1, Reflections on Teachers' Construction of Knowledge Structure System
It is mentioned in the new curriculum standard that "students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning". Students become the masters of learning, which is very different from the previous educational concepts and models. Students have really changed from passive recipients to active explorers, so the change of this role has also changed the focus of teachers' attention, often ignoring the construction of knowledge architecture, including: basic knowledge, and so on. As we all know, the knowledge of mathematics is very precise, rigorous and standardized. However, in the investigation of studying in regular classes, we found that in the teaching of basic knowledge, our teachers themselves made mistakes when reading or speaking nonstandard mathematics language.
For example, a new teacher recorded the lesson of "Crossing the River" in the second year of teaching, with the aim of developing students' ability to ask questions and solve problems through the situation of "crossing the river". In the process of solving problems, students can recognize the function of brackets and correctly calculate the operation with brackets. Its teaching procedure is roughly as follows:
(1) Look at the situation map to understand the meaning of the problem.
(2) Students explore and solve problems independently.
(Students answer questions independently, report in groups, lead to discuss the function of brackets, and understand the operation order. )
(3) Teacher's summary
Teacher: Parentheses can help us change the operation order. If there are parentheses in an expression, we should count them first.
(4) Try "doing" on page 19 independently.
5×(36-29) (83-35)÷6 94-(25+ 19)
After the students are independent, the teacher guides the students to report. )
Teacher: Who can tell what is 5 times bracket 36 minus 29?
The students suddenly lost their minds, and the teacher below looked puzzled. You look at me, I look at you. )
Observing this lesson from the whole teaching process, there is no big problem. But the crux of the problem is that when reading mixed operations, the teacher does not read according to the meaning of the formula, but in the order from left to right, which makes people unable to hear clearly and misunderstand the meaning of the question. Our correct pronunciation is "five times the difference between 36 and 29". Teaching students the wrong reading methods can only make students construct the wrong knowledge in their minds, thus forming the "first cause effect" and ultimately affecting lifelong learning. In fact, we know that in the field of science, there is no uncertainty of knowledge. In addition to enabling students to accumulate knowledge, improve their ability and develop their thinking, it is also very important for students to establish a complete and correct scientific knowledge structure in their minds. Therefore, teachers should respect scientific knowledge in mathematics teaching. Only when these four aspects of knowledge (basic knowledge, subject knowledge, conditional knowledge and practical knowledge) are truly structured can classroom efficiency be truly improved. Then, to build a knowledge structure system, we need to accumulate knowledge, teachers need to sum up and reflect on their experiences, and teachers need to exchange experiences to improve the knowledge structure.
2. Reflections on students' independent exploration, cooperation and exchange.
In the new curriculum standard, "effective mathematics learning activities can not rely solely on imitation and memory, but hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics". Cooperative learning has been introduced into the classroom by more and more teachers, and now it has become one of the important ways for primary school students to learn mathematics. However, in teaching practice, some teachers regard "inquiry" as a cure for all diseases, and ask students to inquire at any time without setting any questions.
Case: In the teaching of the first volume of the second grade "Preliminary Understanding of Multiplication", teachers organize students to communicate on the basis of students' independent arrangement of graphics.
Teacher: What's your figure? How many sticks did you use to draw such a figure? How many sticks did you use to post so many numbers?
Health 1: I put a triangle, I put a figure like this with three sticks, I put two, and * * * uses 3+3 = 6 (root).
Health 2: I also put a triangle. I used three sticks to make such a figure, and I made four. * * * Use 3+3+3 = 12 (root).
Health 3: I put a square, I put a square with four sticks, * * * put three sticks, 4+4+4 = 12 (root).
Health 4: I set up a house. I need six sticks to build a room, * * * to build three rooms, 6+6+6 = 18 (root).
Students' methods are varied. Looking at this teaching clip alone, it should be said that it is a good class in line with the new curriculum concept. But the problem is that "A Preliminary Understanding of Multiplication" does not let students calculate the number of an addition formula, but let students explore how to calculate the number of an addition formula, but let students understand and understand multiplication, so that students can feel that when the number of the same addend is large, it is easier to read, write and calculate by multiplication. Therefore, understanding the meaning of multiplication and several concepts related to multiplication: the same addend and the number of the same addend are the focus of this lesson. In the above-mentioned teaching, teachers are free to explore in key links, wasting time, which will inevitably lead to students having no time to understand and explore the meaning of multiplication, thus making it difficult to complete the teaching objectives of this lesson and achieve real results in teaching.
In addition to spending a lot of precious time on independent inquiry and cooperative learning for problems that don't need to be explored, I also find that teachers often have the following problems when organizing group cooperative learning: First, the problems are too simple to be discussed at all, but in order to reflect new learning methods, students are organized to cooperate in groups; Second, there is no effective integration with other forms of learning. Students are allowed to discuss problems as soon as they come out. Students communicate with others without independent thinking, without forming their own ideas, only listening; Third, as soon as the students began to discuss, the teacher stopped, and there was not enough time and space to study; Fourth, there is no division of labor among group members, and students are talking at the same time, but they are not listening. The discussion is lively in form and empty in substance; Fifth, we often hear "what do I think" instead of "what do our groups think" in the exchange feedback, which shows that we have neglected the process of cooperative learning and the cultivation of students' collective consciousness and cooperative spirit. Therefore, cooperation should not be rushed for success, let alone stay in the form. If you don't have your own point of view, discussing cooperation will kill the habit of independent thinking and become parrot-learned. Before cooperation and communication, children should have enough thinking space, and have enough communication time in cooperation, so that they can cooperate on the basis of autonomy, let their thinking collide and produce sparks of wisdom.
3. Reflection on teaching methods.
The new curriculum standard requires the application of modern information technology to the process of mathematics learning. With the improvement of hardware conditions, multimedia devices are basically installed in primary schools now, so teachers also suffer from "multimedia dependence". There are mainly the following problems: first, the quality of courseware is not high, and many teachers just want to find one for class on the internet for convenience; Second, only pay attention to form but not content. Some teachers' courseware is exquisite, but the content is only a simple demonstration; Third, they excessively pursue and use multimedia. Some teachers present all the contents of the whole class on the courseware, and teachers become operators and commentators, which can be said to be multimedia demonstration classes. Therefore, not every excellent class must use multimedia courseware, and not every class that uses courseware can be rated as an excellent class.
For example, a teacher made a dynamic courseware when guiding students to know cubes and cubes, and turned cubes and cubes over and over on the screen. The teacher at the back of the classroom was dazzled and dizzy, and most students were at a loss. When another young teacher talked about "the area of parallelogram", the whole class didn't use any intuitive teaching methods. He just lets students use their own brains, cut, spell, think and discuss, gives students the initiative in learning, well cultivates students' exploration spirit and innovation ability, organically permeates transformed ideas, and the teaching effect is very ideal. From this perspective, the teaching effect is not all about whether to use multimedia courseware, but more importantly, the teaching skills of teachers. In fact, there are many teaching contents that we don't need to make multimedia courseware, and it is impossible to have enough time to design scripts and collect audio-visual materials. We only need to combine what students like to see and hear, combine the life reality that students are very familiar with, add some simple teaching AIDS and learning tools, design teaching activities reasonably, open students' thinking, and thus cultivate students' innovative consciousness and practical ability.
In short, the efficiency of classroom teaching is the persistent pursuit of every teacher. Through our reflection, we constantly explore and practice classroom teaching, which can really improve the quality of classroom teaching and make students the biggest beneficiaries.