Qin Meifang, Taihu Senior High School, Jiangsu Province
With the expansion of enrollment scale, the phenomenon of "average dilution" has appeared in mathematics education. In order to overcome the difficulties in mathematics learning, it is necessary to return to "hometown" and recreate "childhood", so that students can get in touch with mathematics materials again, experience mathematics experience, participate in mathematical operations and enjoy mathematics happiness; Starting from the new concept of mathematics education, people-oriented and opening up new channels for students' mathematics learning. To this end, I participated in the Tenth Five-Year Plan project-"Teaching Research of Mathematics Experiment in Senior High School (hereinafter referred to as me)", which was planned and presided over by Mr. Bao Weimin, and took the lead in carrying out relevant research work in China. In this process, I encountered many difficulties, gained some, and did some thinking.
I myself and my present situation
ME teaching is a teaching process that allows students to operate by themselves and finally acquire concepts, understand and solve problems through activities such as exploration, discovery, thinking, analysis and induction. It is a process of creating or changing certain mathematical situations according to research objectives, studying the essence of mathematics and discovering mathematical laws through thinking and operating activities under certain conditions. It is a combination of thinking experiment and operation experiment.
Computer technology and network technology provide effective means for multimedia teaching. In teaching, we use software tools to make the elements that constitute and represent a certain mathematical problem into courseware or integrable ware, that is, build a problem situation on the computer platform, and teachers or students can control each element in an orderly way to change various situations, and observe the problem, verify the conclusion, experience the essence and induce and discover new conclusions through cooperative learning of student groups. This is a math experiment in teaching. Focusing on the teaching materials, we carefully explore the experimental factors and topics in the teaching content, compile courseware and compile a database, try to build three teaching modes of "Mathematical Experiment" based on stand-alone computer, network classroom and campus network, study the evaluation system of practical operation points, processes, implementation strategies, evaluation indicators and methods, and form the teaching topic of "Mathematical Experiment" as soon as possible.
In the process of experimental operation, different multimedia environments have different teaching methods and steps.
Based on the experimental research of stand-alone or multimedia comprehensive classroom, the classroom is more about the demonstration and guidance of teachers, and students mainly observe experiments, experience changes and discover laws.
Under the network classroom environment, students will have a wider world, more opportunities and time, stronger interest and higher participation under the guidance of the teacher's experimental scheme or the experimental scheme designed by themselves, group consultation learning will really become possible, the teaching idea of "research learning" will be fully reflected, and the teaching results of learning ability training will be higher.
Microteaching stimulates students' interest in inquiry, improves students' ability of experiment, analysis and inquiry, and can be transformed into extracurricular activities. We are going to choose some open and exploratory topics to put on the campus network, so that students can study individually online after class, and students and teachers can exchange and discuss online.
ME teaching fully embodies the idea of using experimental means and inductive methods to teach mathematics: starting from several examples (including examples designed by students themselves) → doing a lot of experiments on computers → discovering laws → putting forward conjectures → demonstrating, so that students can exert their imagination and creativity as much as possible, which initially reflects the functional transformation of teachers, students, content and media in the teaching process. My teaching has been well received by students and experts inside and outside the school.
Second, some thoughts on mathematics teaching research
1, the renewal of educational concept is the key.
In daily teaching, many teachers have begun to use mathematical experiments, but there are some differences in the content, form and method of application, and there are also differences in teaching effect. The author believes that the differences come from teachers' education, teaching concepts and understanding of modern educational technology.
(1) Mathematics needs experiments-the concept of mathematics. Mathematics has duality. Mathematics teaching should not only attach importance to the formalization of mathematics content, but also attach importance to the experience of mathematics creation process. Mathematical experience is inseparable from mathematical experiments. In mathematical experiments, laws are often discovered through observation, comparison, classification, analogy, induction and data processing. Only with a comprehensive view of mathematics can we consciously grasp some typical contents of "discovery" and "experiment" in the process of preparing lessons and design the teaching process of mathematics experiments, instead of giving the conclusions directly to students or just using experiments as a tool to verify the conclusions.
⑵ Attach importance to students' subjective participation-talk about educational ideas. The process of students mastering knowledge is the construction process of students' individual cognitive structure. Among them, activities are the first. For students at the stage of cognitive development, this kind of activity begins to show external activities. Due to the intellectual participation of the subject, the external activity process is internalized into the psychological process of the subject, thus producing personal experience. At the same time, activities must be actively carried out by students, and the degree of students' participation is an important symbol of teaching success or failure. Therefore, teachers should change from imparting knowledge to teaching instructors and organizers, so that students can make full use of mathematical experiments to participate in the teaching process, not just let students simply observe the teacher's performance.
