Mathematical consciousness refers to observing, explaining and expressing the quantitative relationship, spatial form and data information of things with mathematical concepts and attitudes, thus forming quantitative consciousness and good sense of numbers. Professor Yan Tujian of Beijing Normal University once said, "Although China has made great achievements in mathematics, mathematics has not really integrated into our cultural tradition so far, and people's mathematics consciousness is generally quite weak." This problem deserves serious reflection by mathematics educators.
Second, cultivate the consciousness of mathematical reasoning.
The so-called reasoning consciousness refers to the conscious consciousness of reasoning and reasoning, that is, when encountering problems, consciously speculate, make well-founded statements. Cultivate students' reasoning ability: First of all, when teaching new knowledge, teachers can tell students the essence of mathematical reasoning in popular language on the basis of students' accumulated reasoning experience. Secondly, understand the essence and value of reasoning in mathematics learning activities. Finally, in the process of reasoning, we should always point out the mistakes in reasoning.
Third, cultivate the consciousness of applying mathematics to solve practical problems.
The purpose of popularizing mathematics teaching is to enable students to acquire the ability to solve mathematical problems encountered in daily life and work and other problems that can be solved by mathematics. In short, it is to describe, analyze and solve problems with mathematical thinking habits. The reform of mathematics "application" is imperative, and artificial application problems can no longer meet the needs of cultivating application consciousness. Mathematics classroom should inject new vitality, actively advocate the knowledge theme of "being close to life and connecting with practice", strengthen the teaching of the process of occurrence, development and solution of mathematics knowledge, guide students to know and experience the role of mathematics in daily life through small-scale learning and cognitive practice activities, and cultivate students' ability to describe, understand and solve practical problems with mathematics.