Current location - Training Enrollment Network - Mathematics courses - The eyes of mathematicians
The eyes of mathematicians
Reading the book "The Eyes of Mathematicians" by Academician Zhang Jingzhong was alarmed by one of the articles "The Sum of the Internal Angles of a Triangle", and I felt a sense of awakening at that time, as if I vaguely felt the real value of mathematics teaching. In teaching, most of us only revolve around the inside of a convex polygon, paying too much attention to the changing law of the sum of the internal angles of the convex polygon, while ignoring the more common external angle and constancy law from a wider perspective, and neglecting to guide and cultivate students' ability to observe and analyze things comprehensively and integrally. Mathematics teaching is not only to teach some mathematical axioms and theorems, but more importantly, to cultivate the eyes of seeing things and the methods of analyzing things. So while reflecting on my past teaching, I am thinking: Can I try to take this course and embody this teaching concept in my classroom?

First attempt

? Action is better than action, so start analyzing the teaching materials quickly. In the fourth grade, I will learn the inner angle and knowledge of triangles, and in the seventh grade, I will learn the outer angle and knowledge. After consulting relevant materials, the following teaching process has been preliminarily formulated:

Reflection after class

The first class was a great failure. There are many problems that are not as simple as I think, and what I think is not what the students think. The teachers in the same grade group discussed with me and summed up the following points: first, the integration of teaching content in grade four and grade seven is really quite difficult for children in grade five; Second, the mastery of the internal angle and this knowledge point is not as good as expected. Most students only remember the conclusion of the triangle inner angle and 180 degrees, but they can't clearly recall the process and method of drawing this conclusion (why? It is worthy of our reflection on the teaching at that time. ); Third, restricted by thinking habits, it is difficult for students to actively change the perspective of observing and analyzing things.

? In view of the above problems, I adjusted the teaching plan: First, I adjusted the learning object to sixth-grade students; Second, slow down and properly carry out the first part of the teaching process to help students wake up and consolidate what they have learned; Third, appropriately increase analogy to guide students to complete the transition of thinking naturally.

retry

In the second class, the situation is much better than that in the first class. The whole teaching process can basically come down, but new problems have emerged. The teacher's dominant position in the class is too prominent. Although there is no lack of guidance and inspiration, the trace of control is too heavy, and the students' thinking is "kidnapped" by the teacher. A wonderful speech is like toothpaste, which loses its original freshness. The teachers in the math group agree that to make students feel the vastness of the world, we must first give them a vastness of the world. This is the idea of mathematicians.

? As a result, the design concept of this class has undergone fundamental changes. It is no longer the teacher who leads the students all the way, but the teacher provides the students with a material, and then lets the students learn, discover, feel and experience in free thinking. Teachers need to hand in materials and play drums well. There is no need to change the big links in the lesson plan, but some small details and handling methods must be changed.

Finally got something.

? In the third class, the students were given some pictures to watch. The students stimulated the discrimination of thinking in observation and seemed to feel something. Then, in this state of mind, they naturally enter the learning task, gradually understand concepts and master methods in constant thinking and questioning.

? On the whole, the results of this class are good. For students, they have accumulated knowledge, not only reviewing and consolidating the knowledge of the inner corner, but also understanding the significance and laws of the outer corner. In this process, they feel the safe and free thinking environment and realize the ways and means to know the world. As for teachers, I have a deeper understanding of the starting point of teaching, improved my skills in playing a role in the classroom, and more importantly, improved my understanding of mathematics teaching.

? After this lesson, I feel I have completed a transformation, not technically, but ideologically. Maybe in the past, we just buried ourselves in farming too much and looked up at the sky too little. We are complacent about the explanation of several difficult problems, unhappy about the loss of students, and angry about several vacancies on the roster, just like frogs in the well, only seeing the narrow world, not knowing that the outside world is broader. When we want students to have the same vision as mathematicians, we actually need such vision and courage. We can look at our teaching and education with different eyes and reflect on our behavior. We can appreciate students with different eyes and understand their words and deeds.

? What is right in our eyes is not necessarily right; What we have may not be complete; What we face is more undiscovered or undiscovered but unknown. It may be better to look at the problem from another angle and think about it from another angle! Teaching is not like this!