First, improve the relationship between teachers and students, so that students can truly become the main body in teaching.
In traditional teaching, the form of teaching communication is institutionalized: teacher-centered, podium-centered. The relationship between teaching and learning is not the equal relationship between teachers and students, but the relationship between guidance and being guided, command and obedience, which permeates the authority of teachers, that is, teachers are authoritative spokespersons and students are passive recipients in teaching form.
The new curriculum standard of mathematics puts forward: "Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. Teachers should stimulate students' enthusiasm for learning, provide students with opportunities to fully engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration, cooperation and exchange, and gain rich experience in mathematical activities. " The new standard reveals that the essence of teaching activities is a kind of communication and cooperation. Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. Teaching and learning in teaching activities not only form a one-to-one relationship between teachers and students, but also form a multiple network relationship between students, teachers and student groups, and students and student groups. Teaching is carried out in this network relationship. The realistic teaching analysis shows that there is a mutual subjective partnership between educators and educatees, and the teaching process is neither a simple student nor a simple teacher. Teachers and students are the center of teaching.
Second, understand the essence of mathematics and establish a scientific view of mathematics.
With the implementation of the new curriculum, the teaching concept of mathematics teachers has been further optimized, but there are still quite a few teachers who lack a clear understanding of what mathematics is, what the essence of mathematics is and how to cultivate innovative spirit in mathematics teaching. From a macro point of view, to understand mathematics, we must first understand the essence of mathematics, that is, what mathematics is. Because the essence of mathematics is an unavoidable, primary and basic problem in learning and studying mathematics. Although there is no complete answer to this question so far, the essence of mathematics is put at the beginning in both academic monographs on mathematics, syllabus and curriculum standards. The contemporary general description of the essence of mathematics is that mathematics is a science that studies the spatial form, quantitative relationship, mode and order of the real world. Mathematics is a powerful weapon for human beings to understand and conquer nature. Mathematics is an indispensable tool for people's life, work and study. Mathematics can help people to process data, calculate, reason and prove. Mathematical models can effectively describe natural and social phenomena; Mathematics provides language, ideas and methods for other sciences, and is the foundation of all major technological developments. Mathematics is a powerful weapon for human beings to understand and conquer nature and a key to master nature. The classified query of periodical articles is in the periodical library. Third, pay attention to the cultivation of teachers and students' innovative spirit and practical ability.
Under the concept of new curriculum standard, the relationship between teachers and students is not the relationship between a bucket of water and a bowl of water, but how teachers guide students to find water sources. The origin of mathematics is the logical starting point of mathematics, that is, the source of its emergence and development. Learning mathematics is to transform abstract and incomprehensible mathematical academic forms into vivid, concrete and comprehensible educational forms. Intersections, network points, combination points and connection points between mathematical knowledge and between mathematics and other disciplines. So as to explore the origin of mathematics and understand its essence.
Mathematics comes from life, nature and society. People live in a colorful real society. Knowing, understanding and experiencing mathematics is to explore the life, essence and social origin of mathematics. The new curriculum concept and scientific mathematics view put forward higher requirements for teachers to implement mathematics teaching, but today we are still in the dilemma of "quality education" and "exam-oriented education". However, I believe that as long as we have a new concept of curriculum and a scientific concept of mathematics and a strong ability of innovation and practice in mathematics teaching, we will have the confidence and ability to achieve the best balance between pursuing students' academic achievements in mathematics and improving their quality.
Fourthly, recognize the educational form of mathematics and establish the open view of mathematics teaching materials under the new curriculum concept. Just as water has three forms: liquid, gas and solid, mathematics has three basic forms: primitive form, academic form and educational form. Primitive form is a complicated and tortuous mathematical thinking when exponents discover mathematical truth and prove mathematical propositions. It has the historical value of being imitated by future generations. The academic form of mathematics (scientific mathematics) is a rational speculative system abstracted from objective things. Its formation and development is mainly based on the strict deduction and reasoning of abstract patterns and structures with symbols and logical systems, and all parts of knowledge are closely linked to form a strict scientific system. The basic characteristics of mathematical academic forms are highly abstract, rigorous, unified, systematic, formal and modeled. Because of students' age characteristics and cognitive level, we can't communicate directly with students in the academic form of mathematics. The educational form of mathematics (subject mathematics) refers to that education experts or teachers, according to the principles of pedagogy and psychology, according to students' existing cognitive level and life background, properly return the academic form of mathematics to its original nature, return to the state of mathematicians' original innovation and invention, "disrupt" the linear arrangement of the knowledge of mathematical academic form, integrate the latest achievements of contemporary science and technology, integrate relevant knowledge of different disciplines, integrate teachers' understanding, and rearrange the contents presented in textbooks. In this way, the academic form of mathematics is activated, and mathematical knowledge is transformed into a vivid, interesting, vivid, intuitive and easy-to-understand mathematical education form. To make students really understand mathematics, we should make mathematics closer to life and express it in the language of life; Mathematics should be integrated into the local society, nature, history, politics and life, so that mathematics has the original flavor of real life, thus forming mathematics with national color and strong local flavor.
The new curriculum standard requires that students should be trained into a new generation with initial innovative spirit, practical ability, scientific humanistic quality and environmental awareness, and with basic knowledge, basic skills and methods to adapt to lifelong learning.