Prospective Mathematics Teachers Understanding of Classical and Frequentist Probability

Carmen Batanero, Nuria Begué, Rocío Álvarez-Arroyo and Silvia M. Valenzuela-Ruiz
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Carmen Batanero: Department of Mathematics Education, University of Granada, 18071 Granada, Spain
Nuria Begué: Department of Mathematics, Area of Mathematics Education, University of Zaragoza, 50009 Zaragoza, Spain
Rocío Álvarez-Arroyo: Department of Mathematics Education, University of Granada, 18071 Granada, Spain
Silvia M. Valenzuela-Ruiz: Department of Mathematics Education, University of Granada, 18071 Granada, Spain

Mathematics, 2021, vol. 9, issue 19, 1-15

Abstract: Strengthening the teaching of probability requires an adequate training of prospective teachers, which should be based on the prior assessment of their knowledge. Consequently, the aim of this study was to analyse how 139 prospective Spanish mathematics teachers relate the classical and frequentist approaches to probability. To achieve this goal, content analysis was used to categorize the prospective teachers’ answers to a questionnaire with open-ended tasks in which they had to estimate and justify the composition of an urn, basing their answers on the results of 1000 extractions from the urn. Most of the sample proposed an urn model consistent with the data provided; however, the percentage that adequately justified the construction was lower. Although the majority of the sample correctly calculated the probability of an event in a new extraction and chose the urn giving the highest probability, a large proportion of the sample forgot the previously constructed urn model, using only the frequency data. Difficulties, such as equiprobability bias or not perceiving independence of trials in replacement sampling, were also observed for a small part of the sample. These results should be considered in the organisation of probabilistic training for prospective teachers.

Keywords: probability; relating the classical and frequentist views; teacher’s knowledge; assessment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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