How prospective kindergarten teachers develop their noticing skills: the instrumentation of a learning trajectory

Abstract

The objective of this study was to characterise prospective kindergarten teachers’ development of noticing children’s thinking about length and its measurement. We used the concepts of instrumental genesis and learning trajectories to identify the ways in which prospective kindergarten teachers used a learning trajectory to learn to notice children’s mathematical thinking. Fol- lowing a teaching experiment, we identified three ways in which prospective kindergarten teachers used the learning trajectory to notice children’s mathematical thinking. Two instrumented action schemes supported these ways of using the learning trajectory, namely, a scheme taking into account the mathematics learning progression to interpret children’s answers, and a scheme for proposing instructional tasks based on the interpretation of children’s mathematical thinking. Approaching the development of noticing as an appropriation process of a learning trajectory helps us to understand prospective teachers’ difficulties in endowing meaning to a learning trajectory’s conceptual structure. We suggest that these ways of using learning trajectory knowledge to interpret children’s mathematical thinking and to make instructional decisions can be understood as an instrumentation process that reveals how noticing skills develop.