First of all, teachers should become researchers. Teaching process is not only the process of knowledge reproduction, but also the formation process of knowledge reproduction. This requires teachers to have the experience of personally participating in the research, and reproduce their own research process and research results to students for demonstration and inspiration. On the other hand, there are few ready-made materials in the development of research-based learning topics, and teachers' creative work needs to be brought into play.
Secondly, teachers should have a sense of mission and responsibility to carry out research-based learning. Social development and the development of student education put forward higher requirements for teachers, who shoulder an unshirkable historical mission. Some middle school teachers always think that research-based learning is a matter for college students and graduate students and should be undertaken by university teachers and professors. Inquiry learning is a learning process, regardless of time and stage. Anyone with a certain basic knowledge can carry out research study.
Second, the leading role of teachers in high school mathematics research projects
Teachers make appropriate choices according to students' inquiries, mainly through guidance.
1. Communication and integration.
After thinking, discussion and exploration, individual students or groups have achieved initial results. Teachers use classroom time to organize students' communication, and affirm and praise students' whimsy (even if they are naive) to encourage innovation. Teachers and students learn from each other in equal communication, and finally express the revised conclusion in the form of a paper.
2. Deepen the summary
After the exchange between teachers and students, guide students to sum up and reflect in time. Let the students talk about the blocked thinking in the process of research and study, and talk about the feelings and enlightenment after the exchange. This topic focuses on guiding students to learn the general operating procedures of research problems and master the common thinking methods: inductive reasoning from special to general, analogical reasoning from special to general, etc. Through the reflection and summary of the research process, students gradually accumulate research experience and master research methods, so as to truly learn to learn.
3. Analogy application.
After the exchange and summary, the teacher gives the same type of questions, so that students can use their own research results to solve them independently. It is self-evident that students are happy after completing their tasks independently, thus enhancing their confidence in research-based learning.
4. Promotion and extension.
After the completion of the above topics, teachers guide students to think about whether they can be further promoted and re-explored, so that students with certain abilities can continue to explore and realize that knowledge is infinite and the process of learning and exploration is endless.
Third, the principles that should be followed in developing research-based learning in senior high school mathematics teaching.
1. The principle of facing all students.
Research-based learning should be suitable for students' reality, not too high, and should reflect students' recent development fields, and should not be the patent of a few students. Everyone should participate in the research and gain experience by participating in the research process.
2. The principle of hierarchy.
The selected content should be able to distinguish different levels and embody the principle of individuality, so as to meet the learning needs of students at different levels. Homework after class should also be graded, so as to meet the needs of students with spare capacity for further research.
3. The principle of combining with the teaching content.
In order for all students to participate in the research, the selected content should be related to the teaching content, which is an extension and expansion of the teaching content, so that students can better apply what they have learned.
4. The principle of feasibility.
The selected content should adapt to the actual level of students' learning, have certain depth and research value, and contain rich teaching ideas and teaching methods, so that students can gain something through research.
5. The principle of cooperation.
The selected content should reflect the advantages of cooperative learning, and students should be organized to discuss and cooperate with each other in order to better complete the research.
6. The principle of miniaturization and diversification.
The selected content can be completed in a short time, and the topics should be diversified to attract more students to participate. Especially in the initial stage of research study, students do not have strong research ability, and they need to study as small as possible to achieve better research results.
7. Progressive principle.
Don't set too high a standard for inquiry learning at the beginning. The students are still in the hazy stage. They can start with case studies and gradually turn them into thematic studies to meet the requirements of students' thinking development.
Fourth, let the computer become the helper of research study in senior high school mathematics research projects.
With the advancement of educational modernization, computers and mathematical software are entering general mathematics teaching like "blackboard and chalk", which opens up a broader channel for the development of inquiry learning. Computer technology can combine words, sounds, graphics, animations, colors and flashes, which plays a unique role in exploring problems and cultivating students' innovative ability. For example, students can learn the function y=asin(ωx+φ) with the geometry sketchpad, which can never be achieved by traditional teaching methods. For example, discussing the images and properties of y=asinx+bcosx by computer, the design is as follows: ① Divide students into several groups, guide them to operate, give some values of A and B, display their images on the computer, and carefully observe and record the results of each group; ② Analyze the influence of data A and B on the function image; ③ Guess the function expression corresponding to the image; ④ Using mathematical knowledge to prove conjecture; ⑤ Verifying the research results by computer; ⑥ Write a research report. Through experiments, observations, guesses, proofs and tests, students have personally experienced every occurrence and formation process of knowledge and truly entered the role of a researcher.