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.

This problem is a solar hut photovoltaic cell in the attached and overhead two installation methods, the type of photovoltaic cells and array mode and inverter type optimization design issues. In question 1, since the photovoltaic cells are attached to the roof and exterior surfaces, the direction and angle of the battery are uniquely determined by the direction and angle of the attached surface. The problem is translated to optimize the installation of a certain type on a single surface area (array) of photovoltaic cells, so that the total amount of solar photovoltaic power generation as much as possible, and the unit power generation costs as small as possible, which is a multi-objective optimization problem. The problem can be discussed in the ideal environment in a single surface area of the battery installation optimization program, and then the actual environment of the multi-surface optimization. In the solution to Problem 1, the unit on the south of the roof of the battery at the moment to accept the solar energy formula is generated. The definition of and is the moment of direct radiation intensity, for the moment the sun and the south of the roof of the plane where the angle, for the level of horizontal radiation intensity, for the south of the roof and the horizontal angle, the planefor the plane, the center of the heart, the vertical upward direction is the axis of the positive coordinate system, obtained with the sun height angle , the sun azimuth , red angle, angle and the sun when the relationship is generated. The conclusion is only installed in the small roof surface type of battery C11, and the rest of the surface is not installed. 35 years of electricity generation is 77126 degrees, the economic benefits of 16,488 yuan, the recovery period of 21.3 years. In question 2, because the photovoltaic cells in the roof and the external wall surface can be installed overhead, the panel orientation and tilt will affect the efficiency of photovoltaic cells. Therefore, in the optimization scheme of Problem 1, the orientation and inclination of the panel on each surface are further adjusted to calculate the optimum orientation and inclination of the panel on each surface. The problem can be in the ideal weather environment to establish the sun running and the battery board efficiency model, and then the measured environment test. The optimal orientation of the panel is southward, and the optimal angle with the ground plane is 39.89 degrees. The conclusion is only installed in the small roof surface type of battery C11, and the rest of the surface is not installed. 35 years of generating capacity of 82165.2 degrees, the economic benefits of 18,998 yuan, the recovery period of 13 years. In question 3, by the optimization of the above two issues, in the building to meet the requirements of the hut under the design of the various aspects of the cabin and battery installation, and further optimize the total power generation of the hut, economic benefits. The whole model solver is run in MATLAB7.0.

Intelligent toy design and development talents need to master certain electronic intelligent control, arts and crafts design, product modeling design and other skills. There is a shortage of intelligent toy designers in our country, and toy enterprises are in urgent need of professional and technical personnel engaged in toy product modeling and functional design. Therefore, it is urgent to cultivate intelligent toy design and development talents. This paper explores the necessity of cross-professional training of intelligent toy design and development talents, relies on teachers' scientific research and enterprise projects, etc., takes graduation projects as a breakthrough, pushes back the talent training curriculum system, and proposes an cross-professional collaborative training model. Through cross-professional combination training intelligent toy design talents, so that they have the design thinking of toy designers and a certain degree of electronic engineer design thinking, can better adapt to the rapid development of modern toy design industry, enterprises changing new requirements.

This study aims to explore the design and application of a learning achievement evaluation model, in order to improve the quality of teaching in the field of education and promote student development. This article starts with the importance of constructing a learning effectiveness evaluation model, and then clarifies the basic concepts and related theories of learning effectiveness evaluation, providing theoretical support for subsequent model design. In the model design section of learning effectiveness evaluation, propose the model design principles, indicator selection, and construction process to ensure the accuracy and comparability of the evaluation model construction. In the application and evaluation section of the learning effectiveness evaluation model, the application and evaluation methods of the main models in practical teaching were explored. Finally, the issues that need to be noted in the design process of the evaluation model were proposed in order to design a more high-quality evaluation system and promote the improvement of education quality.

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.