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Promoting sophisticated fraction constructs through instructional changes in a mathematics course for PreK-8 prospective teachers

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Abstract

In a previous study, we validated the fractions schemes and operations trajectory (Norton and Wilkins 2012; Steffe in J Math Behav 20(3): 267–307, 2002; Steffe and Olive Children’s fractional knowledge. Springer, New York, 2010; Wilkins and Norton 2011) with PreK-8 prospective teachers and explored PreK-8 prospective teachers’ understanding of fractions based on fraction schemes and operations (Lovin et al. 2016). In that study, we found that most of the prospective teachers had constructed the lower-level fraction schemes and operations, but less than half had constructed the more sophisticated ones. In the current study, we explored ways of evoking the more sophisticated fraction schemes and operations, in particular, by implementing simple instructional changes to a mathematics course for PreK-8 prospective teachers. One change focused on fraction language, specifically encouraging the use of iterative fraction language (e.g., 3/5 is three equal-size pieces, each of which is 1/5 of the whole). Another change focused on intentional number choice, specifically emphasizing improper fractions. After focused fraction instruction that included these instructional changes, we found significant increases in PreK-8 prospective teachers’ interiorization of coordinating three levels of units as well as in PreK-8 prospective teachers’ construction of the reversible partitive fraction scheme and the iterative fraction scheme. We conclude with implications for practice and research in mathematics courses intended for PreK-8 prospective teachers.

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Notes

  1. In a previous iteration of data collection (Lovin et al. 2016), we found the inter-rater agreement to be “almost perfect” based on the average kappa statistic for RPFS (K = 0.91), IFS (K = 0.93), splitting (K = 1.00), and 3UC (K = 0.81) (Landis and Koch 1977, p. 165). We assumed similar inter-rater agreement for this iteration of data collection due to the fact that the same raters performed both iterations of data collection.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, James Madison University, 305 Roop Hall, MSC 1911, Harrisonburg, VA, 22807, USA

    Alexis L. Stevens, LouAnn H. Lovin, John Siegfried & Richard Busi

  2. School of Education, Virginia Tech, 300C War Memorial Hall, Blacksburg, VA, 24061, USA

    Jesse L. M. Wilkins

  3. Department of Mathematics, Virginia Tech, 434 McBryde Hall, Blacksburg, VA, 24061, USA

    Anderson Norton

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  1. Alexis L. Stevens
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  2. Jesse L. M. Wilkins
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  3. LouAnn H. Lovin
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  4. John Siegfried
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  5. Anderson Norton
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  6. Richard Busi
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Correspondence to Alexis L. Stevens.

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Stevens, A.L., Wilkins, J.L.M., Lovin, L.H. et al. Promoting sophisticated fraction constructs through instructional changes in a mathematics course for PreK-8 prospective teachers. J Math Teacher Educ 23, 153–181 (2020). https://doi.org/10.1007/s10857-018-9415-5

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