Abstract:

Introduction:
Elementary teacher training programs target to develop professional competences in teacher students. Professional competences include cognitive and affective aspects, such as beliefs. Beliefs and their development in teacher students during the first semester are the object of this study. Therefore, we established a specific approach to teach arithmetic and geometry, and intended to investigate how beliefs develop within this approach. Due to the changing conditions caused by the corona pandemic, we were required to change from classroom teaching to virtual teaching. Encouraged by these changing conditions, we decided to focus on how these changes influence the development of beliefs.

Theoretical Background:
Beliefs begin to develop in school and shape during university studies and determine how an individual deals with mathematics (Schoenfeld 1992). For teachers, beliefs are crucial because they influence teaching and affect students (Eichler & Erens 2015).
This study focuses on the folloring aspects. First, we regard the transition problem in mathematic laden studies from school to university that is researched with the construct of transition (Gueudet 2008). Further, we regard the prospective teachers beliefs concerning the relevance of university mathematics for their future professional practice (cf. Albrecht &Karabenick 2018). Finally, we refer mathematical word views according to Grigutsch et al. (1998).
According to Gueudet (2008), students often fail to recognize the coherence of school and university mathematics during the transition from school to university. On the other hand, they do not perceive the relevance of university mathematics for their future work (Albrecht &Karabenick 2018). Since research gained results that teachers´ beliefs are default for the future teacher practice (Skott 2015; Eichler & Erens 2015) to strengthen teachers´ beliefs that university mathematics is relevant is crucial.
The mathematical worldview describes how individuals perceive mathematics. Here, two perpecitves are distinguished: Either mathematics is considered as system of formulas, procedures and algorithms, or as an activity and process for solving problems.

Methods:
This study investigates whether and how the development of selected beliefs in a regular classroom course differ from those in a virtual course. Therefore, we examine and compare two courses (14 single lectures) for freshmen in elementary teacher education in two consecutive winter terms (19/20 and 20/21) with about 270 paricipants per course. In both courses, the same lecturer teaches with the same approach and content. The only difference is the presence of students. While the course in the winter term 2019/2020 took place in a lecture hall as a classroom event, the current course (20/21) is virtual, streamed via video. The lecturer is present and teaches in the lecture hall. A live stream enables students to participate interactively via an assistant-controlled chat.
In the winter term 2019/2020, we collected data at the beginning and the end of the course with a questionnaire. One year later, the students had to fill out the same questionnaire digitally, due to corona pandemic. To measure the beliefs about the relevance of university mathematics, we use scales from Isaev & Eichler (2017). With the scales of Grigutsch et al. (1998), we measured the mathematical worldview.

At the conference, we are going to present and discuss the methods as well as the results.

Keywords:

Virtual classroom, beliefs, development, differences to classroom teaching.