Primary School Mathematics Teaching Thesis —— Cultivating Students' Thinking Ability in Primary School Mathematics Teaching
Cultivating students' thinking ability is a basic task of modern school teaching. One of the basic conditions for cultivating talents needed for socialist modernization is to have independent thinking ability and innovative spirit. Mathematics teaching in primary schools shoulders the heavy responsibility of cultivating students' thinking ability from the first grade. Here are some views on how to cultivate students' thinking ability.
Cultivating students' logical thinking ability is an important task in primary school mathematics teaching.
The content of thinking is very extensive. According to psychological research, there are all kinds of thinking. What kind of thinking ability should be cultivated in primary school mathematics teaching? It is clearly stipulated in the "Mathematics Teaching Syllabus for Primary Schools" that "students should have preliminary logical thinking ability." This rule is very correct. The next interview will be analyzed from two aspects. First of all, from the characteristics of mathematics. Mathematics itself is a definite system composed of many judgments, which are represented by mathematical terms, logical terms and mathematical statements represented by corresponding symbols. And some new judgments are formed by some judgments with the help of logical reasoning. And the sum of these judgments constitutes the science of mathematics. Although the content of primary school mathematics is simple and there is no strict reasoning, it is inseparable from judgment and reasoning, which provides a very favorable condition for cultivating students' logical thinking ability. From the thinking characteristics of primary school students. They are in the transition stage from concrete image thinking to abstract logical thinking. The abstract logical thinking mentioned here mainly refers to formal logical thinking. Therefore, it can be said that the primary school stage is a favorable period for developing students' abstract logical thinking, especially in middle and high grades. It can be seen that it is in line with the characteristics of mathematics and the thinking characteristics of primary school students to cultivate the initial logical thinking ability as the purpose of mathematics teaching in the primary school mathematics syllabus.
It is worth noting that the provisions in the outline have not received enough attention. There was a time when people talked a lot about creative thinking, but little about logical thinking. As we all know, in a sense, logical thinking is the basis of creative thinking, and creative thinking is often the simplification of logical thinking. As far as most students are concerned, it is difficult to develop creative thinking without good logical thinking training. Therefore, how to implement the objective requirements of "Primary Mathematics Teaching Syllabus" and cultivate students' logical thinking ability in a planned and step-by-step manner is still a problem worthy of attention and serious study.
The emphasis on cultivating the initial logical thinking ability in the syllabus only shows that this is the main idea, which does not mean excluding the development of other thinking abilities. For example, although students are transitioning to abstract logical thinking in primary school, thinking in images has not disappeared. In the senior grade of primary school, some mathematical contents, such as the teaching of concepts such as prime number and composite number, are easier for students to understand and master through practical operation or demonstration of teaching AIDS; At the same time, students' thinking in images will continue to develop. For another example, although the cultivation of creative thinking ability cannot be the main task of primary school mathematics teaching, it can promote the creativity of students' thinking when teaching new knowledge closely related to old knowledge and solving some thoughtful exercises. We should pay attention to it consciously in teaching. As for dialectical thinking, theoretically speaking, it belongs to the advanced stage of abstract logical thinking; From the development process of individual thinking, it is later than the development of formal logical thinking. According to preliminary research, primary school students began to sprout dialectical thinking at the age of 10. Therefore, it is not appropriate to take the development of dialectical thinking as the teaching purpose in primary school prematurely, but to combine the teaching of some mathematical contents with some dialectical viewpoint factors to accumulate some perceptual materials for the development of dialectical thinking. For example, the appearance of the first volume of the general textbook can let students intuitively know that the second addend has changed and the number of scores has also changed. There are also some tables in middle school textbooks to let students tell how the multiplicand (or dividend) changes and how the product (or quotient) changes. This has accumulated some perceptual materials for the view that things are interrelated and constantly changing in the future.
Second, cultivating students' thinking ability should run through the whole process of primary school mathematics teaching.
Modern teaching theory holds that the teaching process is not a simple process of imparting knowledge and learning, but a process of promoting students' all-round development (including the development of thinking ability). Judging from the process of mathematics teaching in primary schools, the mastery of mathematics knowledge and skills can not be separated from the development of thinking ability. On the one hand, in the process of understanding and mastering mathematical knowledge, students constantly use various thinking methods and forms such as comparison, analysis, synthesis, abstraction, generalization, judgment and reasoning; On the other hand, when learning mathematics knowledge, it provides concrete contents and materials for using thinking methods and forms. In this way, we should never think that teaching mathematical knowledge and skills will naturally cultivate students' thinking ability. The teaching of mathematical knowledge and skills not only provides favorable conditions for cultivating students' thinking ability, but also needs to make full use of these conditions consciously in teaching and cultivate them in a planned way according to students' age characteristics in order to achieve the expected goals. If we don't pay attention to this point, the arrangement of teaching materials is unconscious, and the teaching method violates the principle of stimulating students' thinking. Not only can it not promote the development of students' thinking ability, but it may also gradually develop students' bad habits of memorizing.
How to cultivate students' thinking ability throughout the whole process of primary school mathematics teaching? Whether it can be considered from the following aspects.
