The Use of a Length and Measurement HLT by Pre-Service Kindergarten Teachers’ to Notice Children’s Mathematical Thinking

Abstract

The objective of the study was to characterise how pre-service kindergarten teachers used a Hypothetical Learning Trajectory on length and its measurement to notice children’s mathematical thinking. A total of 64 pre-service kindergarten teachers enrolled in an Early Years Education mathematics teaching course were asked to notice teaching situations focusing on kindergarten children’s learning of length. On the one hand, three profiles of pre-service kindergarten teachers were found according to the use they made of the Hypothetical Learning Trajectory. These profiles were characterised by three ways of learning to use the Hypothetical Learning Trajectory based on the type of mathematical elements they identified: only mathematical elements related to the magnitude; only mathematical elements related to the measurement of length; or both magnitude and measurement elements. On the other hand, when considering the three skills of professional noticing, by identifying the mathematical elements required to solve the proposed task, a group of pre-service kindergarten teachers within each profile were able to notice the thinking of these elements by children and to suggest activities. Our findings provide learning opportunities to pre-service kindergarten teachers who use a Hypothetical Learning Trajectory. It provides them with ‘check-points’ to answer the proposed questions, in order to learn the specialised knowledge for teaching length and its measurement as well as to develop the skill of noticing student’s mathematical thinking.