Thinking ability is the most important ability in primary school mathematics, including logical thinking ability, intuitive thinking ability, image thinking ability and creative thinking ability. Knowledge is the result of thinking activities and a tool of thinking. Learning knowledge and training thinking are not only different, but also inextricably linked. They are carried out simultaneously in the process of mathematics teaching in primary schools. The process of mathematics teaching should be the process of cultivating students' thinking ability.

Mathematics teaching is closely related to thinking. Mathematics teaching refers to the teaching of mathematical thinking activities. Mathematics teaching is essentially a process in which students learn the results of mathematicians' thinking activities through mathematical thinking activities under the guidance of teachers, develop mathematical thinking, and transform students' mathematical thinking structure into mathematicians' thinking structure.

2 Overview of mathematical thinking ability

2. 1 the significance of mathematical thinking

Mathematical thinking is aimed at mathematical teaching activities. It is a process of understanding the essence and laws of mathematical objects through a series of work such as putting forward, analyzing, solving, applying and popularizing mathematical problems.

2.2 The meaning of mathematical thinking ability

Mathematical thinking ability is the synthesis of various thinking abilities necessary for people to engage in mathematical activities. Mathematical thinking ability mainly includes four aspects: ① observation, experiment, comparison, guess, analysis, synthesis, abstraction and generalization; ② Inductive, deductive and analogical reasoning; (3) will logically and accurately explain their own thoughts and opinions; ④ Being able to use mathematical concepts, ideas and methods to distinguish mathematical relations and form good thinking quality.

2.3 Definition of Mathematical Thinking Ability

The newly promulgated mathematics syllabus defines the conventional mathematical thinking ability as follows: ① the ability to feel and judge numbers and shapes; ② Ability of data collection and analysis; ③ Geometric intuition and spatial imagination; ④ Ability of mathematical expression and mathematical modeling; ⑤ Mathematical operation and transformation ability; ⑥ Inductive conjecture and rational reasoning ability.

3. How to cultivate students' mathematical thinking ability in primary school mathematics teaching?

3. 1 Turn abstraction into intuition and promote students' thinking.

In the teaching of basic knowledge of mathematics, we should strengthen the teaching of forming concepts, rules and laws, which is also an important means to cultivate students' initial logical thinking ability. However, the teaching in this area is abstract, and the students are young, lack of life experience, poor abstract thinking ability and difficult to learn. Students' learning of abstract knowledge is a leap on the basis of a lot of perceptual knowledge. Perceptual knowledge is the basis for students to understand knowledge, and intuition is the way and source of information for mathematical abstract thinking. In teaching, we should pay attention to the transformation from intuition to abstraction and gradually cultivate students' abstract thinking ability. For example, in teaching the knowledge of "angle", in order to make students get the correct concept of angle, we should first guide students to observe the angles formed by objects and models, such as triangles, pentagrams, open scissors and fans, and abstract the angles from these objects. Then through physical demonstration, nail one end of two thin wooden strips together and rotate one of them, which intuitively shows that a ray can get different angles by rotating around its endpoint. Students can demonstrate by themselves with prepared learning tools, and clarify the concept of angle from the perspective of movement, so as to prepare for introducing the concepts of straight angle and rounded corner.

3.2 Contact old and new knowledge to develop students' thinking

Contact old knowledge, make associations and analogies. Old knowledge is the foundation of thinking, and thinking is the bridge to new knowledge. Associating analogy from old knowledge is also an effective way to seek the correct thinking direction. Association and analogy compare two similar or similar knowledge or problems, find the connection and difference between them, and then find the correct answer to the question. Mathematical knowledge has a strict logical system. As far as students' learning process is concerned, some old knowledge is the basis of new knowledge, and new knowledge is the extension and development of old knowledge. Students' cognitive activities are always based on existing old knowledge and experience. Every time you teach a new knowledge, you should review the old knowledge as much as possible, make full use of the existing knowledge to pave the way, and guide students to develop their thinking by using the law of knowledge transfer in the process of acquiring new knowledge. For example, when teaching "the relationship between the parts of addition and subtraction", first review the names of the parts in addition, and then guide the students to draw from 35+25=60: 60-25 = 35; 60-35=25。 By comparison, we can see that the figures in the latter two formulas are actually addends in the former formula. Through observation and comparison, let the students sum up the formula for finding addend: one addend = sum minus another addend. In this way, students are guided to learn new knowledge by reviewing the past, and new knowledge is brought into the original knowledge system, which enriches knowledge, broadens their horizons and develops their thinking.

3.3 Carefully design questions to guide students' thinking.

Pupils have poor independence, are not good at organizing their own thinking activities, and often think of what they see. Cultivating students' logical thinking ability is mainly through the demonstration, guidance and guidance of teachers in the teaching process, so that students can acquire some thinking methods in a subtle way. Teachers carefully design questions in the teaching process, put forward some enlightening questions, stimulate thinking, and mobilize students' enthusiasm and initiative to the maximum extent.

For example, Xiaoling made seven pentagrams and Xiaoyun made eight pentagrams. They gave the kindergarten children 10 five-pointed stars. How much is left?

Solution: Specifically, we can design the following questions:

"What does this question tell us?"

"I know Xiaoling made seven and Xiao Yun made eight. What can I find? "

"I also know that I gave 10 children to the kindergarten. What can I find? "

"So what is the question first, and then what?"

Students' thinking ability can be effectively developed only when they are active in thinking. In the teaching process, teachers should put forward thoughtful questions with moderate depth according to the key points of textbooks and students' reality, so as to activate each student's thinking activities and master the newly learned knowledge through correct thinking methods.

3.4 Reasoning training promotes students' thinking.

Language is the tool and shell of thinking, which strengthens the language in mathematics classroom.