First, the penetration of research-based learning in daily classroom teaching
Curiosity is the intrinsic motivation for people to think and study problems. The higher the students' thirst for knowledge, the stronger their initiative to explore, and they can think positively and find answers to questions. In teaching, our teachers can use various methods such as attracting interest, arousing doubts, suspense and discussion to enliven the classroom atmosphere, stimulate students' enthusiasm for learning and curiosity, and help students get out of the trough of thinking. When teaching new classes, we can create problem situations according to the topics, which will make students feel anxious and eager to know the results of the problems, thus greatly increasing their thirst for knowledge. On the basis of following the teaching rules, lively, enlightening, exploratory and innovative teaching methods are adopted to fully stimulate students' curiosity, cultivate students' interest in learning, and lay the foundation for developing mathematics research-based learning activities.
The process of mathematics inquiry learning revolves around a mathematical problem that needs to be solved, and ends with students directly participating in the research and finally solving the problem. The process of students' learning mathematics itself is a problem-solving process. When students learn a new knowledge chapter, even a new theorem and formula, they face a new problem. In fact, the proof and derivation of many theorems and formulas in textbooks are good materials for mathematical research learning. For example, in trigonometric functions, the derivation of sine and cosine induction formulas; Study on inclination and slope of straight line: the positional relationship between straight line and parabola; Wait a minute. Based on certain mathematical theorems or postulates, appropriate problem scenarios can be designed for students to explore, discover general laws through their own efforts, and experience the fun of research.
Second, the infiltration of research-based learning in mathematical problems
It is necessary to form a "problem center" in the classroom, move the problems in social life into the classroom for research, and make the classroom a platform for problem display and a place for discussion and analysis. Cultivating students' ability of inquiry learning is to cultivate students' ability to find and solve problems. Therefore, in the teaching process, if students accept the knowledge taught by teachers with a strong desire to explore problems, then their brains will be in active activities and the knowledge they have gained will be more profound and solid. Teachers embody the ideas and methods of inquiry learning in the whole teaching process, closely combine the practical problems such as economy, politics, science and technology, culture and education in the teaching materials, infiltrate the research topics of students' independent innovation, cultivate students' innovative spirit, practical ability and research ability, develop students' personality and specialty, and initially learn inquiry learning. Teachers should strive to promote students to ask questions and reflect on the contents of textbooks; Promote students to discuss problems, enhance the awareness of problems and cultivate the spirit of questioning; Promote students to consciously theme the questions.
We carry out the "research study" of mathematics, which is to let students discover and study the problems they are interested in independently and experience the problems themselves. Various problems in mathematics provide many research directions for inquiry learning, and various problems in mathematics teaching are important carriers for infiltrating inquiry learning.
1, infiltrating research-based learning into mathematical application problems
The new curriculum reform aims at cultivating students' innovative spirit and practical ability, and the reform of traditional teaching theory is seriously divorced from reality. It is also an important aspect of our research study to let students apply what they have learned in mathematics to solving practical problems. Using the knowledge of sequence to solve the installment payment problem of buying a house and buying a car, using the method of finding the maximum function to solve the best scheme problem in real life, and so on. Drive students to study mathematics problems in life, make mathematics research-based learning bring endless fun to students, and really let students apply what they have learned. The application of mathematics is not only to apply mathematical knowledge to solve problems, but also to find and ask questions in actual production and life. Through students' social investigation and practice, we find and study mathematical problems in the actual production process, and establish mathematical models to solve various problems, so that students can use the basic mathematical theory they have learned to solve practical problems on the one hand, and abstract concrete cases in daily life into mathematical models on the other hand, and the research-based learning of mathematics is promoted circularly in this process.
2. Infiltrate research-based learning into mathematics open questions.
Mathematical open questions can reflect the thinking method of mathematical research, and the process of solving problems is the process of inquiry, the formation process of mathematical problems and the actual state of the objects to be answered. Mathematics open questions are beneficial to teaching students in accordance with their aptitude, and can be used to cultivate the flexibility and divergence of students' thinking, so that students can experience the sense of accomplishment in learning mathematics and the beauty of mathematics. The application of mathematics open questions in students' research study is of great significance.
