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A design study to develop young children’s understanding of multiplication and division

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Abstract

This design study investigated the use of multiplication and division problems to help 5-year-old children develop an early understanding of multiplication and division. One teacher and her class of 15 5-year-old children were involved in a collaborative partnership with the researchers. The design study was conducted over two 4-week periods in May–June and October–November. The focus in this article is on three key aspects of classroom teaching: instructional tasks, the use of representations, and discourse, including the mathematics register. Results from selected pre- and post-assessment tasks within a diagnostic interview showed that there were improvements in addition and subtraction as well as multiplication and division, even though the teaching had used multiplication and division problems. Students made progress on all four operational domains, with effect sizes ranging from approximately two thirds of a standard deviation to 2 standard deviations. Most of the improvement in students’ number strategies was in moving from ‘counting all’ to ‘counting on’ and ‘skip counting’. The findings challenge the idea that learning experiences in addition and subtraction should precede those in multiplication and division as suggested in some curriculum documents.

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Notes

  1. A measure of socioeconomic status in New Zealand education based on census data.

  2. In later iterations, these problems were omitted as they did not contribute to children’s learning in the same way as division into groups of two or groups of ten.

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Acknowledgments

The data for this paper was extracted from a larger project that was made possible by funding from the Teaching and Learning Research Initiative (TLRI) administered through the New Zealand Council for Educational Research and the interest and support of the teachers and children involved in the project.

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Authors and Affiliations

  1. University of Waikato, Private Bag 3105, Hamilton, New Zealand

    Brenda Bicknell & Jenny Young-Loveridge

  2. Open Polytechnic, Wellington, New Zealand

    Nhung Nguyen

Authors
  1. Brenda Bicknell
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  2. Jenny Young-Loveridge
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  3. Nhung Nguyen
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Correspondence to Brenda Bicknell.

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Bicknell, B., Young-Loveridge, J. & Nguyen, N. A design study to develop young children’s understanding of multiplication and division. Math Ed Res J 28, 567–583 (2016). https://doi.org/10.1007/s13394-016-0180-4

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  • DOI: https://doi.org/10.1007/s13394-016-0180-4

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