1、 The influence of modeling teaching on students' scientific and technological innovation ability
1. Students' insight in analyzing problems can be improved through modeling teaching.
Mathematical modeling, as its name implies, is a subject that simplifies an actual problem through assumptions, finds the appropriate mathematical direction through the inherent laws of the problem itself, establishes a mathematical model that can explain and solve the problem, and verifies the accuracy of the model built through mathematical software and actual data. Due to the variety of problems encountered, if there is no certain insight, and the nature of the problem cannot be seen through the phenomenon, students may be unable to move forward, or even go the opposite way. The actual problems of modeling come from all walks of life. Although the professional background of each problem may be different, the mathematical models of these problems may ultimately be the same or approximate as long as they are based on reasonable simplifying assumptions. Mathematical modeling requires students to have eagle like insight, be able to draw inferences from one instance, see through the same internal mathematical relationship from the different "faces", and then use the theoretical knowledge and programming knowledge they have mastered to build mathematical models. Insight is essential to distill mathematical models from practical problems. Through the training of mathematical modeling, students can find the common characteristics of their mathematical knowledge from the fields that seem to have never been involved before, extract appropriate mathematical models from them, and finally propose solutions to problems according to the models. This ability is just what college students need for scientific and technological innovation activities. Mathematical modeling has changed the thinking habits of students, making them more rational and less emotional when looking at problems. Through the training of mathematical modeling, the students' insight has been exercised, laying a solid foundation for their participation in the scientific and technological innovation project of petroleum college students.
2. Students' innovative consciousness can be cultivated through modeling teaching.
The so-called innovation consciousness refers to a comprehensive skill with novelty and originality, which is formed by the complex synthesis of a person's intelligence, knowledge, independence and other good qualities, and can explore the unknown from the known without direction and constraint. The current pedagogy believes that innovation consciousness is an important standard to distinguish between first-class talents and second-class talents. For the cultivation of talents, innovation consciousness is the most critical. Because the solution of mathematical modeling is very flexible, there is only a specific solution direction, but there is no standard solution method and unified correct answer. What students need to do is to read out the direction of problem solving required by the topic, whether to predict or test, whether to classify or simplify, and then, according to the specific direction of problem solving, find the appropriate angle and mathematical method of problem solving, and find the appropriate mathematical software to complete and test the model. Therefore, students are no longer guided by teachers in the whole modeling process as before, but draw conclusions through their own thinking, which greatly improves students' innovation awareness.
3. Students' divergent thinking can be cultivated through modeling teaching.
Drawing inferences from one instance and understanding by analogy are the abilities that students should have when they participate in college students' scientific and technological innovation activities, and also an important way to solve many scientific research problems. In mathematical modeling, it is possible to eat all the fresh food in one move, but the premise is that students have divergent thinking and can find the point that is consistent with the problem itself. Mathematical modeling has a high requirement for divergent thinking. College students' scientific and technological innovation activities and research projects also require students to have divergent thinking. The cultivation and improvement of students' innovation ability can not be separated from the infiltration of divergent thinking. Divergent thinking can strengthen students' ability to discover, master and apply mathematical laws, improve their ability to extend the knowledge involved in the subject they are exploring, and develop their habit of using divergent thinking in scientific and technological innovation projects and scientific research. It can be seen from the above that students' divergent thinking can be cultivated through mathematical modeling teaching, and can be strengthened through mathematical modeling competitions. Having divergent thinking is the top priority for students to flexibly apply the mathematical knowledge they have learned to solve practical scientific research problems.