Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited, especially compared to topics such as number and operations. To contribute to the establishment of a research base for instruction in measurement, we evaluated and refined a previously developed learning trajectory in early length measurement, focusing on the developmental progressions that provide cognitive accounts of the development of children’s strategic and conceptual knowledge of measure. Findings generally supported the developmental progression, in that children reliably moved through the levels of thinking in that progression. For example, they passed through a level in which they measured length by placing multiple units or attempting to iterate a unit, sometimes leaving gaps between units. However, findings also suggested several refinements to the developmental progression, including the nature and placement of indirect length comparison in the developmental progression and the role of vocabulary, which was an important facilitator of learning for some, but not all, children.
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This study is part of a larger project to validate and refine measurement learning trajectories. Later developmental levels are investigated in connected studies (e.g., see Barrett et al., 2011 and Barrett et al., this issue).
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The research reported here was supported by the National Science Foundation through Grant No. DRL-0732217, “A Longitudinal Account of Children’s Knowledge of Measurement”. The opinions expressed are those of the authors and do not represent the views of the NSF.
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Sarama, J., Clements, D.H., Barrett, J. et al. Evaluation of a learning trajectory for length in the early years. ZDM Mathematics Education 43, 667 (2011). https://doi.org/10.1007/s11858-011-0326-5
- Learning trajectory
- Developmental progressions
- Hierarchic interactionalism