Mathematical modeling into the "new curriculum standard", can you still get high scores by brushing and gambling
2022-03-22
Mathematics, once a "compulsory course" in the off campus training class, is a necessary option for various selection examinations. In the early years, the vigorous "Olympic mathematics class" was lively for a time. Now, with the promulgation of the new high school mathematics curriculum standard and the implementation of the "double reduction" policy, although the mathematics curriculum structure has changed, it is still the subject that "can distinguish the most", and it is also one of the subjects that teachers and students pay most attention to. Where is the change? "An important point of the reform of curriculum standards is to strengthen mathematical modeling and mathematical inquiry activities in content, and take it as a carrier to improve students' practice and innovation ability." In the words of Liu Laifu, vice president of Beijing Mathematics Association, "what we emphasize is no longer 'knowledge' but 'ability'. Now the test questions have increased the application background to examine the students' ability to solve problems in a more real situation. In this sense, it is basically impossible to get high scores by 'taking questions' and' brushing questions'." Mathematical modeling has been paid more and more attention by teachers and students. The mathematics curriculum standard for senior high schools (2017 edition, 2020 Revision) (hereinafter referred to as the "new curriculum standard") once again makes it clear that the core literacy of mathematics discipline includes mathematical abstraction, logical reasoning, mathematical modeling, visual imagination, mathematical operation and data analysis. Li Yanlin, a professor at Capital Normal University, felt the same way. In January this year, he participated in the project design exchange meeting of "practical research on mathematical modeling in primary and secondary schools" (phase I) in the experimental area of basic education curriculum reform of the Institute of curriculum and teaching materials, "At the scene, teachers from all over the country shared cases such as' optimization of dining table layout in student canteens', 'mixed nucleic acid detection' and 'distribution of students in urban schools'. The content was vivid, wonderful, realistic and practical, highlighting the important value of mathematical modeling to the cultivation of students' mathematical ability." What is mathematical modeling? Is it the "password" for future students to learn mathematics well? 1. Guide children from "solving difficult problems" to "paying attention to reality" With regard to mathematical modeling, the definition given by the "new curriculum standard" is: "mathematical modeling is the process of mathematical abstraction of real problems, expressing problems with mathematical language and building models to solve problems with mathematical methods. Mathematical modeling activity is a kind of comprehensive practical activity based on mathematical thinking and using models to solve practical problems. It is an important content of mathematics curriculum in senior high school." "As an important basic discipline and a precise scientific language, mathematical science appears in a highly abstract form. This highly abstract form is likely to cover up the rich connotation of Mathematical Science and form an obstacle to the practical application of mathematics." Academician Li believes that building a bridge between mathematics and application is undoubtedly an important way for the Chinese Academy of mathematics to build a strong bridge between mathematics and application. Lin Qun, an academician of the Chinese Academy of Sciences, also believes that all aspects of today's society involve mathematical knowledge or mathematical ideas, and mathematical modeling breaks through the traditional mathematical education paradigm and allows students to find and solve problems. It is a good mathematical learning model. "It is of great benefit to promote mathematical modeling in middle school. Mathematical modeling can enable students to re recognize the subject of mathematics, personally solve practical problems with mathematical methods, and improve students' fun in learning mathematics. The idea of mathematical modeling is very useful for students to apply what they have learned and integrate knowledge with practice." Lin Qun stressed. Li Daqian said that mathematical modeling is a golden key to open the door of mathematics. It is extremely important to develop mathematics and promote the application of mathematics. It is not only an important way to find and cultivate innovative talents, but also a key link to promote the reform of mathematics education and implement the curriculum standards of senior high school. 