Young children's composition of geometric figures: A learning trajectory

Children's abilities to define, use, and visualize the effects of composing (putting together) and decomposing (taking apart) geometric shapes constitutes a major conceptual field within the domain of geometry. A hypothetical learning trajectory was developed which posits that children move through several distinct levels of thinking and competence in the composition of geometric figures. An assessment instrument was then designed to elicit behaviors from children in the domain of shape composition.;Formative research on the hypothetical learning trajectory and the assessment instrument, involving researchers, classroom teachers, and graduate students concluded that the items constituted valid assessment of the kind of thinking described by each level of the learning trajectory. In addition, they indicated that they could reliably classify children as exhibiting thinking at specific levels, or in transition between levels, on the learning trajectory. This thesis reports the findings of a large-scale study that extends the formative research on shape composition competencies in young children, to assess the validity of the hypothesized trajectory and the reliability of the instrument with a larger sample of children across multiple grade levels.;The analyses in this study were both quantitative and qualitative. The quantitative analyses provided support for the levels forming a disjunctive scale; that is, the behaviors characteristic of higher levels in the learning trajectory successively displace those behaviors characteristic of lower levels and the reasoning in adjacent levels is more similar than reasoning in nonadjacent levels. The qualitative findings provided additional support for the validity of the trajectory through detailed analyses of children's behaviors as they worked on the tasks. The data reliably differentiated reasoning on the tasks, and thus, children could be reliably assigned to a level of development (including those in transition to the next level). Lastly, the qualitative findings support previous research on young children's geometric thinking and identify several areas for future research.;Thus, the findings support the learning trajectory as a valid model that accurately describes how children move through levels of thinking in the composition and decomposition of 2-D figures, as well as support the reliability of the instrument used to assess these levels of thinking.