Leveraging a set of visualization principles of VLA strategies (e.g., multiple visualization), the approach will be refined to analyze and visualize online lesson video data which can facilitate teacher reflection.

After prolonged face-to-face class suspension in Hong Kong, synchronous online instruction―a fallback teaching approach during the COVID-19 pandemic―is currently used to provide after-school support for students lagging behind in mathematics. However, ensuring student learning and engagement in online lessons is challenging. Teachers also lack the knowledge and skills to engage students in problem solving and online class discussion. To address these challenges, we first propose improving the design and practice of synchronous online mathematics instruction using  

1. variation theory which can guide designing a series of problems and teachers’ mathematical discourse to facilitate students’ online learning and  
2. academic productive talk which can inform how teachers engage students in online class discussion.  

Second, we propose supporting teacher improvement using our visual learning analytics (VLA) approach. Leveraging a set of visualization principles of VLA strategies (e.g., multiple visualization), the approach will be refined to analyze and visualize online lesson video data which can facilitate teacher reflection. With this theoretical foundation, we will conduct a two-year design-based study involving 10 secondary schools. As many schools give priority to students lagging behind, we will develop a 16-lesson supplementary program covering a series of essential foundation topics in Hong Kong secondary mathematics curriculum. In each school, two to four teachers, each of whom teaches the program three times across three semesters, will participate in the study with their Grades 11–12 students (i.e., about 30 teachers and a total of 1,350 students). Both quantitative (analytics from lesson videos, student survey, and student achievement tests) and qualitative (lesson video content, teacher reflection records, and participant interviews) data will be collected and analyzed via the mixed methods approach. This study has four design phases:  

1. identify problems via small-scale interventions by analyzing lesson videos and participant interviews (e.g., decreased student responsiveness to questions);  
2. develop initial solutions to the problems (e.g., using an “explain other” talk move to invite specific students in class discussion);  
3. evaluate and refine the outcomes of Phase 2 through three one-semester iterations by analyzing teachers’ discourse practice, students’ engagement in class discussion, their mathematics achievement, participants’ perceptions, and their suggestions. The findings from each iteration will inform the interventions in the next one; and  
4. conduct overall reflection.  

We expect this study will contribute to generating design principles that teachers can use in synchronous online mathematics instruction and a VLA-supported approach that helps them review and improve their teaching practice.