[
Key words: behavior-oriented teaching method, mathematical modeling.
At present, China's vocational education is booming, and emerging vocational education takes the road of characteristic education. According to the training objectives and requirements of vocational education "training skilled and practical front-line management talents, technical talents and skilled workers", theoretical courses and practical courses are gradually moving towards integrated teaching, which reduces the class hours of mathematics courses with strong theory and abstract content, and proposes to apply what they have learned to serve the profession. It is a new teaching goal and requirement to improve students' ability to solve practical problems by applying mathematics and to improve students' ability of inquiry learning and autonomous learning. Traditional teaching methods can't achieve and complete this teaching goal, and mathematics class must be reformed. Mathematics class should not only learn mathematics knowledge, but also pay attention to the cultivation of students' abilities in all aspects, so as to lay a good foundation for students' employment.
In the reform of mathematics teaching, the first thing is the orientation of mathematics curriculum. Mathematics is an essential basic course for engineering majors, and each major has its own emphasis on its application. All majors teach the same teaching content, which can't meet the needs of all majors. Through the communication and research with teachers of various majors, we can understand and master the emphasis of various majors on mathematics content. For example, senior technicians use more knowledge of set, calculus and complex variable function in electromechanical class, while computer majors pay more attention to the application of set, logical mathematics, linear algebra and graph theory, while economic majors use calculus, linear algebra and probability statistics. Therefore, courses and textbooks can be selected appropriately according to the math class hours of each major. Because mathematics knowledge is very systematic, rigorous and logical, we can only reduce the difficulty appropriately, omit long proofs and theoretical derivation, and pay attention to the application of conclusions, instead of deleting a lot of chapters, which will neither destroy the systematicness and logic of the textbook, nor cause learning difficulties due to the incoherence of knowledge in the learning process, and affect the formation of students' thinking ability.
Teaching objectives must be achieved through classroom teaching, and new teaching objectives need new teaching methods. However, whether it is mathematics in middle school or calculus in high school, most of the contents are pure theoretical knowledge, which is far from real life. It is very difficult for students to do inquiry learning and it is not in line with their actual level. However, after the theoretical knowledge has accumulated to a certain extent, we can set up appropriate cases that are closely related to reality, so that students can learn to transform their theoretical knowledge of mathematics into the ability to solve practical problems.
For example, in the course of calculus, when students have learned the concept of derivative, the calculation of derivative and the calculation of extreme value, and accumulated theoretical knowledge to a certain extent, they will enter the study of maximum and minimum values. All the textbooks are taught with two or three examples. If we follow the textbook step by step, students will not pay attention to the application of derivatives, and most students will accept the application problems as theoretical knowledge, which is completely complete.
The following is a concrete method of my math class. The theme of this course is maximum and minimum.
In the first class, first review the concepts of maximum and minimum learned in middle school, then give a graph, answer the question after observation, and let y=f(x) be continuous on [a, b].
Question 1: At what point can the maximum and minimum values be obtained?
Seeing the graph, students will naturally come to the conclusion that the maximum and minimum values can only be obtained at the maximum point, minimum point and end point.
Question 2: How to find the maximum and minimum values?
Give students five minutes to discuss, because they have learned the method of finding the extreme value. With the above conclusion, students can logically sum up the method of finding the maximum value and the minimum value through analogy: the maximum value is the maximum value, and the minimum value is the minimum value.
Question 3: If y=f(x) has only one extreme point in (a, b), then
Y=f(x) Is there a maximum or minimum in (a, b)? If so, at which point is the maximum or minimum value obtained?
With the previous foundation, some students only need a few minutes to get the answer: the extreme point must be the most valuable point. Made a chart.
