This research is single-group quasi-experimental teaching research, which controls the teaching form of the course for the participants. Based on literature analysis, it is pointed out that online live teaching is a vital teaching form, and the research on it has both theoretical value and practical significance. The research framework and measurement tools are constructed. The researchers selected the course on mathematical methodology as the teaching content. Twenty-six pre-service mathematics teachers were taught 17 times with 51 class hours in online live teaching. Pretest and post-test were carried out. The study found that online live teaching is effective. However, the interview result shows that most participants hope to combine online and offline learning. They prefer to communicate with teachers face to face in the classroom.

Preservice mathematics teachers’ accurate understanding of mathematical problem solving and its teaching is key to the performance of their professional quality. This study aims to investigate preservice mathematics teachers’ understanding of problem solving and its teaching and compares it with the understanding of in-service mathematics teachers. After surveying 326 in-service mathematics teachers, this study constructs a reliable and valid tool for the cognition of mathematical problem solving and its teaching and conducts a questionnaire survey on 26 preservice mathematics teachers. Survey results reveal that preservice mathematics teachers have a good understanding of mathematical problem solving and its teaching and are more confident in the transfer value of problem solving ability. By contrast, in-service teachers are more optimistic that problem solving requires exploration, continuous thinking, and the participation of metacognition. This article concludes that preservice mathematics teachers should focus more on the initiative and creativity of students and put students at the center of education. In addition, teacher educators should provide more teaching practice opportunities for preservice teachers. The findings also show that in-service teachers’ understanding of problem solving and its teaching is inferior to that of preservice teachers on some indicators, implying the importance of post-service training for in-service teachers.

Since the outbreak of COVID-19, online teaching has been widely practiced. Ensuring the quality and efficiency of online teaching has become an important research topic. Teachers’ views of online teaching directly affect the quality of instruction. The study aimed to understand whether there are differences in the basic perceptions of online teaching among teachers in different disciplines. Through a web-based questionnaire, the researchers surveyed 198 teachers from different disciplines about their perceptions of online teaching. The research method was a convergent mixed-method design. SPSS 22.0 was used to analyze quantitative data, and qualitative data were analyzed using NVivo 11. The results showed significant differences in the attitudes of teachers to adopt online teaching as the norm in different disciplines. Social science teachers preferred online education not to be the norm, while natural science teachers preferred online education to be the norm. In addition, there was little difference in the perceptions of online teaching among teachers of different disciplines. Most of them pointed out the problem of interactive communication in online teaching and gave suggestions about it. Online teaching has value, but there is still much room for improvement. It is necessary to strengthen the construction of facilities for online education, consider the characteristics of disciplines, and train teachers in teaching methods, learning psychology, and technology.

No abstract