Mathematics education is a comprehensive scientific system that holds significant importance in studying the seamless integration between university mathematics education and secondary mathematics education. This research paper delves into the challenges encountered during the transition from high school to university mathematics and offers analytical strategies and recommendations for both teachers and students. The objective is to enhance the continuity and coherence of mathematics education. Furthermore, tailored recommendations are provided to bridge the gap between high school and university mathematics education, taking into consideration the unique characteristics of students from different provinces and cities.

This research focused on the design and implementation of the flipped classroom approach for higher mathematics courses in medical colleges. Out of 120 students, 60 were assigned to the experimental group and 60 to the control group. In the continuous assessment, which included homework and quizzes, the average score of the experimental group was 85.5 ± 5.5, while that of the control group was 75.2 ± 8.1 (P < 0.05). For the final examination, the average score in the experimental group was 88.3 ± 6.2, compared to 78.1 ± 7.3 in the control group (P < 0.01). The participation rate of students in the experimental group was 80.5%, significantly higher than the 50.3% in the control group (P < 0.001). Regarding autonomous learning ability, the experimental group spent an average of 3.2 hours per week on self-study, compared to 1.5 hours in the control group (P < 0.005). Other potential evaluation indicators could involve the percentage of students achieving high scores (90% or above) in problem-solving tasks (25.8% in the experimental group vs. 10.3% in the control group, P < 0.05), and the improvement in retention of key concepts after one month (70.2% in the experimental group vs. 40.5% in the control group, P < 0.01). In conclusion, the flipped classroom approach holds substantial promise in elevating the learning efficacy of higher mathematics courses within medical colleges, offering valuable insights for educational innovation and improvement.

While the rapid development of artificial intelligence has affected people's daily lives, it has also brought huge challenges to high school mathematics teaching, such as restructuring the classroom teaching structure, transforming the role of teachers, and selecting classroom teaching methods. Based on this, the article explores the application strategies of AI technology in improving knowledge introduction, improving mathematics classroom efficiency and stimulating students' learning interest, with a view to optimizing classroom teaching links, improving students' core discipline quality, and promoting the development of high school mathematics teaching informatization.