⑶ Innovating the idea of mathematics education-about teaching idea. The basic idea of innovative education is to design the middle school mathematics teaching process as a process for students to rediscover and create. Without the creative process, innovative education is water without a source and a tree without a root. Therefore, the application of mathematical experiments should mainly be reflected in letting students discover, explore and create, and guiding students to participate in the process of re-creation.
⑷ Computer is not only an auxiliary tool for "teaching"-about technical concepts. With the rapid development of science and technology, modern high-tech is increasingly manifested as mathematical technology. In order to make students adapt to the requirements of the times, it is necessary to integrate modern technology with the content of mathematics, so that students can rediscover and recreate relatively independently under the guidance of teachers. Therefore, we should not use computers as general teaching AIDS, but should give full play to their advantages, from "teaching" tools to "learning" tools, from auxiliary teaching methods to mastering mathematical techniques, from learning knowledge to improving students' quality in an all-round way, from a single teaching method reform to the overall reform of curriculum, teaching materials, teaching methods and evaluation.
2. The improvement of education process is the key.
At present, many teachers still adopt the single teaching mode of "teachers talk and students listen", lacking the links of students' independent inquiry and cooperative discussion, which hinders the cultivation of students' ability. In ME teaching, we should pay special attention to the reform of teaching mode instead of "wearing new shoes and taking the old road". As we all know, there is no fixed teaching mode in mathematics education. This is itself an open and innovative process. However, in the teaching process, according to the teaching ideas and teaching rules, some relatively fixed teaching procedures and methods are often formed, which we can also call models. In ME teaching, I mainly think about the following modes:
(1) discovery rule. It requires students to actively explore and discover with materials under the guidance of teachers. Its procedure is: creating scenarios → analyzing and exploring → guessing hypotheses → demonstrating and evaluating. This teaching mode is mainly suitable for the teaching of concepts, rules, formulas, theorems, examples and other knowledge formation processes, which embodies the students' dominant position in the discovery process and pays attention to the cultivation of discovery strategies and methods.
(2) Application mode. The application of mathematical knowledge is the way and goal of cultivating mathematical ability. The general procedure of application mode is: practical problem → mathematical modeling → model solving → practical problem solving. The cooperation between TI and CBL (or CBR) can collect real-world data conveniently and quickly, which is convenient for students to analyze and process intuitively, and thus draw experimental conclusions.
(3) Structural model. Mathematics has systematic characteristics, and its definitions, axioms, theorems, rules and formulas all have systematic logical structures. Structural model is to use this feature to teach the whole structure. Often, after a problem is initially solved, students are guided to divergent thinking, and in the open environment of mathematical experiments, conditions and conclusions are changed, multiple solutions to a problem are sought, and new conclusions or the same laws are found. The teaching procedure of structural model is: overall structure → local research → forming system → overall structure.
When implementing the above-mentioned basic teaching mode, students can be guided to discuss with each other and between teachers and students, and classroom experiments and extracurricular experiments can be combined to explore new teaching forms. Teaching mode reflects the basic laws of teaching, but it should not be the framework of teaching. Attention should be paid to the flexible and comprehensive use of various teaching modes to optimize the teaching process as a whole.
3. Modern educational technology is the foundation.
To carry out ME teaching, teachers should first master computer technology and graphic computer technology. Teachers' technical training has become an important basic work.
Teachers must master the "Geometry Sketchpad", use the "Z+Z Intelligent Education Platform" developed by Academician Zhang Jingzhong, and skillfully use the TI-CBL(CBR) system. It is best to master a computer language.
In teacher training, two measures should be taken, one is to train teachers, and the other is to combine content teaching with mutual discussion. Teachers train teachers, have the same language, combined with teaching practice, it is easy to see the actual results. In the process of training, it is beneficial to renew ideas and advance technology to carry out discussions and strengthen mutual communication so that teachers can learn in an open environment.
4. Integration with curriculum is the direction.
We live in a high-tech era. High-tech has changed people's way of thinking and ideas, and also changed the structure of mathematical knowledge. What people used to think is important may not be so important today, but what people used to think is not important can now become very important. In addition to the change of content, the order of knowledge presentation will also change. With the development of science and technology, the reform of mathematics curriculum is imperative. ME is just at the intersection of modern educational technology and mathematics textbooks with computer technology as the core, and the integration of ME teaching and curriculum is the development direction of mathematics education.
The support of the school is the guarantee of success.
The attention and support of leaders at all levels is very important for the smooth development of medical engineering teaching. To carry out experiments, the research group must have experimental equipment such as computers, purchase relevant software, have a suitable experimental site, and have a certain number of experimental classes and corresponding class hours. In addition, due to the higher requirements for teachers in ME teaching, relevant teachers should have corresponding learning opportunities and time guarantee. Because the existing teaching tasks of front-line backbone teachers are already very heavy, it is necessary to establish a reasonable incentive mechanism to train them and let them do research. Only in this way, teaching and scientific research will not become a mere formality, and can serve education in a down-to-earth manner and put wings on school education.