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Confident or familiar? The role of familiarity ratings in adults’ confidence judgments when estimating fraction magnitudes

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Abstract

Understanding fraction magnitudes is especially important in daily life, but fraction reasoning is quite difficult. To accurately reason about fraction magnitudes, adults need to monitor what they know and what they do not know. However, little is known about which cues adults use to monitor fraction performance. Across two studies, we examined adults’ trial-by-trial fraction estimates, confidence judgments, and ratings of fraction familiarity. Adults were more confident when their estimates were more precise as well as when estimating fractions they rated as more familiar. However, adults judged their confidence in estimating fraction magnitudes, in part, based on their familiarity with each fraction. The role familiarity cues play in judgments of confidence with fractions suggests that people may be less likely to check for errors when reasoning about highly-familiar fractions.

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Notes

  1. We acknowledge that there is an ongoing debate as to which measure of metacognitive accuracy is best (Fleming and Lau 2014; Higham and Higham 2019). However, we chose to calculate gamma given the similarities between gamma and other signal-detection measures of metacognitive sensitivity (Higham and Higham 2019). Furthermore, gamma is appropriate for our continuous measure of number line estimation precision, whereas signal-detection analyses such as AROC require a dichotomized response (e.g., correct/incorrect), and PAE is a continuous measure of performance.

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Funding

Support for this research was provided in part by the U.S. Department of Education, Institute of Education Sciences grant R305A160295 to Dr. Clarissa A. Thompson and the Kent State University Judie Fall Lasser Award to Charles J. Fitzsimmons.

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Authors and Affiliations

  1. Psychological Sciences, Kent State University, Kent, OH, 44240, USA

    Charles J. Fitzsimmons & Clarissa A. Thompson

  2. Department of Psychology, University of Kentucky, Lexington, KY, 40506, USA

    Pooja G. Sidney

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  1. Charles J. Fitzsimmons
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Correspondence to Charles J. Fitzsimmons.

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Part of this report was accepted as a conference proceeding to the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA, 2019). The authors retain full copyrights of the submission. Pre-registrations and project information can be viewed here: https://osf.io/4uygd/.

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Table 5 Smaller and larger component stimuli presented in Experiment 1 (top) and 2 (bottom)
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Fitzsimmons, C.J., Thompson, C.A. & Sidney, P.G. Confident or familiar? The role of familiarity ratings in adults’ confidence judgments when estimating fraction magnitudes. Metacognition Learning 15, 215–231 (2020). https://doi.org/10.1007/s11409-020-09225-9

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