It took only a short time of 15 minutes, and the students themselves drew two conclusions and a method by observing the graph. By using this way of questioning, old and new knowledge can be linked up, students' observation ability, thinking ability and autonomous learning ability can be exercised, and their learning enthusiasm can be mobilized to enliven the classroom atmosphere. Next, the design case of using guide grammar to set up cans in behavior-oriented teaching method is cited. Suppose the classroom is the design room of Pepsi cans, divide the students into 5-6 design groups, and give each group a task book. The task book is as follows
After receiving the task book, each group began to work as required until the end of the first class.
In the second class, each group continues to work. 15 minutes later, (each group has been working for 45 minutes), each group basically has results and each group stops working. Select a representative from each group to present the results for 20 minutes, including the calculation process, calculation results, teamwork process and a work record. Although the design process of each group is not complete, several combinations are combined to get one.
1, measurement data
The height is about 12cm, and the diameter of the bottom surface is about 6.2cm.
The ratio of diameter to height is about 1: 2.
2, the basis of modeling
When the capacity is 355ml (net weight), what is the bottom area and height, which is the most economical material, that is, how to design the diameter and height of the bottom surface to minimize the surface area under the condition of a certain volume.
3. Mathematical model
Let: the volume is v, the radius is r, the height is h, and the surface area is s.
At this time, the ratio of diameter to bottom height is 1: 1, which is different from the measured results. The students questioned the difference between the calculated results and the actual results. What role does our calculation play in the actual design? I asked you to calculate the actual surface area of cans, which is cm2, which is very close to the minimum surface area we calculated. Students understand that the base diameter and high design ratio are changed for aesthetic and easy-to-use reasons, but they are still based on the calculation results (the least raw materials). Mathematical calculation is the basis of design and is indispensable in actual production and life. Everyone is aware of the importance of learning mathematics.
The last 10 minute is the teacher's comment time. First of all, we must affirm and praise the work of each group. No matter whether their grades are good or bad, and the degree of oral expression, we should find their strengths, praise them and point out the shortcomings of each group, so as to arouse their enthusiasm and interest in mathematics. At the same time, we should select the best design team, give them extra points for their usual achievements, and establish a sense of competition among all groups. Summarize the knowledge points of this lesson and the second lesson will be over.
This 90-minute class completed the transition from theory to practice. During the design team work, students have experienced the process of division of labor, discussion and research, and self-study of teaching materials, which is a complete process of professional activities. At the same time, they have exercised their oral expression ability, teamwork ability and leadership ability of the team leader, especially. From the work records of each group, I found that the most difficult thing in the whole process is to establish a mathematical model, which takes the most detours and takes the longest time, and modeling is the link to turn theory into practice. Therefore, it is an important mission and responsibility of mathematics teaching to introduce the idea of mathematical modeling into daily teaching and cultivate students' mathematical modeling ability, which will promote the development of the whole mathematics teaching.
Practice has proved that this teaching method has achieved good teaching results and is well received by students. It emphasizes that students are the main body of the classroom and teachers are the protagonists of the classroom, which breaks the traditional "lecturing" teaching method and highlights its practicality. It shifts the focus of teaching from "teaching" to "learning", fully arouses students' learning enthusiasm and stimulates their thirst for knowledge, which fully meets the training objectives and requirements of vocational education. However, this teaching method can only be used after theoretical knowledge has accumulated to a certain extent, so that students will not encounter too many difficulties and knowledge gaps, and the whole learning process can be completed by students themselves, otherwise students' emotions will be greatly affected and they will lose confidence in themselves and their studies. No matter what kind of teaching method, only by fully considering students' actual situation and practical ability can teaching methods play their due role.
Finally, there are two issues that need to be discussed by colleagues:
(1) At present, all majors in technical schools are engaged in integrated teaching and modular teaching. How to break the professional boundaries and establish mathematical modules for different majors in mathematics modular teaching to meet the needs of various majors within 40 hours?
(2) The reform of mathematics textbooks is imminent. How does the new textbook embody modularity, highlight practicality and pay attention to the cultivation of students' ability?
[References] Advanced Mathematics compiled by Tongji University Mathematics Teaching and Research Section, Fifth Edition