2. Through mathematical modeling, the children designed their own parking lot "Mathematical modeling also plays a key role in related disciplines and applications." Li Daqian introduced for example that in the third century BC, Euclidean geometry established by Euclid on the basis of summarizing previous achievements is a mathematical model of the spatial form of the real world. This model is very effective and has been playing an important role so far. "There are also some important basic differential equations of mechanics and physics, such as Maxwell equation in electrodynamics, Navier Stokes equation and Euler equation in fluid mechanics and Schrodinger equation in quantum mechanics. They are also mathematical models that grasp the essence of the discipline. They are the core content and basic theoretical framework of relevant disciplines, containing all important results and all possible applications." Seeing the unique value of mathematical modeling, Huang Haiyang, a professor at the school of Mathematical Sciences of Beijing Normal University, has been promoting and teaching mathematical modeling for many years. Since she taught the course of mathematical modeling in 2004, she has been exploring the transformation from basic mathematics to applied mathematics teaching. Since 2005, she has also organized mathematical modeling competition in Beijing Normal University with other teachers. Now, she has not only become the deputy director of the Organizing Committee of Beijing College Students' mathematical modeling and computer application competition, but also continued to promote mathematical modeling for middle school students. "The topics of mathematical modeling are realistic and targeted, with application scenarios, which is very interesting." Huang Haiyang introduced that Mingyuan Experimental Primary School in Chaoyang District, Beijing is located in a residential area, and parking is a difficult problem. The neighborhood committee opened up an open space to build a parking lot. Tao Wendi's team, a teacher of the experimental primary school, and the fifth grade students completed the parking lot design in combination with practical activities. Combined with the idea of mathematical modeling, this practical activity was designed as a five hour mathematical modeling course. "In the end, the children not only made the parking lot model, clarified the production ideas and methods, but also expanded and solved some other problems." After that course, Professor Cui Li, who has long been engaged in mathematical modeling research and teaching at Beijing Normal University, called it "very good". "Students move in an all-round way, from thinking to action, devote themselves wholeheartedly and actively contribute their wisdom." Huang Haiyang said: "it can be seen that the mathematical modeling course is very important, which can let students understand what is the use of mathematics and how to use it." 3. Asking questions is more valuable than solving them Liu Laifu introduced that in 1997, the Beijing Mathematics Association hosted the "Beijing first middle school students' mathematics knowledge application competition", which has been held for 21 consecutive sessions. "The competition is divided into preliminary and final competitions. It will also allow students to complete a small paper on the application of mathematics, that is, let students observe society, nature and life, find problems, put forward problems, and use their learned mathematics and other knowledge to turn the problem into a mathematical problem, so as to solve this problem." The students who participated in the competition felt very deeply. In 2017, as a senior high school student in Beijing No. 8 middle school, Liu Zhiya submitted her entry paper - "optimization of keyboard arrangement". This paper comes from her daily observation and Reflection on life—— "A long time ago, I read an article saying that the current keyboard was produced in the era of English mechanical typewriter. If the adjacent print heads act one after another, it is prone to mechanical failure. Therefore, the designer specially arranges the letters with high continuous use frequency in English in non adjacent positions. In fact, this is not conducive to improving the input speed. Affected by path dependence, the electronic computer keyboard still uses this design." Liu Zhiya thought, can we design a more reasonable keyboard on the premise of Chinese Pinyin input method? "After consulting many materials, I finally selected 1011 Chinese characters with high frequency in the modern Chinese Frequency Dictionary, converted them into Pinyin Codes, counted the occurrence frequency of a single letter and the occurrence frequency of two adjacent letters, made appropriate assumptions about the keystroke speed of different key positions, and tried to unify 'high frequency' and 'fast speed', so as to design a more reasonable keyboard." After participating in the competition for two consecutive sessions, Liu Zhiya gradually realized that in the face of problems in real life, what needs to be considered is not "what I have learned and what I haven't learned", but "what I should learn and use" in order to solve such a problem. "This is exactly the value of mathematical modeling." Liu Laifu told reporters that the education and competition activities related to mathematical modeling have broken the self-contained and self closed situation of the original mathematics curriculum, and opened a channel and provided an effective way for mathematics to contact the external world. By participating in the practice of mathematical modeling, asking, analyzing and solving problems, students can obtain valuable experience and personal experience that can not be obtained in class and books, which will enlighten their mathematical mind and promote them to better apply mathematics and taste mathematics. "For students, asking questions is more valuable than solving problems." Li Yanlin said that doing so will further promote the development of students' application, innovation consciousness and ability, and is an important breakthrough and focus for cultivating innovative scientific and technological talents with large scale, reasonable structure and excellent quality. (outlook new era)
Edit：Yuanqi Tang Responsible editor：Xiao Yu
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