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Aim/Purpose Our research aims to explore which design elements and aspects of online learning environments are relevant for teachers when introduced to educational innovations such as flipped learning and, thereby, to enable facilitating the dissemination of these innovations Background Integrating educational innovations from academic discourses or professional teacher development into teachers' classroom practices is challenging Sustaining and reinforcing their effects on professional development is also difficult especially because of the lack of continuous support and inspiration for long term pedagogical changes Online learning environments could facilitate such assistance, inspiration, and assist in developing supportive teacher communities The current coronavirus pandemic and the associated homeschooling illustrate that supportive off-and online teacher communities and mutual support and inspiration of teachers will become increasingly significant, especially in virtual learning environments Methodology To discover key elements and aspects of such learning environments, an online learning environment for flipped mathematics education was developed, and its application was investigated following design-based research principles Contribution In this paper, specifications of design elements and aspects of our online learning environments for teachers embedded into flipped education and other educational innovations will be introduced Findings The evaluation of the research data using grounded theory principles indicated that if online learning environments was to promote flipped approaches in mathematics education for teachers in our study the following categories were essential: (a) teachers want to be able to make decisions concerning online learning, (b) online learning environments should illustrate advantages of approaches/technologies as well as their practical relevance, (c) online learning environments should not lead to additional work for teachers, and (d) privacy and security of online learning environments Recommendations for Practitioners Following results of our study, teachers should be provided with a variety of high-quality learning materials and opportunities for teachers to share their own learning materials through online learning environments in professional teacher development However, when providing a variety of learning materials, course leaders should ensure not to overburden participants of professional teacher development Recommendations for Researchers For researchers, it is necessary to verify results of our qualitative study quantitatively and to apply our results in other fields of online learning as well Focusing on the contradictions between the visibility and dissemination of innovation through OLE and teachers' request for closed OLE could be fruitful Impact on Society Results of our study could also have an impact on working lives as a whole, and not just schools or professional teacher development The corona pandemic has increased the relevance of online working and related online learning for a growing part of our society High-quality online learning environments could play important roles in this professional transformation Future Research Our consecutive research step will be, on the one hand, to explore how online learning environments and their elements could support teachers in their everyday professional lives and thus shifting our research focus from professional teacher development to teaching and learning mathematics in schools On the other hand, our future research will focus on developing quality standards for learning materials for online learning environments Furthermore, research should also be continued in regions and subjects with less favorable conditions This enhancement of research setting should improve the generalizability of our results

Designing Online Learning Environments for Flipped Approaches in Professional Mathematics Teacher Development