What Mathematical Knowledge Do Prospective Teachers Reveal When Creating and Solving a Probability Problem?

Marlén Alonso-Castaño,Pedro Alonso,Luis J Rodríguez-Muñiz,Maria Mellone

doi:10.3390/math9243300

Marlén Alonso-Castaño, Pedro Alonso + Show 2 more

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https://doi.org/10.3390/math9243300

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Abstract

The teaching of probability is conditioned by teachers’ mathematical knowledge. In this paper, an exploratory study is carried out with prospective teachers. A training task was designed requiring them to create and solve a probability problem using the values of euro coins, which was adapted to students aged 11 to 12. The study aimed at determining what mathematical knowledge prospective teachers show when dealing with the task. The data were collected through the Moodle online Campus. We framed the data analysis in the Mathematical Knowledge for Teaching model and we used content analysis as the methodological approach. The results indicate that, despite finding evidence of adequate common and specialised mathematical knowledge, in approximately half of the prospective teachers participating in the study, too many of them still show a lack of knowledge in both subdomains. There was also little evidence of knowledge of the curriculum. The main finding of the research is that, when prospective teachers get involved in complex creative tasks, they mobilised together specialised and common mathematical knowledge, working into different mathematical processes such as problem posing and solving, communication, and argumentation, which reinforces the need to continue working on these types of complex tasks.

Highlights

IntroductionThat introduction is justified based on the great importance of understanding the language of chance in our daily lives, as random phenomena permeate our lives in many ways [1,2,3,4,5,6,7]
Correct problems corresponding to sixth grade of primary education and adapted to the wording model in which the PTs show evidence of deep Common Content Knowledge (CCK) and Specialized Content Knowledge (SCK)
Correct problems corresponding to sixth grade of primary education, but which do not follow the proposed wording model, in which the PTs show evidence of deep CCK and SCK

Summary

Introduction

That introduction is justified based on the great importance of understanding the language of chance in our daily lives, as random phenomena permeate our lives in many ways [1,2,3,4,5,6,7]. Notions such as probability or uncertainty appear frequently during our adult life, for example, when we calculate forecasts of medical, financial, or environmental risks, when we study the reliability of a product, or when we make weather predictions. Necessary to deal with the language of chance (to distinguish impossible, sure, more or less likely, and rank them) and probability, as the mathematical tool that quantifies and measures degrees of beliefs about chance

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