Mathematical thinking includes:
1. Establish a sense of number, symbol and space, initially form geometric intuition and operational ability, and develop image thinking and abstract thinking.
2. Understand the significance of statistical methods, develop the concept of data analysis, and feel random phenomena.
3. Develop the ability of rational reasoning and deductive reasoning and express your ideas clearly by participating in mathematical activities such as observation, experiment, guess, proof and comprehensive practice.
4. Learn to think independently and understand the basic ideas and ways of thinking of mathematics.
From the new curriculum reform of 200 1 to the promulgation of the new curriculum standard of 20 1 1, many changes have taken place in our mathematics textbooks, and students' mathematical thinking has been paid full attention to in both form and content. The small version has become a big version, with refreshing and beautiful layout, beautiful pictures and texts, exquisite binding and accurate words, which can attract primary school students to read and learn and stimulate students' mathematical thinking; From the teaching content, the new mathematics textbook is rich in content, attaches importance to students' experience and understanding, and reflects the reasonable teaching order and rhythm according to the law of primary school students' learning mathematics, which provides clear ideas and steps for cultivating students' ability to solve problems and teaches students general methods to solve problems. What is presented in the textbook is: known, that is, understanding the realistic problem situation and finding the mathematical problem to be solved; How to answer, that is, analyze the problem, find a solution and solve the problem; Whether the answer is correct is to test, review and reflect on the results and solutions of the answer. Every mathematics textbook has designed a comprehensive practical activity. Starting from the textbook of the second volume of senior one, we set up a "mathematical wide angle" unit to infiltrate important mathematical thinking methods in an intuitive way. After the content of each unit is finished, a process evaluation section is set up, and a small growth file is established to provide students with opportunities for self-reflection and evaluation, so that students can get a good learning experience in mathematics and form good learning habits. After the end of the semester, set up a self-evaluation form and conduct self-evaluation around academic performance. These are not only conducive to the realization of the goal of "four basics and four abilities", but also conducive to the realization of the goal of "mathematical thinking".
Paying attention to the process of students' mathematical thinking can better stimulate students' curiosity about mathematics and stimulate and maintain students' enthusiasm for active and independent learning. Teachers are the real executors and implementers who really make students think effectively about mathematics. First of all, teachers must really grasp the textbook, make clear the editor's intention, and combine different teaching contents to implement the goal of "mathematical thinking" in classroom teaching. The content of number algebra should focus on establishing number sense and symbol consciousness, initially forming operation ability, understanding model thinking, developing image thinking and abstract thinking; The content of space and graphics should pay attention to geometric intuition and the cultivation of space concept; The content of statistics and probability should focus on developing the concept of data analysis; The content of synthesis and practice should pay attention to the cultivation of application consciousness and innovation consciousness. The cultivation of reasoning ability should permeate all fields of mathematics curriculum. Of course, different years have different emphases. The lower grades emphasize the accumulation of experience and mathematical thinking experience; Senior three should pay attention to the depth of thinking and cultivate students' various mathematical abilities. Secondly, teachers should pay attention to the following points when designing teaching:
1, effectively creating problem situations
Problems are the core of mathematics, and only good questions can arouse students' positive thinking. Teachers should seriously create novel, challenging and practical problem situations to stimulate students' mathematical thinking. Basically, every part of the textbook creates a good situation, and teachers should make full and effective use of it. In addition, realistic and life-oriented themes can be used as problem situations, and the content of mathematics itself can also be used as problem situations.
2. Carefully design classroom questions.
Teachers should carefully design classroom questioning, because classroom questioning is an important content to support students' mathematical thinking and the whole teaching activity, and it is the direct motivation for teachers to stimulate students' mathematical thinking. Reflection on our math classroom questions: some questions are repetitive and delay time; Some problems are not clear in direction; Some problems are trivial; Some questions are not accurate enough; In particular, some problems lack thinking. So how should teachers carefully design classroom questions? In my opinion, when designing classroom questions, teachers must combine the teaching content with the students' reality and ask questions at the junction of old and new knowledge; Ask questions in the comparison of knowledge; Ask questions where knowledge changes; Ask questions in summing up the laws of knowledge. When asking questions, we should pay attention to the problems from easy to difficult, in-depth and interlocking.
3. Give students enough time and space to think.
In the course of listening to lectures, we found that some teachers and students in classroom teaching are having simple conversations, especially when observing, discovering, summarizing and summarizing methods and laws. Teachers are always in a hurry, and students are not allowed to say or prompt rather than say before they express their ideas, which does not provide students with sufficient time and space for thinking. In teaching, teachers should provide students with sufficient time and space to think, let students think independently first, and don't directly give thinking ideas about problems; Don't deny students' ideas easily; It is necessary to present the questions or specific ideas put forward by students to other students in time for everyone to exchange and discuss. The children of poor families are in charge early, and the children whose parents let go are self-reliant and self-care, which means that the children have experienced a lot personally. Similarly, only when teachers let go and are willing can students fully experience and think about mathematics. It is also necessary to create a relaxed classroom atmosphere for students, and cultivate students to dare to ask, love to ask and know how to ask, thus stimulating students' mathematical thinking.
4. Design thoughtful exercises.
Exercises are generally divided into basic exercises, comprehensive exercises and extended exercises. Teachers can design one or two more thoughtful and challenging comprehensive exercises or expansion questions based on the teaching content and students' actual class, thus stimulating students' interest in learning, activating students' thinking and improving students' mathematical thinking.
In a word, our mathematics classroom teaching should create a good thinking environment for students, arouse students' mathematical thinking, constantly promote students' mathematical thinking, feel the charm of mathematical thinking, make students become people who can think and like mathematical thinking, and really let our children receive good mathematical education and form good mathematical literacy!