First, students' mathematics learning process. 1. What is the starting point of students' learning and what are the different types of learning starting points in mathematics teaching? 2. How to find and effectively use students' learning starting point? 3. A case study of students with learning difficulties who are weak in mastering mathematical concepts, calculation skills or problem solving skills. 4. How to provide targeted counseling for learning cows? 5. About the causes of "polarization". 6. Systematic research on learning difficulties. 7. Research on the homework design of basic investigation before junior high school mathematics class.

Second, the study of teaching resources. 1. What teaching resources are available in the math class? What are the different types of teaching resources? 2. How to use the wrong resources in classroom teaching? 3. How to use teaching materials reasonably, such as small examples and exercises? 4. How to creatively organize the chaotic teaching materials and put forward new ideas? 5. Research on the knowledge background of the harmony between space and graphics, statistics and probability. 6. Frontier research on application problems and problem solving. 7. Sort out and analyze the mathematical thinking methods infiltrated by each grade. 8. How to embody mathematical ideas in computing teaching? 9. How to play the role of learning tools?

Third, the study of instructional design. 1, the general strategies and key factors of mathematics concept teaching in junior high school. 2. Research on the teaching strategy of combining calculation with application. 3. General strategies and key reasons of problem-solving teaching. 4. Design strategy of practice class. 5. Development and application of exercises. 6. Research on tangent number teaching in application problem teaching. 7. Research on the effectiveness of hands-on practice in mathematics teaching.