Middle school mathematics is an important basic subject, which shoulders the historical responsibility in the process of promoting quality education and is of great significance to the cultivation and development of middle school students' quality. In mathematics teaching, how to cultivate and improve middle school students' mathematics quality to meet the needs of socialist modernization is a major issue facing the majority of mathematics educators.

First, what is mathematics quality?

1. One definition in Professor Zhang Dianzhou's Design of Mathematics Quality Education (Draft) is to analyze and study from four aspects: mathematical knowledge concept, creative ability, thinking quality and scientific language; Professor Zhu pointed out in "Introduction to Teaching Research of Mathematical Thinking Methods" that mathematical quality includes four aspects: ideological and political quality, scientific and cultural quality, mental health quality and labor skill quality.

2. The traditional expressions in China are: basic computing ability, logical thinking ability, spatial imagination ability, and the ability to analyze and solve practical problems with mathematical knowledge. It is suggested to increase "the ability to establish mathematical models".

3. According to American mathematics curriculum standards, the goal of mathematics education should be to have the following five mathematical qualities: ① to understand the value of mathematics; (2) Have confidence in their mathematical ability; ③ Ability to solve mathematical problems; ④ Learning mathematics communication; ⑤ Master mathematical thinking methods.

Second, how to cultivate students' mathematical quality

Facing all, teaching students in accordance with their aptitude and attaching importance to the cultivation of mathematical consciousness.

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, organically combining "teacher-led" and "student-centered" and student-centered teaching in accordance with students' aptitude, that is, teachers conduct differentiated and targeted teaching according to students' individual differences in knowledge, skills, abilities, interests and specialties, starting from the actual situation of students, so that students of different degrees can gain something and do their best to make each student's mathematical quality comprehensive. 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". This is what we usually say: "teach people to fish, not just teach people to fish."

So, how to cultivate students' mathematical quality in classroom teaching? Let's take the training of top students as an example to talk about this problem.

1, pay attention to the foundation, and the change is the same.

To cultivate top students in mathematics, we must first pay close attention to the foundation. Only with a solid foundation can we study deeply, further cultivate our ability and develop our intelligence. But top students are the best among the students, and they are easy to be complacent. They are often ambitious in their studies, which are manifested as: paying more attention to skills than routines, paying more attention to thinking than calculation, and leaving out details. In teaching, we should be good at setting traps reasonably, discovering and excavating students' mistakes, so that students can have a correct understanding in thought. When marking examination papers, top students should strictly check the rigor of thinking and the neatness of paper, and don't give high marks easily. For top students, we should affirm our achievements in time and build up our confidence. But we should not praise it too much, but also point out its shortcomings. Follow the trend and ask them to slow down and be steady.

2. Change for the sake of change and expand your thinking.

School education is inseparable from classroom teaching, which is the main way for students to learn knowledge. "Change" in teaching can fully mobilize students' learning enthusiasm, train students' thinking flexibility, cultivate students' innovative ability, and contribute to the development of students' intelligence and ability.

First, the change of teaching content. As top students, reading the course according to the script will make them feel "not enough to eat". Therefore, we should talk less about the simple content, and "change" it appropriately, increase the relevant content that is not in the textbook but closely related to the textbook content, and introduce some background knowledge and some applications of the learned knowledge. Strengthen the infiltration of mathematical thinking methods.

The second is the change of teaching methods, changing the previous "spoon-feeding" teaching mode and paying attention to the integration of inquiry learning and imparting learning. Inquiry learning can maximize students' participation and cultivate students' problem awareness, scientific attitude and problem-solving ability. Combining with the spirit of the new curriculum standard, through designing questions and creating inquiry situations, we should pay attention to cultivating students' research consciousness, so that students can develop the thinking habit of "finding problems-putting forward assumptions-exploring each other-discussing and evaluating".

Third, a topic is changeable, pay attention to expansion. When preparing lessons, you should carefully choose examples of exercises. While emphasizing conventional methods, we should also pay attention to multiple solutions to one problem, multiple solutions to one problem and changeable problems, and pay attention to cultivating students' thinking and research ability.

Textbooks are the basis of teaching. It is very important to tap the potential of teaching materials, give full play to the role of teaching materials and handle the teaching of teaching examples and exercises. In teaching, based on the teaching materials, we should evolve, explore, expand and apply the examples and exercises of typical teaching materials, dissect a case from point to surface, from questions and categories, bring a series of exercises to life, and pay attention to the infiltration of mathematical thinking methods.