The core of open questions is to cultivate students' creative consciousness and innovative ability, and to stimulate students' independent thinking and innovative consciousness, which is the concrete embodiment of a new educational concept. As the starting point of carrying out research-based learning in mathematics, mathematics open questions promote the openness and individuality of mathematics education, and cultivate students' innovative spirit and practical ability from finding and solving problems. Open-ended questions usually change the structure of propositions, change the way of setting questions, enhance the exploration and multi-angle thinking of problems in the process of solving problems, give new explanations to propositions and then form and discover new problems. Mathematics teachers should make full use of the opportunity of research-based learning to design open-ended mathematics questions and improve students' ability to use open-ended mathematics questions. However, whether it is to transform old problems or create new ones, the writing of open-ended mathematical problems should focus on the purpose of using open-ended problems. The open question should change with the purpose and object of use, and should be a supplement to the standard question. Open-ended questions used in research-based learning can help problem solvers make full use of existing mathematical knowledge and ability to solve problems. Open-ended questions should embody a complete mathematical thinking method and have distinct mathematical characteristics, so as to help problem solvers understand what mathematics is, why and how to learn mathematics.
Thirdly, research-based learning should be infiltrated into social practice.
In the research study of mathematics, social practice is an important channel to obtain information and research materials. Students can obtain first-hand information by observing, understanding and personally participating in things, which can be solved with the mathematics knowledge they have learned.
Inquiry learning emphasizes the connection between theory and society, science and life practice, and pays special attention to environmental problems, the influence of modern science and technology on contemporary life and major issues closely related to social development. It is necessary to guide students to pay attention to real life and participate in social practice activities in person. At the same time, the design and implementation of inquiry learning should provide conditions and possibilities for students to participate in social practice activities.
For high school students, to carry out research-based learning, it is necessary to cultivate their practical ability. Specifically, it mainly includes the following abilities: the ability to find, ask, analyze and solve problems; Hands-on ability; Ability to participate in social activities. For example, let students try to learn "Investigation on Bank Deposit Interest and Profit Tax": first, let students do research topics, find out the contents of bank deposit interest and profit tax from textbooks, extracurricular reading materials and the Internet, and then group students into CCB, ABC, rural credit cooperatives, national tax, local tax and other relevant departments according to actual needs to collect original data, and establish a mathematical model through analyzing and sorting out the original data. In the research process, students' enthusiasm and innovation ability are fully displayed, so that they can find the fun of learning mathematics and enjoy the joy of success.
Fourth, teachers should grasp the guidance of research-based learning.
Research-based learning emphasizes the main role of students, but also attaches importance to the guiding role of teachers. In the process of implementing research-based learning, teachers should take students as the main body of learning, exploring and solving problems, and pay attention to changing their own guidance methods.
Inquiry learning is an autonomous and exploratory learning activity for students under the guidance of teachers. Students gain direct experience through personal practice, develop scientific spirit and attitude, master basic scientific methods, and then improve their comprehensive quality and ability. As the organizer and instructor of this activity, teachers can neither replace students' autonomous learning according to the existing teaching mode, nor let themselves go. To achieve the ultimate goal of research-based learning, teachers must grasp the degree of guidance.
Because inquiry learning is a learning activity that students choose and determine topics from nature, society and life under the guidance of teachers, and actively acquire knowledge, apply knowledge and solve problems in the research process. However, there are various problems to be solved in social production, life and study. Different types of problems are suitable to be solved by different methods and means. In other words, different types of problems have different solutions or research models. Therefore, in the initial stage of inquiry learning, they should be familiar with and master as many research models as possible. For example, students should be familiar with the most basic scientific research methods such as observation, experiment, investigation and literature review, and at the same time let them know what topics are suitable for what methods. In the process of carrying out research-based learning, instructors are participants, instructors, organizers, promoters and collaborators of students' learning, that is to say, teachers should actively participate in students' research projects on an equal footing, express their opinions through exchanges with students, learn from each other and make progress together; Teachers should guide students' research ideas and methods; Teachers should do a good job in organizing and coordinating scientific research projects, create a good environment for students' learning activities, help students overcome difficulties and build confidence.