Abstract:

Mathematics and informatics in didactics are closely related [1]. The new Slovak curriculum [2], which is in the pilot phase, speaks of mathematics and informatics as one educational area, which is only later divided into 2. One of the main foundations of effective educational practice lies in recognizing the importance of understanding students' beliefs and their development [3]. In this article we aim to find out and explore the attitudes of pre-service teachers who will teach the subjects in question. Obviously, these two subjects are very broad, so we decided to focus only on reasoning and prove (R&P) in mathematics and informatics.
According to Simon & Tzur [4] practice is defined to include not only teaching activities and strategies, but also what the teacher thinks, believes and feels about them. There is an assumption that if a prospective teacher believes and wants to incorporate something into their teaching, they will continue to try to do so in the future ( [5], [6]). Therefore, in our paper we try to clarify the current state of pre-service teachers' ideas and beliefs about R&P and how they would imagine it in the future. We compare these views among pre-service mathematics and informatics teachers and try to find some common or opposed views on the issue.
We elicit opinions using semi-structured interviews, then we do content analyzing where we search for patterns using open coding as defined in Creswell [7]. We conduct these interviews with pre-service teachers who are attending the first year of Master’s degree in Teaching Mathematics or Informatics at Comenius University in Bratislava.
The results indicate some resemblance in usage of R&P between these two groups. Empirical and standard forms of proof have been mentioned but with different degrees of intensity. Both groups of respondents wreaked some possible limitations of using R&P in classes. The most adduced was time. Respondents also expressed some plausible topics where they could imagine R&P in their future teaching.

References:
[1] S. Modeste, "Impact of Informatics on Mathematics and Its Teaching," in 3rd International Conference on History and Philosophy of Computing (HaPoC), Pisa, Italy, 2015.
[2] Štátny pedagogický ústav, "Matematika a informatika, Upravené ciele a obsah vzdelávacích oblastí a vyučovacích predmetov," 2020. [Online]. Available: https://www.statpedu.sk/files/sk/svp/pilotne-overovanie/upravene-ciele-obsah/aktualizovane-vs/vo_mai.pdf. [Accessed 2 7 2023].
[3] J. A. Cady and K. Rearden, "Pre‐service teachers' beliefs about knowledge, mathematics, and science," School Science and Mathematics, pp. 237-245, 2007.
[4] M. A. Simon and R. Tzur, "Explicating the teacher’s perspective from the researchers’ perspectives: Generating accounts of mathematics teachers’ practice," Journal for Research in Mathematics Education, vol. 30, no. 3, pp. 252-264, 1999.
[5] J. Nespor, "The role of beliefs in the practice of teaching," Journal of curriculum studies, vol. 19, no. 4, pp. 317-328, 1987.
[6] A. J. Stylianides and S. Delaney, "Pre-service mathematics teachers’ knowledge and beliefs," Research advances in the mathematical education of pre-service elementary teachers: An international perspective, pp. 219-228, 2018.
[7] J. W. Creswell, 30 Essential Skills for the Qualitative Researcher, Thousand Oaks, California: Sage, 2015.

Keywords:

Pre-service teachers' beliefs, mathematics education, informatics education, reasoning and proof.