MEASURING PERSPECTIVE OF FRACTION KNOWLEDGE: INTEGRATING HISTORICAL AND NEUROCOGNITIVE FINDINGS

Abstract

In this theoretical investigation, we describe the origins and cognitive difficulties involved in the common conception of fractional numbers, where a fraction corresponds to some parts of an equally partitioned whole. As an alternative, we present a new notion of fraction knowledge, called the perspective of measure-proportionality. It is informed both by the historical-cultural analysis of the emergence of fractions in social practice and by neuroscientific evidence of the propensity of human beings to perceive from childhood nonsymbolic proportionality between pairs of quantities. We suggest that this natural neurocognitive propensity of individuals may be an instructional link to develop students’ robust knowledge about fractional numbers.