(A) to cultivate students' thinking ability should run through the mathematics teaching of all grades in primary schools. To be clear, all grades have the responsibility to cultivate students' thinking ability. From the first year of high school, we should pay attention to conscious training. For example, when we begin to understand the size, length and quantity, there is a problem of initially cultivating students' comparative ability. When we began to teach the addition and subtraction of numbers within 10, there was a problem of initially cultivating students' abstract generalization ability. From the beginning, there is the problem of cultivating students' comprehensive analytical ability. This requires teachers to guide students to compare, analyze, synthesize, abstract and generalize step by step through practical operation and observation, form the concept of numbers within 10, understand the meaning of addition and subtraction, and learn the calculation method of addition and subtraction within 10. If we don't pay attention to guiding students to think, we may unconsciously lead students to recite the composition of numbers from the beginning and mechanically recite the road of addition and subtraction of numbers. I got into the habit of memorizing in the first grade, and it is difficult to correct it in the future.
(2) Cultivating students' thinking ability should run through every link of every class. Whether reviewing for the first time, teaching new knowledge or organizing students to practice, we should pay attention to conscious training combined with specific content. For example, when reviewing carry addition within 20, experienced teachers should not only ask students to say numbers, but also their own ideas, especially when students make calculation mistakes. Telling the calculation process is helpful to deepen their understanding of the "rounding" calculation method, learn analogy and effectively eliminate mistakes. After a period of training, students are guided to simplify their thinking process, think about how to calculate numbers quickly, and cultivate their agility and flexibility in thinking. When teaching new knowledge, we should not simply talk about conclusions or calculation rules, but guide students to analyze and reason, and finally get the correct conclusions or calculation rules. For example, the key to teaching two-digit multiplication is to intuitively guide students to decompose into one-digit multiplication and integer ten-fold multiplication. The key point is to guide students to find out where the product obtained by integer ten multiplication is written, and finally summarize the steps of two-digit multiplication. Students know how to calculate and abstract the calculation method from intuitive examples, which is not only impressive, but also develops their thinking ability. In teaching, some teachers also pay attention to developing students' thinking ability, but not through a class, but at the end of a class, give one or two slightly difficult topics as activities to train thinking, or open a special thinking training class. It is worth studying to limit the cultivation of thinking ability to a certain class or a certain link in a certain class. Of course, under the premise of always paying attention to cultivating thinking ability in the whole teaching process, in order to master a special content or method, this special thinking training can be carried out, but it cannot replace the task of developing thinking in the whole teaching process.
(3) The cultivation of thinking ability should run through all parts of teaching. In other words, when teaching mathematical concepts, calculation rules, solving application problems or operating skills (such as measurement and drawing), we should pay attention to cultivating thinking ability. Any mathematical concept is the result of abstracting and summarizing the quantitative relationship or spatial form of objective things. Therefore, when teaching each concept, we should pay attention to guiding students to analyze, compare and find out their similarities through various objects or examples, reveal their essential characteristics, make correct judgments, and thus form correct concepts. For example, when teaching the concept of rectangle, it is not appropriate to draw a rectangle directly and tell students that it is called rectangle. Instead, let students observe all kinds of objects with rectangles, guide them to find out what their edges and corners have in common, and then abstract the graphics and summarize the characteristics of rectangles. The teaching of calculation rules and regularity knowledge should pay more attention to cultivating students' judgment and reasoning ability. For example, when teaching the law of additive association, it is not appropriate to draw a conclusion simply by giving an example. It is best to give two or three examples, one for each, to guide students to judge independently (for example, (2+3)+5 = 2+(3+5), first add 2 and 3 together and then add 5, and then add 3 and 5 together and then add 2, and the result is the same). Then guide the students to analyze and compare several examples to find out their similarities, that is, the left end of the equal sign adds the first two numbers and then the third number, and the right end of the equal sign adds the last two numbers and then the first number, and the result remains unchanged. Finally, a general conclusion is drawn. This not only enables students to understand the laws of addition and association more clearly, but also learns the method of incomplete inductive reasoning. Then apply the general conclusion to the specific calculation (such as 57+28+ 12) and tell what can make the calculation simple. In this way, I learned the method of deductive reasoning. As for solving application problems and guiding students to analyze quantitative relations, I won't go into details here.
Thirdly, designing exercises plays an important role in improving students' thinking ability.
Cultivating students' thinking ability, like learning calculation methods and mastering problem-solving methods, must also be practiced. Moreover, thinking is closely related to the process of solving problems. The most effective way to cultivate thinking ability is through problem-solving practice. Therefore, designing exercises well has become an important part of improving students' thinking ability. Generally speaking, a certain number of exercises are arranged in textbooks to help develop students' thinking ability. But not all of them can meet the needs of teaching, and because of the different situations in the classroom, the exercises in the textbook are difficult to fully meet the needs of various situations. Therefore, it is often necessary to make some adjustments or supplements according to the specific situation in teaching. To this end, the following suggestions are put forward for reference.
(1) Design exercises should be targeted and designed according to the training objectives. For example, in order to know whether students are clear about mathematical concepts and cultivate their ability to judge concepts, we can give some exercises to judge right or wrong or choose the right answer. Give a concrete example: "All prime numbers are odd numbers. () "To make a correct judgment, students should analyze whether there are prime numbers in even numbers. To understand this, it is necessary to find out what is an even number and what is a prime number, and then apply the definitions of these two concepts to analyze whether there is a number in the number divisible by 2, and its divisor is only 1 and itself. I think 2 is an even number and a prime number, so I can conclude that the above judgment is wrong.
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