Firstly, it is emphasized that mathematics language teaching is the basis of mathematics thinking teaching.
Language is the shell of thinking. Thinking is output through one's own spoken and written language, and the premise of being accepted and understood is that the language itself represents a clear and concrete meaning. Chinese teaching requires accurate and specific learning of "words", and attention should be paid to situational understanding. If we call the mathematical ideas that express mathematical concepts, mathematical relations, mathematical symbols, mathematical figures, mathematical judgment and reasoning, and problem solving all mathematical languages, then it is the primary teaching task to let students understand the connotation of these mathematical languages in teaching. However, many math teachers often ignore the teaching of math language in math textbooks, because students can't accurately understand the meaning of math language, which makes it difficult for students to learn new knowledge and be passive in future learning. I think it is very important to emphasize the accurate understanding and mastery of mathematical language for students to learn and master mathematical knowledge and cultivate mathematical thinking. Therefore, in the teaching process, teachers must strengthen the effective teaching of mathematical language, so that students can accurately understand, master and apply the learned mathematical language, and lay a solid foundation for the development of mathematical thinking.
So, how can we make students clear the connotation of the mathematical language they have learned? I generally achieve my teaching goals through the following steps.
1. The student said.
It can be divided into "speaking first" and "speaking later". Whenever learning new mathematics knowledge, let students talk about their understanding of new words and phrases to express their knowledge, and find out their existing reserves of learning new knowledge from their understanding. For example, when learning addition, students can talk about their understanding of "a * * *" in "a * * *", and teachers can understand students' knowledge reserves on the basis of what students say and determine the next teaching strategy. "Post-lecture" means that students constantly exercise their mathematical language expression ability in the process of mastering and applying knowledge, so as to consolidate and internalize knowledge.
2. The teacher said.
For students, whenever they learn new mathematical knowledge, teachers must give accurate conceptual explanations to avoid confusion and inconsistency in students' understanding of mathematical knowledge. Although new textbooks rarely express new knowledge in written words and do not advocate rote learning, it is very necessary for students to understand it accurately in teaching and then express it accurately in their own language.
Do it yourself
Students' hands-on knowledge is not only conducive to memory, but also to understanding and mastering. For example, what does "one * * *" mean? Students will understand that "one * * *" means to "combine" similar things to measure. The practical situation of hands-on operation will certainly form a concrete image in students' minds, which is not only conducive to understanding and mastering new knowledge, but also the brewing and foreshadowing of students' thinking when solving problems in the future.
4. Homomorphization.
When students learn new knowledge, they must be provided with exercises of the same situation, type and structure, so that they can consolidate and internalize their knowledge through analogy.
5. Mutation interference.
In order for students to truly understand and master new knowledge, a certain number of variant practice groups must be designed. Through interference training, students can understand that although the narrative context of the topic sometimes changes, the connotation of the new knowledge expressed has not changed, so the ways and means to solve the problem have not changed.
6. Contrast.
After students have a certain knowledge reserve, teachers should design a certain number of comparative exercises. Through comparative exercises, let students know the connection and difference of mathematics language in different situations, and let students know the connection and difference between old and new knowledge, so as to consolidate old knowledge and master new knowledge more accurately.
Second, unveil the veil of mathematical modeling and correctly understand the connotation of mathematical thinking.
Mathematics is a process in which people qualitatively grasp and quantitatively describe the objective world, gradually abstract and summarize methods and theories, and apply them to practice. This definition of "mathematics" fully embodies the essence of mathematical modeling. What students learn in class is mathematics recorded in mathematical language, which is the product of patterning itself. Therefore, in order to train students' real mathematical thinking, it is necessary to let them know how the modeled mathematics comes from and how it is modeled, that is, to understand the process of establishing mathematical models.
How is the objective world modeled as mathematics? Let's take a look at the origin of the number "7": The Big Dipper has seven stars, there are seven days a week, my mother buys seven apples, and there are seven little monkeys living on the mountain ... These numbers are abstractly summarized by human beings and modeled as "7". If you want to know 7, you should know those specific 7 separately, and those specific 7 are the starting point of learning the number 7. As Suho Molinski said, "Nature is the source of human thought." All the ideas of mathematics are modeled from the objective world, so understanding the process of establishing mathematical models will also clarify the starting point of students' mathematical thinking learning.
The teaching content of mathematical thinking in primary schools has a strict internal logical structure and is a relatively complete system. As a teacher, it should be fully reflected in the teaching process, so that students can understand and master it systematically. Only in this way can the knowledge that students have learned be integrated, form a system, and finally form their ability and develop their intelligence. One of the logics contained in primary school mathematical thinking is the general order of mathematical knowledge arrangement. For example, why should we learn addition first in primary school mathematics? Because subtraction is the inverse operation of addition, multiplication is a simple operation to find the sum of several identical addends, division is the inverse operation of multiplication, addition is its father, and other methods are its descendants, so it is natural to learn addition first. For another example, the presentation of geometric knowledge is from plane geometry to solid geometry, and plane geometry is arranged in the order of "rectangle (square)-parallelogram-triangle, trapezoid and rectangle (square)-circle". Why do you want this arrangement? The teacher knows very well that the knowledge arranged in this way is closely linked. The former knowledge is the starting point of the latter knowledge, and the latter knowledge is the change and development of the former knowledge, or they can be transformed under certain conditions. Students don't really understand, so when teaching every kind of graphics, teachers should guide students to think and find out the reasons. When all the learning is over, teachers should guide students to explore deeply and find out the ins and outs, so that the knowledge that students finally precipitate in their minds can form a system and be comprehensively used.
The second logic contained in primary school mathematical thinking is the connection between mathematical models. For example, in the process of teaching the practical application of mathematical knowledge represented by problem solving, we must first clarify the relationship between the parts of the problem, that is, the order and connection mode between the models. For example, the old monkey said, "I picked three baskets, each of which is 12", and the little monkey said, "I picked six". How many did the two monkeys pick? The correct formulas are 12× 3+6 and 6+ 12× 3. The two formulas are because there is a distinction between the old monkey and the young monkey, but regardless of the order, they all say the same thing at the same level, which is a parallel equivalence relationship and a correct mathematical expression of the problem. Why can't it be listed as 12+3× 6, because 3 baskets have nothing to do with 6; Why not list it as 3× (12+6)? Because according to the comprehensive method, the three baskets are only related to 12, but not to 12 and 6 at the same time. Considering from the analysis method, to ask how many monkeys "a * * *" picked, we must first know how many monkeys were picked. It is clear that the number of young monkeys is six, and the number of old monkeys is "three baskets per basket 12". Of course, we have to figure it out first. The above analysis also proves the four algorithms of "multiply (divide) first and then add (subtract)", and the question of how many monkeys are picked by "one * * *" also clarifies the quantitative relationship between two monkeys. This kind of mathematics learning will make students' logical analysis ability clear and full gradually.