Since post-pandemic educational environments are more intertwined with distance education all over the world, pre-service teachers’ current teaching knowledge may not be sufficient in these environments such that they need to include new technological developments and tools in our teaching process (Koehler, Mishra & Zellner, 2015; Mishra, 2019; Saralar-Aras & Gunes, 2022). For an effective teaching and learning experience for teachers and students, students need to be more active learners and manage their learning processes (Nixon & Crook, 2021). Moreover, pre-service teachers are also required to have some roles which require various competencies which are recently summarized under the following seven headings: technological, managerial, evaluative, instructional designer, pedagogical, facilitator and social (Aydin, 2017; Kavrat & Türel, 2013):

1. Technological role: This role indicates that pre-service teachers should know the qualifications and limitations of a Learning Management System (LMS) in their technological roles, be able to use the advanced file upload feature (such as audio and video) to the LMS, and be aware of the resources that can be used on the platform by revising the files when necessary. In addition, they should be able to use the tools (group, calendar, forum, quiz, wiki, note) on this platform for in-class activities.

2. Managerial roles: What is expected in these roles is being careful about time management, being able to plan lessons and organizing events. In the course management, pre-service teachers should be able to intervene in extracurricular student activities when necessary by informing and reminding the course rules to the students and ensuring the smooth functioning of the course. They should be able to implement administrative procedures and direct students to the relevant places in case of problems related to the institution when necessary.

3. Evaluative role: Within the scope of these roles, pre-service teachers should be able to apply alternative assessment and evaluation techniques, be able to score fairly and ethically and ask questions to students in a way that covers all the course content.

4. Instructional designer roles: In these roles, it is expected from pre-service teachers to define the learning objectives of the course, to develop teaching activities in line with these goals, to inform the students about the course content, and to take measures to reduce the possible negative effects that distance education may cause. In addition, it is necessary to organize the course materials simply and originally, ethical and facilitating individual work.

5. Facilitator roles: Within the scope of these roles, pre-service teachers should give real-life examples to help students understand the subject better, provide immediate feedback to students, and pay attention to using strategies that will increase their interest in the lesson.

6. Pedagogical roles: In this role, what is expected from pre-service teachers is to present a road map that can be followed when necessary for effective communication with students. Moreover, they should be able to guide students in taking their learning responsibilities by creating a student-centred learning environment, assisting students in gaining life skills, organizing their professional development by keeping their subject area information up to date, and receiving support when necessary.

7. Social roles: Within the scope of these roles, pre-service teachers are expected to adopt an approach that can find friendly solutions when there are conflicts in the classroom, plan activities that will increase cooperation and group work among students, and increase the sense of community in the classroom by strengthening human relations.

Given these, this study aimed at answering the following research question: What is the perceived competency levels of pre-service mathematics teachers in the seven roles of distance education?

This study followed a case study approach (Merriam, 1988) being an exploratory case study as in Pan and Scarbrough (1999) where 20 pre-service mathematics teachers’ development of proficiencies in teaching mathematics during distance education was detailly investigated through a course. In this study, a 14-week course for pre-service teachers was designed based on the needs analysis in an earlier study (Saralar-Aras & Gunes, 2022) and sample courses (e.g., Ak, Gökdaş, Öksüz & Torun, 2021). In this course, applications that pre-service teachers can use in their distance education mathematics lessons for each of the seven roles were introduced. We suggested (but not limited to) GeoGebra for the technological role, Edmodo for managerial role, Kahoot and Mentimeter for the evaluative role, instructional design models used in distance education for the instructional designer role, Padlet and Tricider for pedagogical, Powtoon and Canva for the facilitator role and discussion boxes on Edmodo for the social role. At the end of the 14-week process, pre-service teachers were asked to give a presentation, a micro-teaching, on the mathematics subject of their choice individually, via Zoom. Their micro-teaching sessions were recorded and peer-reviewed. Hence, the data was generated through lesson observations, recordings of micro-teaching, peer evaluations, and analysed using a rubric to assess pre-service teachers’ proficiency in roles. The first week of the course was devoted to managerial and instructional designer roles where students' needs, preparing syllabuses, models of teaching activities that can be used and the ethical behaviours in distance education and their sustainability were discussed. The second, third, and fourth weeks were on technology roles where pre-service teachers worked on effective use of available software and tools that are widely used in mathematics. The content of the lessons of the fifth week was evaluative roles which focus on alternative measurement and evaluation techniques that can be used in distance education; and the sixth week was on social, pedagogical and facilitator roles which aimed at developing knowledge on various topics in distance education including ice-breaking activities, giving feedback, student-student and student-teacher interaction, methods of taking students' attention to the lesson, and teachers' involvement in communities and social networks that will feed their professional development. The remaining lessons were more student-centred where pre-service teachers presented their designed lessons for 30 to 45 minutes on a topic of their choice by paying attention to seven roles.

To conclude, this study aimed at improving pre-service teachers’ teaching skills in distance education. Hence, an instructional intervention was carried out to improve and support those areas that are reported by pre-service teachers as open for improvement. The course was found to help pre-service teachers develop the basic skills they need to gain for each role. In particular, they have enriched their content knowledge by learning new tools especially in social and technological roles, as well as having started to follow the developments in their fields in the social role. The reason for this probably was the course context where they learned pedagogical approaches, activities and tools specific to the mathematics that they could use with their students in synchronous or asynchronous lessons. Another reason for the improvement might be receiving and giving feedback on their micro-teaching since the participants received feedback on their micro-teaching performance from their peers; as found in the study of Acikgul and Aslaner (2019), the use of microteaching and GeoGebra improved pre-service teachers' TPACK skills and self-efficacy skills; they reported that pre-service teachers who gave feedback to each other about their micro-teaching performance established student-student communication among themselves. Moreover, we found that the improvement of the teaching performance was more obvious after the second micro-teaching experience of the participants. This finding confirms the results of the study of Mutlu, Polat and Alan (2019) that reported that teachers perform better in their second presentations in micro-teaching than in their first presentation, so it seems necessary to provide at least two micro-teaching chances to them to see the development (Koech & Mwei, 2019). Hence, we suggest teaching these roles to pre-service teachers not only in our context but also in wider Europe so that they could make a better start to their teaching practices.

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