Assessing young children’s ability to compare probabilities

  • Anne-Sophie SupplyEmail author
  • Wim Van Dooren
  • Stephanie Lem
  • Patrick Onghena


Comparing probabilities is a useful skill in life. Binary choice tasks are popular means in research on probabilistic reasoning. Falk, Yudilevich-Assouline, and Elstein (Educational Studies in Mathematics, 81(2), 207–233 2012) noted that many of these tasks contain design flaws. We designed and evaluated an extended and improved binary choice item set. In each trial, children were shown two boxes containing desired and undesired elements and had to identify the best box to blindly draw from. We took into account four necessary item set characteristics: (un)desired elements in the correct box, total number of elements in the correct box, and difference between desired and undesired elements in the correct box. Furthermore, some extensions to Falk et al.’s design (2012) were implemented: items in which one box certainly provided a desired element, items with three competing colors of elements, and items with lower “countability” of the elements. Results showed that extensions added to the design did not imperil internal consistency and validity. Younger children were more likely to give correct answers when the correct box contained more desired elements and older children are better at comparing probabilities than younger ones overall.


Mathematical development Probabilistic reasoning Ratio comparison Uncertainty 



This research was supported by the Grant KU Leuven project C16/16/001 “Development and stimulation of core mathematical competencies.”

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

The study was approved by the social and societal ethics committee of KU Leuven (G-2016 07 591).

Informed consent

Informed consent was obtained from all parents of individual participants included in the study.

Supplementary material

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Centre for Instructional Psychology and TechnologyKU LeuvenLeuvenBelgium
  2. 2.PXL University of Applied Sciences and ArtsHasseltBelgium
  3. 3.Methodology of Educational Sciences Research GroupKU LeuvenLeuvenBelgium

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