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.
Highlights
As well as being a relevant part of mathematics, and applicable to other curricular areas, probability is necessary in many fields of science, where it enables us to describe the laws governing random phenomena [1]
When 3 white and 7 black balls in the first urn and 5 balls of each colour in the second urn are estimated from the relative frequency, by correctly relating the classical and frequentist approaches to probability
Most of the prospective teachers taking part in the study showed their competence in Task 1a, when estimating the most feasible composition of both urns from the frequentist data of 1000 extractions, and found the theoretical probability of obtaining balls of the two given colours
Summary
As well as being a relevant part of mathematics, and applicable to other curricular areas, probability is necessary in many fields of science, where it enables us to describe the laws governing random phenomena [1]. Given this relevance, the teaching of probability in. An essential issue to ensure the success of this teaching is the adequate training of the teachers who are responsible for this content This preparation should include both the mathematical characteristics of probability and the related pedagogical knowledge [3,4]. Some references can be found in several sources [5,6,7,8] or in journals such as the Journal of Mathematics Teacher
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
