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How to cultivate students' "reasoning ability" in primary school mathematics teaching?
The new mathematics curriculum standard holds that students should "develop their reasonable reasoning ability and preliminary deductive reasoning ability through observation, experiment, guess and proof". It can be seen that guessing is one of the important ways to develop mathematics and learn it well. Through the further interpretation of curriculum standards, we know that sensible reasoning is a reasonable reasoning, which mainly includes observation, comparison, incomplete induction, analogy, conjecture, estimation, association, consciousness, epiphany and enlightenment. As educators, we should strengthen the cultivation of middle school students' rational reasoning ability in teaching, so that students can apply the experience and methods accumulated in their daily study to their study and improve their learning interest and problem-solving ability. Among them, the rational reasoning in the natural state will be promoted to a more reasonable and scientific level, which may become the "golden key to scientific discovery." On how to cultivate students' ability in this respect, we should do the following specifically: 1. Guide and guide students to explore and discover mathematics by perceptual reasoning; 2. Pay attention to guiding students to use perceptual reasoning to find conclusions and clear goals, which is the starting point of research. Using perceptual reasoning to find the conclusion of the problem is equivalent to clarifying the direction, thus making the thinking more concrete, deformation or reasoning more purposeful and targeted. 2. It is an important way to cultivate students' creative thinking ability to pay attention to guiding students to use perceptual reasoning to find ways and methods to solve problems, to simulate mathematicians' thinking activities, to guide students to find theorems (formulas) plausibly and to conceive methods to prove theorems (formulas). 3. Attention should be paid to guiding students to use perceptual reasoning to extend or popularize problems. Many problems in mathematical research are extended or popularized in some form. Using perceptual reasoning to extend or popularize problems conforms to the development law of mathematical knowledge itself and students' individual psychology, creating space for students' perceptual reasoning. Secondly, Paulia said: "Effective application of rational reasoning is a practical skill", "We should learn it through imitation and practice, and develop rational reasoning ability in practice". Therefore, teachers should give full play to the leading role and guide students to participate in teaching. The creation of problem situations is the premise for students to participate in learning. Concealing the subject content into the situation, providing students with enough mathematical materials to explore, creating a thinking space with certain reasonable freedom, highlighting problems (which should be difficult and open), putting problems at the forefront of the contradiction between "needs" and "cognitive structure", and paying attention to the creation of students' emotional background. It is necessary not only to create situations that introduce problems, but also to create situations for each link. The creation of situations should meet the following requirements: a. It may lead to discovery; B. a certain interest; C. facilitate students' participation, but prevent students from reading the conclusions in the book. For example, create an operating situation for students when learning the "understanding of the circle": you can provide materials such as thumbtacks, pencils and cotton thread, so that students can discover the basic properties and concepts of the circle when exploring how to draw the circle independently. Third, the application of perceptual reasoning in life and games In addition to mathematics classroom teaching activities can promote the development of students' perceptual reasoning ability, there are many activities that can effectively develop students' perceptual reasoning ability. The new curriculum standard points out that students should "go through the process of mathematical activities such as observation, experiment, guess and proof, develop their reasonable reasoning ability and preliminary deductive reasoning ability, and be able to explain their views clearly". In the process of students' reasonable reasoning, teachers, as collaborators and instructors of students' learning, must evaluate students' reasonable reasoning. Teachers should encourage students to make bold and reasonable guesses and dare to break the mindset. Teachers should support and encourage students' unique guesses and give them appropriate evaluation; Teachers should pay attention to guiding and helping to correct unreasonable guesses put forward by students. In mathematics teaching, we should consciously cultivate and develop students' rational reasoning, and often carry out mathematical activities such as operation, experiment and observation, so as to cultivate students' rational reasoning ability throughout mathematics teaching. The general guiding ideology of our mathematics discipline is to strengthen the education of scientific thinking methods, and the coordinated development of rational reasoning and thinking methods in other disciplines will make the science park blossom. Only by using the guidance and infiltration of scientific thinking methods and dialectics in the acquisition, revision, verification and proof of conjecture, and organically combining perceptual reasoning with the education of other thinking methods, can we really improve scientific quality and develop ability. If we only pay attention to perceptual reasoning and ignore the education of other thinking methods, it may lead to meaningless learning, which is contrary to our original intention, and the cultivation of perceptual reasoning ability will be a dead letter with no characteristics. Similarly, it is not advisable to attach importance to the education of other ways of thinking and ignore the cultivation of reasonable reasoning ability.