Development and evaluation of a revised developmental progression of a learning trajectory for volume measurement in the early years
Van Dine, Douglas W.
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This dissertation is a compilation of three related papers: * Paper 1: Development of a Learning Trajectory for Volume Measurement - A review of research * Paper 2: Verifying and Refining a Developmental Progression for a Learning Trajectory for Volume Measurement - Pre-K through Grade 2 * Paper 3: Evaluation of a Revised Developmental Progression of a Learning Trajectory for Volume Measurement - Kindergarten through Grade 2 The first paper provides a framework for the study of volume measurement within a constructivist paradigm. A review of research focused on volume as well as learning trajectories is presented. This culminates in a learning trajectory for volume measurement developed by Clements and Sarama (2009). Research with young children is sparse, however, leading to the conclusion that further evaluation and refinement of this learning trajectory for volume measurement is warranted. The second paper begins with the learning trajectory for volume measurement developed by Sarama & Clements (2009). Through qualitative analysis of longitudinal data from 8 children followed from pre-K through Grade 2, as well as quantitative analysis of assessment data from a larger sample of children in pre-K through Grade 5, evidence was found to support much of the initial learning trajectory, but also highlighted the need for revision. As a result, a revised developmental progression for this learning trajectory was developed. This revised developmental progression incorporates four schemes related to volume identified in young children: filling, packing, building, and comparing. Finally, the third paper presents research completed to further evaluate this revised developmental progression. Using 48 items assessing volume understanding adapted from previous research on volume (Curry & Outhred, Battista, Clements & Sarama), 82 children from pre-K through Grade 3 were interviewed. The data was submitted to Rasch modeling and the outcome used to answer two research questions: 1. Are the hypothesized developmental progressions for filling, packing, building, and comparing volume valid for a larger sample of children? 2. Is the hypothesized developmental progression for volume, incorporating the subtrajectories for filling, packing, building, and comparing, valid when considered as a single, unidimensional developmental progression or should there be more than one developmental progression for volume measurement? Rasch modeling results support the unidimensionality of the volume construct as measured by the instrument. Thus, in answering Research Question 2, there is evidence of a single, unidimensional developmental progression for volume incorporating the subtrajectories for filling, packing, building, and comparing. Results also support that Research Question 1 is validated and that the developmental progressions for filling, packing, building, and comparing volume are valid for a larger sample.