Countermeasures: divergent thinking and open teaching.
In actual teaching, we find that some teachers' teaching methods are nominally open, and teachers take the initiative to let students answer questions and operations, and the cooperation between students and teachers makes teachers very satisfied. For example, some teachers ask students to look at the picture first and answer:%&; The child on the left has some paper cranes in his hand! The child on the right has some paper cranes in his hand! % # How many paper cranes are there? Then the teacher writes the formula on the blackboard and teaches # (&; )$。 Finally, the teacher instructed the students to do one thing in the book. The teacher said that one student does one thing, and the teacher said that two students do two things ... These teachers' teaching methods seem to let the students solve their own problems, but in fact, the students are still turning around in the teacher's box. This unified and closed teaching is not conducive to their development, which not only restricts the divergence of students' thinking, but also psychologically relies on or is used to following teachers.
The development of divergent thinking activities of primary school students is of great significance to changing the established thinking mode. From the perspective of cognitive psychology, it is often difficult for primary school students to get rid of the existing thinking direction in the process of abstract thinking activities because of their physical and mental characteristics. That is to say, the thinking patterns of individual students and even groups often affect the solution of new problems, thus creating illusions. Therefore, in order to cultivate and develop the abstract thinking ability of primary school students, we must pay great attention to cultivating their divergent thinking. For example, the variant training of language narrative is carried out, that is, students can change the narrative form into several sentences on the basis of one sentence. This will help students not to be limited to the existing mindset, so that students can gradually form multi-angle and multi-directional thinking methods and abilities in training.
The new curriculum teaching embodies an open culture. Only openness can bring space, choice and cooperation. Therefore, in teaching, teachers must change their teaching concepts, boldly let students learn independently, let students think, talk and do, truly implement open teaching, fully meet the different needs of different students, and maximize the development of students.
Puzzle 2: Theorem recitation, lack of understanding
Countermeasures: self-construction promotes students' active development
Primary school students' thinking is in a period of gradual transition from image thinking to abstract thinking. Some teachers ask children to memorize formulas and theorems in order to let them master knowledge faster. This practice of encouraging children to learn from images can not only help them transition from image thinking to abstract thinking, but also make them fear and even hate mathematics. Constructivism theory holds that different people have different understandings of the same objective object. As Ausubel said: "Any meaningful learning is the assimilation and adaptation of old knowledge to new knowledge." Different cognitive structures lead to different fixed points of new knowledge, and different ways, methods and habits of assimilation and adaptation. Therefore, the curriculum standards have repeatedly pointed out that different people learn different mathematics. The mathematics thus obtained is the students' own mathematics, living knowledge and useful knowledge.
In practice, we can see that some students are good at understanding mathematics three-dimensionally with image thinking; Some students tend to understand mathematics abstractly with logical thinking. Therefore, our teaching is to understand mathematics and promote the improvement of students' thinking ability on the basis of adapting to students' thinking characteristics. For example, during class, some students understand the process of 1- 1: 30 as follows: the slender minute hand is uncle, and he runs fast; The short and fat hour hand is an old man. He runs very slowly. Uncle has run half a lap, and the old man has only run half a small lap. Obviously, children understand mathematics in their own way, so it is easy to master it.
Therefore, only what has been constructed independently is the students' own, and what the teacher teaches the students, no matter how profound and thorough the teacher teaches in the teaching process, is a sense of distance to the students. For students, what they need is what really belongs to them in their minds after reorganization. It can be seen that what students need is to understand mathematics in their own way, rather than simply memorizing it.
Puzzle 3: the method is single and inefficient.
Countermeasures: Close to life and enhance practicality.
Why do students lose their aura and vitality as soon as they learn? Why can't students feel happy in the process of mathematics learning? We find that some teachers are not good at choosing effective teaching methods, and often get used to their own teaching ideas and methods, thinking that as long as students can do problems correctly, it is good teaching. Turn the lively classroom into a classroom for imparting and instilling knowledge.
According to a survey of local students in Hong Kong, students use numbers, symbols and formulas to describe mathematics. And simplify mathematics into operation. There are also some answers with a strong shadow of "classroom mathematics", such as thinking that mathematics is a subject of "calculating with formulas" and "memorizing methods", and "many calculation methods can get the same answer" and "accurate answer", which is probably because most of their mathematical views come from classroom teaching. Only 30% students talk about the practical function of mathematics.
Therefore, when we choose teaching materials, we should try our best to extract math problems directly from students' real life, which is what we usually call math problems living! For example, when teaching carry addition within 20, I contacted the situation of supermarket shopping in the moral and life class, stipulating that each child can only take 20 yuan, and listed some products that children like, and then let them buy. The children put forward various purchase plans. Then I asked, if you could only buy three things, and they could not exceed 15 yuan, which three would you choose? Finally, how to buy the most things with the least money? The design of this series of questions has aroused children's interest in solving necessary and common problems in daily life. As Rutak, an ancient Roman educator, pointed out, a child's mind "is not a jar that needs to be filled, but a fire that needs to be lit." In other words, only by lighting the fire in students' hearts can students be moved to study science; Only by transcending the "scientific world" and paying attention to the life world can students be moved to learn mathematics.
