Primary-school children’s knowledge of transitivity of probability and of bounds of probability

ABSTRACT

Primary-school children aged between 7 and 10 years were questioned about their conceptual knowledge of the first two axioms of qualitative probability. Children were questioned with prespecified examples and it was subsequently evaluated whether their answers were consistent with axioms. In addition, children’s knowledge of qualitative probability was investigated with universal and existential statements about axioms. Children showed good knowledge of probability with prespecified examples. In contrast, majority showed poor knowledge when asked about some of the universal and existential statements. An age-related improvement was not detected. In particular, only 25% said that the transitivity was necessary, i.e. that it applied to all events. 60% said that an event may be both possible and impossible. Only 42% said that all impossible events were equally likely and 54% said that all certain events were equally likely. Only 56% said that probability has both upper and lower bounds.

KEYWORDS:

• Probability
• abstract measurement theory
• transitivity
• conceptual development

Acknowledgements

Frederike Knöffel and Lisa Wolf helped with data collection.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are openly available in repository at https://github.com/simkovic/probbounds.