive of activity emerges as the real outcome of the learning activity. The authors use these results to propose (a) a different conceptualization of the zone of proximal development, (b) activity theory as an alternative to learning as individual/social construction, and (c) a way of understanding the material/ideal nature of objects in activity.Wolff-Michael Roth is Lansdowne Professor at the University of Victoria, Canada. He researches scientific and mathematical cognition along the life span from cultural-historical and phenomenological perspectives. He has conducted research in science and mathematics classrooms as well as having realized multi-year ethnographic studies of science and mathematics in workplaces and scientific research.Luis Radford is full professor at Laurentian University in Canada. His research interests include the investigation of mathematics thinking and knowing from a cultural-semiotic embodied perspective and the historical and cultural roots of cognition. For many years he has been conducting classroom research with primary and high-school teachers about the teaching and learning of mathematics.