Confusion 4: deal with teaching materials, give up the basics and get rid of the end.
Countermeasures: According to the actual situation, handle it appropriately.
Traditional teaching emphasizes "teachers should stick to textbooks", and the new curriculum standard emphasizes breaking through textbooks when necessary. The latter put forward higher requirements for teachers. If we combine the actual situation of students with the local environment, we can change some simple topics and appropriately change the arrangement order of some class hours in the teaching materials, which can really improve teaching efficiency and promote students' development. However, some teachers believe that the new curriculum standard advocates creative treatment of teaching materials, which not only makes the teaching content in the teaching materials fragmented and unfocused, but also disposes of all the good contents in the teaching materials.
For example, when teaching the understanding of cuboids and cubes, the teacher did not use the topics in the textbook and did not follow the arrangement intention of the textbook. Instead, he first showed a cuboid object for students to observe and master the characteristics, and then showed a cuboid object and taught it to students in the same way. Finally, the teacher asked the students, "What kind of cuboid is a cube!" The students can't answer, so the teacher can only say the word "special" by himself. On the surface, this kind of teaching seems to be a teaching behavior under the new concept, but in fact, it is against cuboids and cubes to let students learn, and "handles" important sentences such as "cuboids are equal in length, equal in width and equal in height" which are closely related to cuboids and cubes in textbooks, resulting in bad consequences. Therefore, the author believes that in teaching, teachers should not blindly pursue "hot" textbooks, so as to give up the basics, but should properly handle textbooks according to actual needs to achieve high efficiency.
In the process of implementing the new curriculum, teachers need to design teaching methods according to new ideas and new requirements. Teachers should first reflect on how I used to teach, and what are the usual teaching methods? What are the characteristics of this teaching method? Whether it contributes to the development of students and conforms to the concept of the new curriculum. Looking at some cases of teaching reform, we will find that teaching can still be organized in this way, and students can also learn in this way. Think about the roles of students and teachers in the past, and try to change the roles of teachers and students in the teaching process. Think about what will happen if the roles of teachers and students change. After putting thinking into action, it is not just confusion that is solved. ...
First of all, it is difficult to change the teaching concept.
In actual teaching, we find that some teachers have outdated teaching concepts, closed teaching methods and open nominal teaching methods, and teachers take the initiative to let students answer questions and operate. The teaching methods of these teachers seem to let students solve their own problems, but in fact, students still turn within the framework set by the teachers. This kind of teaching seriously hampers the development of students' thinking. Then, how should teachers change their teaching concepts and methods and implement open teaching?
Second, cooperative learning is difficult to achieve.
Group cooperative learning can fully embody teaching democracy and give students more time for free activities and opportunities for mutual communication. But many religions
The teacher's group cooperative learning mode is only a mere formality, which is manifested in the following aspects: time is not guaranteed, a question is discussed for students, and students stop at the beginning of speaking, which has no due effect at all; It is a waste of time to discuss some simple problems that don't need to be discussed at all. Lack of equality in communication, so-called cooperative learning, has become a stage for several top students to show themselves, and most students have become spectators; It's an active discussion, but it's actually a passive response. When the teacher gave the order, everyone began to discuss, not because of the students' inner needs. Such cooperative learning has little effect. In teaching, how to play the role of group cooperative learning and improve the effectiveness of cooperative learning?
Third, the process of solving problems is difficult.
"Application problem" has always been one of the key contents of mathematics textbook reform. The application problem teaching under the background of the new round of curriculum reform is an all-round reform from the goal, content to teaching methods under the guidance of new ideas. In the curriculum standards, applied problems are defined as "solving problems" in "developing fields". The so-called "problem solving" is the process of comprehensively and creatively applying the learned mathematical knowledge and methods to solve new problems. Accordingly, there is no longer a separate chapter in the new textbook to teach applied problems, and it is often arranged in the form of calculation combined with application. This challenges the traditional understanding of application problems in the minds of front-line teachers for a long time. At the same time, it also brings confusion to front-line teachers. How to teach application problems under the background of new curriculum?
Fourth, it is difficult for top students and poor students to make progress together.
Under the guidance of the new curriculum concept, teachers' teaching behavior and students' learning methods are undergoing obvious changes, and teachers and students are equal and teach people.
Masters have become a common practice, and the classroom situation of teacher-student interaction and equal participation has been formed. However, due to the changes in teachers' teaching methods and students' learning methods, good students have more opportunities and are given extraordinary play. Students with learning difficulties have become bystanders, unable to think and express independently, and have little benefit. In this way, the growth of students has formed polarization. In mathematics teaching, how to make all students make progress together and get all-round development?