Keywords: number and algebra, knowledge relationship before and after effective transfer of knowledge system
Text:
The 20 1 1 version of the new mathematics curriculum standard divides mathematics knowledge into five fields: number and algebra, graphics and geometry, statistics and probability, and comprehensive practical activities. Number and algebra are one of the most important contents in mathematics learning. From the teaching point of view, the knowledge of numbers and calculations covered by numbers and algebra is difficult for teachers and students to learn. And number and algebra can best reflect the characteristics of mathematical knowledge connection, so effective transfer is widely used in the teaching of number and algebra.
? What is migration?
? It is said in educational psychology: Generally speaking, learning transfer refers to the influence of one kind of learning on another, or the influence of acquired knowledge and experience on the completion of other activities. In the development of pedagogy and educational psychology, educators devote themselves to the study of transfer theory.
? Is migration feasible in the teaching of numbers and algebra?
Many math teachers and scholars use theory and time experience to verify in many aspects. Judging from the content setting of number and algebra, the knowledge content of the first phase and the second phase is basically similar. In fact, experts also follow the transfer law when compiling current textbooks. Take the teaching of calculation as an example: the addition and subtraction of senior one is the basis of the method of senior two, and the significance of mathematical multiplication is to transfer through continuous addition, which makes the calculation easier. Then, division is the inverse operation of multiplication and must be based on multiplication. In fact, the initial division operation is also realized by multiplication formula table, and then to the mixed operation and algorithm of addition and subtraction. In this way, a set of operation methods and learning processes have been established, and a new operation knowledge based on these foundations will be learned in the future. With the deepening of the understanding of numbers, the most basic operational knowledge will not change.
? How to use migration skillfully?
First, skillfully import and realize the migration of old and new knowledge.
? We have heard many open classes, and in order to stimulate students' enthusiasm for learning, we will create certain scenes for students to quickly enter the classroom teaching state. Careful analysis of each scene actually contains some old mathematical knowledge. The old knowledge scene is packaged, students are willing to think seriously, and at the same time they are slowly entering the classroom state set by the teacher. And these old knowledge points are often the basis of learning this new lesson.
For example, in the lesson "Fraction and Division" provided by the fifth-grade math teacher's book of People's Education Edition, the teacher gradually infiltrated the knowledge points related to fraction and division from the beginning of the dialogue, and every small link was closely connected, whether in activity or language. Listening to the teacher's class is not only learning, but also enjoying. If the math class is compared to article creation, such a class is a prose with beautiful language, and there is no obvious link boundary, but every link, every activity and even every sentence contributes to the focus of the class and captures the students' hearts. There are many ways to introduce new courses, but the most important thing is to grasp the subtle connection between new knowledge and old knowledge, and then carry out creative packaging to realize the first step of migration.
? Second, clever contrast, to achieve the transfer of learning methods
The key of operation teaching lies in the mastery of algorithm and arithmetic. Combined with the calculation method, the internal relationship can be realized by using the migration theory. The understanding of large numbers in the first unit of the first volume of the fourth grade, the reading, writing, writing and reduction in the first half are based on the concept of numbers. The number is actually infiltrated by the number of sticks in the first grade. A number, ten ones are ten, ten tens are ten, ten tens are one hundred, eleven hundred is one thousand ... The establishment of the concept of numbers will further lead to the establishment of the concept of large numbers.
? The understanding of numbers within 100 million provides a knowledge base for the understanding of numbers above 100 million. In the reading method, because the time interval between the contents is very close, it is more appropriate to use comparison. On the basis of reading and writing numbers within 1 100 million, students can easily migrate, effectively reducing teaching difficulty and improving teaching efficiency.
? Third, skillfully expand and realize the transfer of subject literacy.
? Mathematics knowledge has a very important connection with life. Mathematical knowledge comes from life, and we can abstract mathematical problems from the actual problems in life, thus causing students to think. Conversely, mathematical knowledge can be a tool to solve practical problems in life. The understanding of mathematics teaching content is divided into three levels:
At the first level, ordinary people can use knowledge, such as decimal multiplication and division to calculate the buying and selling price, and use statistical charts to predict the probability of events; The second level of practical thinking, mathematical knowledge contains many mathematical ideas, such as the optimization, collocation and combination of figures; The third layer uses theory, and mathematicians will use basic mathematical ideas to study knowledge in unknown fields.
Therefore, the promotion of mathematics literacy in the classroom should be divided into three levels: the first level is the transfer of previous mathematical knowledge, the second level is the transfer of mathematical ideas, and the third level is the transfer inside and outside the discipline. Many times, we will find that mathematical literacy is not limited to numbers, figures and topics, but also includes the improvement of thoughts and emotions.