Mathematics should face all, that is, it should be responsible for every student. While teaching most students, we should give consideration to those students who have difficulties and spare capacity in learning, so as to "make all students meet the basic requirements" and improve as much as possible. Modern teaching requires people-oriented, teaching students in accordance with their aptitude, that is, according to students' individual differences in knowledge, skills, abilities, interests, specialties and other aspects, starting from the actual situation of students in a differentiated and targeted manner, so that students of different degrees can earn money and do their best to "eat enough" and "eat enough", so that each student's quality can be fully and harmoniously developed. This is quality education. Teachers should make use of the classroom as the main position in time, constantly mobilize students' learning initiative, establish students' self-confidence in learning, teach students mathematical knowledge and mathematical thinking methods, and make them form a scientific view of mathematics. Only in this way can all students like and love mathematics, change passive learning into active learning, and consciously become the masters of learning. Over time, students' mathematical consciousness has been enhanced. They will consciously use mathematical thinking methods to deal with various practical problems, and will also turn some seemingly unrelated problems in daily life into mathematical problems. Once students reach this level, we can say with relief, "Our training goal has been achieved".
2. Strengthen the cultivation of logical thinking ability and form good thinking quality.
Mathematics education should not only pay attention to specific problem-solving skills and methods, but also pay attention to thinking methods in the process of generating mathematical knowledge, so as to cultivate students' mathematical ability and excellent mathematical quality. In teaching, we should attach importance to the process of knowledge formation and discovery, let students explore independently, enter mathematics teaching activities and overcome the passivity of students' thinking. Infiltrate mathematical thinking methods in teaching: show the occurrence process of knowledge, expose the background of knowledge, create problem situations for students, teach students the methods of discovery and creation, inspire and guide students to think and create, let students learn in creation, gain in discovery and sublimate in success. Specifically, we can use the teaching of concepts, formulas and theorems to cultivate the generality and creativity of students' thinking; Using knowledge application teaching to cultivate the continuity and extensiveness of students' thinking; Use the multiple solutions and extended changes of typical examples and exercises to cultivate the agility and profundity of thinking; Use the accumulation of experience and the process of correcting problems in learning to cultivate students' directionality and criticism of thinking.
3. Strengthen the teaching of thinking methods, teach students to guess and cultivate innovative ability.
Teachers should fully explore the mathematical thinking methods contained in textbooks, highlight the teaching of mathematical thinking methods, and cultivate students' innovative ability. If conjecture is a very important mathematical thinking method, then scientific breakthroughs, technological innovations and other inventions often start with conjecture. However, in our daily teaching, we often overemphasize the rigor and scientificity of mathematics knowledge, while ignoring the cultivation of reasonable reasoning ability such as experimental conjecture, which makes students feel that mathematics is boring and difficult to learn. Teachers should teach students to guess through observation and experiment; Through the analysis of special cases, the general (* * *) law is summarized and a guess is made; Through comparison and generalization, we get a guess; To make a macro estimate, there must be a guess first, and then a strict mathematical proof. In this way, "guessing and proving are both taught", which stimulates students' desire to guess and makes them realize that mathematics is also a lively, passionate and philosophical subject.