Evaluating and Improving a Learning Trajectory for Linear Measurement in Elementary Grades 2 and 3: A Longitudinal Study

Abstract

We examined children's development of strategic and conceptual knowledge for linear measurement. We conducted teaching experiments with eight students in grades 2 and 3, based on our hypothetical learning trajectory for length to check its coherence and to strengthen the domain-specific model for learning and teaching. We checked the hierarchical structure of the trajectory by generating formative instructional task loops with each student and examining the consistency between our predictions and students' ways of reasoning. We found that attending to intervals as countable units was not an adequate instructional support for progress into the Consistent Length Measurer level; rather, students must integrate spaces, hash marks, and number labels on rulers all at once. The findings have implications for teaching measure-related topics, delineating a typical developmental transition from inconsistent to consistent counting strategies for length measuring. We present the revised trajectory and recommend steps to extend and validate the trajectory.

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ACKNOWLEDGEMENTS

We appreciate the comments of Cheryl Lubinski on an early draft of this paper. This material is based on work supported by the National Science Foundation Research Grants (DRL-0732217). This report reflects the views and positions of the authors, and not necessarily the views of the National Science Foundation.

An early version of this research report was presented at the Annual Meeting of the American Educational Research Association, San Diego, California on April 16, 2009.

Notes

¹TE 5 was omitted from Table 2 because it applied only to this student.