Mr. Li, a Singaporean mathematics educator, said that mathematics education must achieve eight words: "Learn mathematics and give it to the classroom". The so-called mathematics is to understand the connotation of mathematical knowledge and reveal the essence of mathematics. However, in today's public class display and evaluation, teachers mostly focus on the embodiment of educational ideas, the choice of teaching methods, the creation of classroom atmosphere, and the enthusiasm of students to raise their hands to speak. As for the expression of mathematical content, the revelation of mathematical essence and the presentation of mathematical value, it is often lacking. In fact, the content determines the form, and whether students can master the mathematics content is the main symbol to evaluate the success of classroom teaching. Therefore, when preparing lessons, teachers need to think about how to dig the mathematical essence of textbooks.
First, look at the essence through the phenomenon
The essence of mathematics is often hidden behind the formal expression of mathematics, which needs teachers' mathematical literacy to reveal. For example, what is the essence of plane rectangular coordinate system in mathematics? The shallow understanding is to determine the position of a point with a pair of numbers, so a large number of cases in junior high school mathematics teaching interpret the value of coordinate system as the determination of "position", and many teaching plans also require playing the game of "which row is which seat" in class. In fact, this low-level life-oriented activity can't increase the understanding of the coordinate system at all. Determining the position with a pair of numbers is the task of geography class, and even Chinese class will deal with such problems as rows and seats. Therefore, such activities have no distinctive disciplinary characteristics, nor do they touch the essence of mathematical concepts. I think the essence of plane coordinate system is to express the motion trajectory of points with equations satisfied by numbers, that is, the idea of "combination of numbers and shapes" The first lesson of introducing coordinate system can be based on position determination, and more importantly, it should guide students to observe and think: what are the figures of two points with the same coordinates? What area does a point with two positive coordinates form? What figure is the point with zero abscissa? In this way, it has the taste of mathematics and touches the essence of mathematics at a deeper level.
Second, mathematical operations should embody the essence.
In the new mathematics curriculum standard, the basic mathematics activity experience is included in the mathematics teaching goal, so that students can not only obtain objective knowledge in mathematics learning, but also form their own subjective knowledge, which is helpful for students to truly understand mathematics. In many teaching designs, they also pay attention to the accumulation of experience in mathematical activities, which is very correct. However, mathematical operations should not only stay on the surface, but also be guided, and the mathematical essence behind operations should be reflected through mathematical activities.
"Measuring a quantity" is a common mathematical activity. For example, it is required that the sum of the internal angles of the triangle is 180 degrees. Students have deepened their understanding of the sum of the internal angles of a triangle, and experienced the fun of independent inquiry through their own hands-on and operation. However, it must be noted that mathematics is a rigorous discipline, and this mathematical conclusion drawn from "quantity" is only a "confirmation" behavior of "physics". "Quantity" inevitably leads to the essence of mathematics, so we should think about the value of mathematics. Measuring the sum of the internal angles of a triangle can be achieved here in primary school. For this reason, it is necessary to explain that there are errors in the "quantity" of middle schools, so the following conclusions are insufficient. Further logical argument is needed to get the view that the sum of the internal angles of any triangle is a constant value, that is, "there is a constant in change" This is the essence of mathematics.
Good measurement activities need profound mathematical value as guidance. For example, students can find out the ratio of the big hand drawn on the blackboard to their own hand, and design the size of books, tables and chairs for giants according to this ratio. There are a lot of measurement activities here, but they are all measured closely around the similar feature of "ratio", so quantity has mathematical value and essence.
Third, reveal the essential relationship between mathematical knowledge.
Mathematical knowledge is organically related and has the characteristics of rigor and systematicness. Teachers should gradually guide students to classify the knowledge accumulated at ordinary times through certain standards, so that it is organized and systematic, which is the continuation of the knowledge learned and the continuation of students' thinking process. On the basis of analyzing and comparing the internal relations of knowledge, students' knowledge is connected in series to form systematic knowledge, so as to realize analogy and truly grasp the essence of mathematics. For example, the trinity relationship among "point", plane vector and complex number in plane coordinate system: point A(a, b) corresponds to →OA=(a, b) and z=a+bi one by one, which is essentially a set of ordered number pairs, but in different meanings, the properties of this set of ordered number pairs are expanded and improved. First of all, points cannot participate in the operation, and plane vectors can be added and subtracted, and it is an inverse operation. However, the product of vectors is no longer a vector. In addition, vectors are inseparable. As for complex numbers, there are addition, subtraction, multiplication and division, and they still maintain the characteristics of "number".
A lot of mathematical knowledge, such as the above, is often scattered in many chapters, and the correlation between them is often not written in textbooks, so it is easy to be ignored in teaching. If teachers don't talk and students don't learn, the essence of mathematics will be lost inadvertently. Therefore, how to establish the relationship between mathematics and reveal the essence of mathematics should become a problem that teachers need to think about in mathematics teaching.
In short, teachers should not only pay attention to the embodiment of educational ideas and the choice of teaching methods, but also reveal the essence of mathematics from a strategic perspective, so that the classroom will have the taste of mathematics!