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What are the advanced ideas in mathematics teaching?
The basic idea of "Guiding Outline of Curriculum Reform of Basic Education" points out: "Effective mathematics learning activities can't rely solely on imitation and memory. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics." In other words, to change students' learning style, teachers should stimulate students' learning enthusiasm and make students willing to participate in exploratory and creative learning activities. The new curriculum standard also clearly puts forward three goals: improving students' knowledge and skills, attaching importance to students' learning process and methods, and cultivating students' evaluation ability and aesthetic ability. Therefore, the mathematics classroom design under the new curriculum standard concept should have the following characteristics: true, vivid, novel, beautiful and interesting.

(1) Reality means that the process of forming and improving students' knowledge and skills in classroom teaching should be solid, which is not only the basis of classroom teaching objectives, but also the basis of students' creative learning. Therefore, the design of classroom teaching must pay attention to practical results and improve students' quality.

(2) The new textbooks compiled by Beijing Normal University are rich in content, flexible and changeable, and open from traditional book knowledge to real life knowledge, such as "observation and measurement" and "statistics" in Grade One and "direction and position" and "conjecture" in Grade Two, so that students can learn vivid mathematics, life mathematics and valuable mathematics and solve practical problems with knowledge.

(4) In the classroom teaching under the new aesthetic concept, students are not only the masters of learning, but also form correct emotions, attitudes and values under the guidance of teachers. Therefore, classroom teaching also fully embodies the humanistic goal of cultivating students' evaluation ability and aesthetic ability.