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Teachers’ Knowledge of Fraction Magnitude

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Abstract

This article explores three attributes of teachers’ understanding of fraction magnitude: the accuracy and reasonableness of teachers’ estimations in response to fraction arithmetic tasks as well as the alignment of the estimation strategies they used with the concept of fraction magnitude. The data were collected from a national sample of mathematics teachers in grades 3–7 in which fraction concepts were taught (N = 603). The results indicated the teachers’ estimations were only partially accurate and reasonable, particularly when fraction division was involved. Furthermore, teachers’ credentials and the grade level at which they taught mathematics were significantly related to teachers’ understanding of fraction magnitude.

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Notes

  1. Participants were first completed a screening survey to ensure the data were collected from the targeted sample. The screening survey began with general questions regarding the participant’s career and was followed by specific questions, such as at what grade level the teacher taught mathematics. Those who were eligible to participate in the study were allowed to continue to take the survey, and they completed an additional set of questions regarding their educational background. Teachers who participated in the study were compensated with an online gift card.

  2. Teachers saw these questions in a randomized order to reduce the error in their responses.

  3. Teachers’ accuracy score was reverse-coded because a higher score indicated lower accuracy.

  4. Indeed, the accuracy of teachers’ estimations for the division of fractions was statistically lower than the accuracy of their estimations for the addition problem, t(559) = −9.01, p < .001.

  5. A significantly higher percentage of teachers provided a reasonable estimation for the addition of fractions (75.6%) compared with the division of fractions (54.1%), McNemar’s chi2= 71.05, p < .0001.

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Funding

This work was supported by the National Science Foundation (DRL-1751309) and the Herman & Rasiej Mathematics Initiative. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation or Herman & Rasiej Mathematics Initiative.

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  1. University of Southern California, Los Angeles, USA

    Yasemin Copur-Gencturk

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  1. Yasemin Copur-Gencturk
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Correspondence to Yasemin Copur-Gencturk.

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Copur-Gencturk, Y. Teachers’ Knowledge of Fraction Magnitude. Int J of Sci and Math Educ 20, 1021–1036 (2022). https://doi.org/10.1007/s10763-021-10173-2

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