Abstract:
Mathematical caring relations (MCRs), a framework for conceptualizing student-teacher interaction, was used in a year-long constructivist teaching experiment with 4 6th grade students. MCRs supported (1) the extension of previous research on how students construct improper fractions and (2) the learning of students and their teacher (the researcher). Establishing a MCR entails aiming for mathematical learning while attending to affective responses of both student and teacher. Although all students entered the experiment with the splitting operation deemed necessary for constructing improper fractions (Steffe, 2002), during the experiment 2 students did not construct improper fractions. One of these students is the focus of this paper. The current hypothesis is that splitting does not automatically engender the coordination of 3 levels of units that seems necessary to construct improper fractions. Analyzing MCRs in research is seen to facilitate interactions that can lead to learning and to validate the experiential difficulties of learning.
