First, improve students' mathematical knowledge structure
Since students majoring in five-year preschool education enter kindergarten teachers after graduating from junior high school, most of them are girls. On the one hand, they should engage in the professional study of preschool teachers in the future, and prepare the necessary mathematical literacy for the enlightenment education of preschool mathematics in the career of preschool teachers in the future. On the other hand, as a social citizen, to prepare for the future social life, we need to complete the necessary senior high school mathematics courses to lay the foundation for further study. From the above two aspects, mathematics education has a basic position. Therefore, it is necessary for us to take a look at the nature of "mathematics curriculum" in the mathematics curriculum standard of ordinary senior high schools [1]:
Mathematics course in senior high school is a main course in ordinary senior high schools after compulsory education, which contains the most basic content of mathematics and is the basic course to cultivate citizens' quality.
Mathematics curriculum in senior high school plays a fundamental role in understanding the relationship between mathematics and nature, mathematics and human society, the scientific and cultural value of mathematics, improving the ability to ask, analyze and solve problems, forming rational thinking, and developing intelligence and innovative consciousness.
..... At the same time, it lays a foundation for students' lifelong development and forms a scientific world outlook and values, which is of great significance to improving the quality of the whole nation.
On the whole, if we compare the mathematical knowledge and theoretical system in the mathematics textbook [2] of preschool teachers' college with that of ordinary high schools (or compulsory courses in curriculum standards), we can see that their knowledge subject structures are basically the same: including algebraic content with function as the main line and geometric content with solid geometry and analytic geometry as the main body.
Taking the first chapter of the textbook for kindergarten teachers-set, mapping and function as an example, the arrangement system of the textbook for kindergarten teachers' mathematics is consistent with that of the textbook for senior high school. The concept of mapping is emphasized first, and then the concept of function is emphasized, which embodies the deductive thinking of the knowledge structure from general to special, which is consistent with the traditional textbook for senior high school, and reflects the characteristics of appropriately broadening the knowledge of the textbook for secondary normal school teachers. As far as the concept of function is concerned, its content is to analyze and understand the concept of function from the perspective of mapping definition and correspondence, and then study the monotonicity, parity and inverse function of function, and construct a complete concept and property system of function.
Kindergarten teachers' mathematics curriculum system basically embodies the characteristics of integrity, systematicness and foundation of high school mathematics curriculum. Therefore, this determines that the mathematics teaching of kindergarten teachers should not arbitrarily delete the course content, but should aim at establishing students' perfect knowledge system.
Second, highlight the mathematical thinking method.
Mathematics textbooks for kindergarten teachers reflect the systematicness and integrity of the knowledge structure of mathematics courses, and the course content cannot be deleted at will. However, this is very contradictory to the actual situation of mathematics teaching in kindergarten teachers. For example, kindergarten teachers' textbooks condense the contents of several high school mathematics textbooks into two volumes, with many courses but few class hours; Students have weak mathematical foundation and great learning difficulties; People around students don't fully understand the pre-school education major, which leads to students' misunderstanding of mathematics and lack of motivation to learn mathematics. How to achieve the teaching goal in a limited time without deleting the course content? Most math teachers believe that this contradiction can only be solved through mathematical thinking methods. First of all, mathematical thinking method can permeate more mathematical knowledge. Secondly, the study of mathematical thinking method is also an important part of the development of citizens' mathematical literacy.
Taking function teaching as an example, the application of mathematical thinking method in mathematics teaching is realized from the following two aspects:
First, from the function itself, it is a model to describe the relationship between two quantities in the process of real world change, such as: the relationship between distance and time, the relationship between oil consumption and time, and the relationship between distance and oil consumption; In engineering problems, the relationship between engineering quantity and work elements (time, number of people ……); In the trajectory of the projectile, the relationship between displacement and time and so on. Describing these changes with functions is the essence of the concept expression of functions in junior middle schools, and it also has a good realistic background, which is easy for students to understand.
From this perspective, the teaching of function should be reflected in the following aspects: the first level is the abstraction of quantitative relations in real problems. Function reflects the model of the changing process of the real world, so when analyzing real problems, we should focus on analyzing the variables and constants in these problems and what the significance of these quantities is. In the second level, the quantitative relationship in real problems is expressed by some specific resolution functions, so as to abstract a specific functional model. Through the analysis of these functional models, we can return to real problems and clarify the meaning of symbols. The purpose is to let students establish the connection between abstract function models and specific practical problems, specifically, to let students understand the objects in the practical problems represented by symbols in the function models in specific problems, especially to let students distinguish the meanings and relationships of variables and constants in these models, rather than using letters or numbers to distinguish them. At the third level, the common features of different functional models are summarized, thus the general meaning of functional concepts is summarized. This process can be summarized as: concrete practical problem-abstract function model-clear function concept. This is a "mathematical" process [3], which embodies the thinking method of "abstraction and modeling" [4].
