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Children’s unit concepts in measurement: a teaching experiment spanning grades 2 through 5

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Abstract

We examined ways of improving students’ unit concepts across spatial measurement situations. We report data from our teaching experiment during a six-semester longitudinal study from grade 2 through grade 5. Data include instructional task sequences designed to help children (a) integrate multiple representations of unit, (b) coordinate and group units into higher-order units, and (c) recognize the arbitrary nature of unit in comparison contexts and student’s responses to tasks. Our results suggest reflection on multiplicative relations among quantities prompted a more fully-developed unit concept. This research extends prior work addressing the growth of unit concepts in the contexts of length, area, and volume by demonstrating the viability of level-specific instructional actions as a means for promoting an informal theory of measurement.

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Notes

  1. See Evaluation of hypothetical learning trajectory for length in the early years (Sarama et al., 2011).

  2. Portions of the assessment were validated in other work.

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Acknowledgments

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 views of the NSF.

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Authors and Affiliations

  1. Illinois State University, 4520 Math, 313 STV Hall, Normal, IL, 61790-4520, USA

    Jeffrey E. Barrett, Craig Cullen, Amanda L. Miller & Chepina Rumsey

  2. University at Buffalo, State University of New York, 505 Baldy Hall, Buffalo, NY, 14260, USA

    Julie Sarama & Douglas H. Clements

  3. Trinity Christian College, 6601 West College Drive, Palos Heights, IL, 60463, USA

    David Klanderman

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  1. Jeffrey E. Barrett
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  7. Chepina Rumsey
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Correspondence to Jeffrey E. Barrett.

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Barrett, J.E., Cullen, C., Sarama, J. et al. Children’s unit concepts in measurement: a teaching experiment spanning grades 2 through 5. ZDM Mathematics Education 43, 637–650 (2011). https://doi.org/10.1007/s11858-011-0368-8

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