MATHEMATICS LEARNING THROUGH THE LENSES OF CULTURAL HISTORICAL ACTIVITY THEORY AND THE THEORY OF KNOWLEDGE OBJECTIFICATION [1]

This paper draws upon analysis of an adult student as he learns to read fractions-of-an- inch on a measuring tape with the researcher as tutor. This provides a basis for comparing two activity-theoretical perspectives: cultural historical activity theory as developed by YrjoEngestrom and his collaborators and Luis Radford's recent elaboration of activity theory, the theory of knowledge objectification. The former perspective provides a general framework for analyzing activity as a whole, whereas the later draws attention to particular genetic aspects of the mathematics learning and thinking of individuals. Insights gleaned through the use of each theory in analysis of this activity are summarized in-turn and contrasted for the purpose of showing the utility of each approach for the analysis of mathematics learning.