Reasoning under uncertainty within the context of probability education: A case study of preservice mathematics teachers

Interpreting phenomena under uncertainty stands as a substantial cognitive activity in our daily life. Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. From this aspect, a central inquiry has been raised through this study: how do preservice mathematics teachers (PSMTs) reason under uncertainty? A multiple case study design was operated in which a purposive sample of PSMTs was selected to justify their reasoning in two probabilistic contexts while their responses were coded by NVivo, and corresponding categories were developed. As a result, PSMTs’ probabilistic reasoning was classified into mathematical (M), subjective (S), and outcome-oriented (O). Besides, several biases emerged along with these modes of reasoning. While M thinkers shared equiprobability and insensitivity to prior probability, the prediction bias and the belief of Allah’s willingness were yielded among S thinkers. Also, the causal conception spread among O thinkers.

Preservice Mathematics Teachers’ Knowledge about the Potential of Tasks to Promote Students’ Mathematical Reasoning

The use of tasks to promote mathematical reasoning (MR) in teaching practice is essential to meet curricular goals. However, that practice is often a huge challenge for teachers, and particularly for prospective teachers and thus it is essential to highlight it as a goal for initial teacher education. This study focuses on preservice mathematics teachers’ (PTs) knowledge about the potential of mathematical tasks to promote students’ MR, in a teacher education course. Results show that PTs were able to justify their option for a mathematical task with potential to promote students’ MR, and through its implementation in one 8th grade classroom they have deepen their knowledge and gave greater meaning to task design principles and acknowledging their students’ knowledge. Thus, the activity of selecting and adapting a task, although less demanding than the design of a new task, can still provide PT with important reflection and knowledge about its potential to promote students’ MR. The study stresses the relevance for initial teacher education of considering four domains associated with the recognition of the potential of tasks to promote MR.

Reflections of the Distance Education Process on Higher Education: A Probability Course Example

Evaluating the effects of the Coronavirus (Covid-19) pandemic on distance education applications in higher education is important for future practice. In this context, the aim of the study is to determine preservice mathematics teachers’ conceptual-procedural knowledge level competencies and general thoughts about distance education in the distance education probability course in the department of mathematics teaching. In the study, a questionnaire consisting of 18 questions was prepared in the light of the literature as a data collection tool for 52 preservice mathematics teachers who took the probability course with distance education in the 2020-2021 academic year. After the implementations, one-to-one interviews were made with the lecturer conducting the course. The data of the study were analysed with the descriptive analysis method. As a result, it was determined that the conceptual-operative knowledge of the preservice mathematics teachers in the probability course in the distance education process was at a medium level. Although it was determined that the participation in online lessons was quite low compared to the lessons taught face-to-face, the preservice teachers mostly followed the lessons from asynchronous recordings, but there was no low performance or unwillingness in the preservice teachers who attended the lessons online. It has been determined that the biggest problem with distance education is the internet access and the low reliability of evaluation process. To increase the reliability, it has been determined that the transition to camera-controlled exams and the use of the safe exam browser (SEB) have been introduced.

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

This paper presents a long-term study of Preservice Mathematics Teachers (PMTs) at the Faculty of mathematics, physics and informatics, Comenius University in Bratislava (FMFI UK), focusing on the implementation of digital technologies (DT) into the teaching of theoretical and practical (or applied) subjects. We conducted parallel research into two aspects, one on Calculus lessons as a theoretical subject, another on the Financial Mathematics module as an applied subject. The implementation of DT and the way this was measured varied from year to year and also in the method of implementation into the aforementioned subjects. The methods of implementation and the results are briefly described, and a comparison of these two subjects in the PMTs’ preparation is also discussed.