Secondly, from the perspective of set and correspondence, the concept of function is derived from the concept of mapping. Describing mathematical objects in set language is the result of the influence of set theory on the development of modern mathematics, which embodies the abstract characteristics of modern mathematics. At the same time, mapping is also an abstraction of the concept of intuitive correspondence on the basis of set theory, and it is the key to the evolution of function concept from junior high school function concept in kindergarten teachers' curriculum (also high school curriculum).
The mathematics curriculum of kindergarten teachers follows the traditional mathematics curriculum.
The deductive thinking of "mapping-function", and in order to highlight the concept of function, high school textbooks regard the concept of mapping as a natural extension of the concept of function. How to realize the connection and transition between mapping and function in mathematics teaching of kindergarten teachers needs to be paid attention to. First of all, we should highlight the "correspondence" idea of mapping concept. Correspondence is a basic and basic mathematical thought. Starting with children's counting, the concept of "correspondence" is established through activity experience, and further, it is the main expression in textbooks: using "charts" to express the correspondence in mathematics. Therefore, the idea of "correspondence" is not difficult to understand. It can be said that analyzing the corresponding relationship from "activity" to "graph" is the basis of establishing the concept of mapping. Secondly, on the basis of establishing the concept of mapping, the functional model of analyzing real problems with mapping as a tool is realized. Only by clearly analyzing the quantitative relationship in the function model with the help of the mapping concept can we realize the abstraction of the function concept from the variable relationship to the mapping relationship.
In the process of mathematics teaching for students majoring in five-year preschool education, highlighting mathematical thinking methods can make teaching not stick to specific details and methods, nor be limited to the teaching of mathematical knowledge, but can promote the overall learning of mathematics and enable students to gradually form the necessary mathematical literacy in the learning process.
Third, contact children's mathematical experience.
As a student majoring in five-year preschool education, mathematics teaching is undoubtedly a great challenge, but it is also a professional problem that has to be considered. With the support of "high-viewpoint elementary mathematics" and other courses in normal universities. As a kindergarten teacher, the mathematics teaching of kindergarten teachers should combine students' mathematics learning with the needs of future kindergarten teachers. This paper attempts to discuss the relationship between mathematics teaching and children's mathematics experience.
In fact, children's mathematical experience is very extensive, and they have many profound mathematical ideas, such as: one-to-one correspondence, counting, classification, measurement [5] and so on. These concepts are completed in the process of children's activities, but similar to those of adults, they are the content of children's physiological, social and cognitive growth and development. In the mathematics teaching of five-year preschool education, combined with the content of mathematics teaching, this paper introduces the relevant theories about children's mathematics experiential learning, which not only helps students to understand mathematics learning, but also helps students to combine mathematics learning with their own professional needs, and further improve their understanding of preschool education, so as to correctly understand the importance of mathematics in the teaching process of preschool teachers and strengthen their own mathematics learning during school. Taking the learning of "correspondence" in the concept of function as an example, this paper introduces how to link it with children's experience.
Piaget divides children's cognitive or mental development into four stages, which are called "pre-operation" stage between the ages of 2 and 7, and this stage has a theory of "conservation" principle.
Learning is a key step in the development of children's abstract ability. The conservation of quantity shows that children's thinking is reversible, and it also makes children's quantitative thinking possible. Only by mastering the conservation of quantity can children's thinking ability develop rapidly in profundity and flexibility. What is the "conservation" principle? "The ability to keep the original image of things in mind and psychologically reverse the process of object change is' conservation'" [5]. A classic example is that when the water in a tall thin cup is poured into a thick cup, children will think it is less, because the water has changed from "high" to "short". This is an example of a child who has not learned the principle of conservation. And "number, one-to-one correspondence, shape, space and ratio" are all preparations for forming the concept of "conservation" In the study of function concept, the application of corresponding concept is the key to understand function concept (whether it is junior middle school definition or senior high school definition), which is just like the study of "conservation" concept in children's concept. For example, the following is the learning process of children's conservation concept (as shown below).
In the picture (1), children learn to be equal up and down by comparing two rows of coins. In Figure (2), if the child can expand,
When the upper two rows become one row, it becomes the illustrated situation (1), at this time, children realize the "reversibility" of cognitive psychology of physical changes; Furthermore, children can count the coins in the upper two short rows and the lower row, so that the coins in the upper two rows and the lower row in Figure (2) are equal. This kind of children can realize the abstraction of quantity in the process of physical change through equal amount.
The above-mentioned process of children's learning "conservation" is not only the result of cognitive development, but also the result of mathematicization. Similar to the learning process of function concept in high school mathematics textbooks, the corresponding concepts in function concept can also be linked with children's learning "conservation" concept. In this way, by linking students' mathematics learning with children's experience and future children's mathematics enlightenment education, the demands of professional development can be realized to some extent, and the connotation of mathematics teaching in five-year preschool education can be transformed and developed.
Generally speaking, the first two aspects are aimed at the development of students' own mathematical literacy in preschool education, and the third aspect is the expansion of preschool teachers' professional requirements. If we can consider and unify the above three aspects in teaching, it will be the correct direction of mathematics teaching for five-year preschool education majors.