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Construction of subitized units is related to the construction of arithmetic units

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Abstract

This study investigates the relationship between children’s subitizing activity and their construction of arithmetic units. In particular, the study hypothesizes a positive association between children’s construction of subitized units and their construction of arithmetic units, and hypothesizes that children who can subitize larger units, such as five items, in kindergarten, are more likely to construct arithmetic units by the beginning of first grade. Data for this study were drawn from 3,660 children surveyed at the beginning of kindergarten in 2014, 2015, and 2016, and at the beginning of first grade in the following year. The children are from a single school district in the southwest United States. Logistic regression was used to model the likelihood of constructing arithmetic units based on children’s earlier construction of subitized units. Findings provide evidence of a positive relationship between children’s construction of subitized units and arithmetic units, and, on average, children who have constructed subitized units at the beginning of kindergarten are more likely to construct arithmetic units by the beginning of first grade. Based on the findings, theoretical and instructional implications are discussed.

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Notes

  1. For our theoretical framing, we focus our attention only on the first stage of the number sequences, the INS. However, the number sequences consist of a hierarchy of four stages (Steffe, 1992; Ulrich, 2015, 2016): (1) initial number sequence, (2) tacitly nested number sequence (TNS), (3) explicitly nested number sequence (ENS), and (4) generalized number sequence (GNS). Each stage represents a more sophisticated understanding of number in terms of arithmetic units and the coordination of those units when working with the counting numbers. Briefly, the construction of an INS involves the coordination of arithmetic units of one, the TNS involves additive coordinations of units of units (composite units), the ENS includes multiplicative coordination of composite units, and finally the GNS involves the coordination of units of units of units.

  2. A comparison of kindergarteners with missing data to kindergartners without missing data by gender, ethnicity, evidence of subitizing, and evidence of arithmetic units in kindergarten found no differences in the groups by gender, ethnicity, and evidence of arithmetic units. A statistically significant difference was found for subitizing; however, the effect size associated with this relationship, Cramer’s V = .045, did not substantiate practical significance. Given no practical relationship between missingness and the demographic and study variables, we felt comfortable proceeding with the reduced sample.

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Acknowledgements

We would like to thank David Woodward for making it possible to obtain and use the data in this study and for helping with understanding the interview protocols and data collection.

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Authors and Affiliations

  1. School of Education, Virginia Tech, Blacksburg, VA, USA

    Jesse L. M. Wilkins

  2. School of Teacher Education and Leadership, Utah State University, Logan, UT, USA

    Beth L. MacDonald

  3. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

    Anderson Norton

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  1. Jesse L. M. Wilkins
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  2. Beth L. MacDonald
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Correspondence to Jesse L. M. Wilkins.

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Wilkins, J.L.M., MacDonald, B.L. & Norton, A. Construction of subitized units is related to the construction of arithmetic units. Educ Stud Math 109, 137–154 (2022). https://doi.org/10.1007/s10649-021-10076-7

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