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.

The purpose of this study is to predict the frequency of mortality from urban traffic injuries for the most vulnerable road users before, during and after the confinement caused by COVID-19 in Santiago de Cali, Colombia. Descriptive statistical methods were applied to the frequency of traffic crash frequency to identify vulnerable road users. Spatial georeferencing was carried out to analyze the distribution of road crashes in the three moments, before, during, and after confinement, subsequently, the behavior of the most vulnerable road users at those three moments was predicted within the framework of the probabilistic random walk. The statistical results showed that the most vulnerable road user was the cyclist, followed by motorcyclist, motorcycle passenger, and pedestrian. Spatial georeferencing between the years 2019 and 2020 showed a change in the behavior of the crash density, while in 2021 a trend like the distribution of 2019 was observed. The predictions of the daily crash frequencies of these road users in the three moments were very close to the reported crash frequency. The predictions were strengthened by considering a descriptive analysis of a range of values that may indicate the possibility of underreporting in cases registered in the city’s official agency. These results provide new elements for policy makers to develop and implement preventive measures, allocate emergency resources, analyze the establishment of policies, plans and strategies aimed at the prevention and control of crashes due to traffic injuries in the face of extraordinary situations such as the COVID-19 pandemic or other similar events.

The six core competencies of mathematics in vocational schools are becoming increasingly important in mathematics learning. The reverse teaching design of vocational school mathematics, which focuses on core competencies, precisely grasps the internal logic of knowledge from a holistic perspective, and designs it on a unit by unit basis. The design process is to infer the starting point from the endpoint. Therefore, how to use reverse thinking in teaching design research in vocational school mathematics teaching under the background of core competencies will be the main content of this article.

The promulgation of the Curriculum Standards for ordinary high School (2017 edition, 2020 revision) has effectively promoted the reform of high school mathematics classroom. In order to cope with the change of textbook content in the new curriculum reform, it has become one of the important tasks for high school mathematics teachers to implement teaching activities better and sort out and analyze the differences between the old and new textbooks. This paper analyzes the differences between old and new textbooks from the three dimensions of system structure, course content and example exercises, and gives some reasonable teaching suggestions. Among them, the new textbook uses 2019 "Ordinary High School Textbook" person-taught A version of Compulsory Mathematics 1, and the old textbook uses 2004 "Ordinary High School Mathematics Curriculum Standard Experimental Textbook" person-taught A version of compulsory Mathematics 4. In general, the adjustment of the new teaching materials is more in line with the cognitive characteristics of students, pay attention to the penetration of mathematical culture and pay attention to the development of students' mathematical core literacy.

With the continuous development of education, the double reduction policy has gradually become the focus of educators. Especially for junior high school mathematics classrooms, there is an indelible connection between whether students can learn mathematics well and whether classroom teaching is effective, and the effectiveness of the classroom is often related to factors such as students' stress level. Therefore, as a qualified junior high school mathematics teacher, it is necessary to carefully do pre class work in daily teaching and research practice, design different forms of teaching and research plans under the double reduction policy, establish a unique learning atmosphere for students, and improve their core mathematical qualities. This article proposes corresponding solutions and strategies on how to carry out mathematics classroom teaching under the double reduction policy.