Looking back on the course of new curriculum reform in recent years, we used to have fun with children in classroom life. But we also have confusion and anxiety. With the deepening of curriculum reform, we have more calm thinking, objectively reflect on the past, face today realistically, and analyze the problems existing in today's classroom teaching with a peaceful mind and the spirit of scientific research. What's the problem? The question is, what did the students learn in class? In other words, what we gain is the effectiveness of classroom teaching. Studying the effectiveness of classroom teaching is the desire of educators and the need of classroom teaching development.

First, the status quo of classroom teaching

In order to promote the development of curriculum reform and explore how to improve the effectiveness of primary school mathematics classroom teaching, we must first talk about the current situation of classroom teaching, that is, the existing problems. Through investigation, lectures, personal experience, communication with peers and consulting experts, I think there are the following problems in today's classroom teaching.

1. In some classes, behind "participation" and "activity", there is a tendency of impetuousness, obedience and formalization. Students' inner thoughts and emotions are not really activated, which is typically manifested as "autonomy" becoming "self-flow". What is shown in the classroom is the superficial or even false subjectivity of students, while what is lost is the targeted guidance, teaching and specific help of teachers to students.

2. Some classes have "temperature" but no depth. In class, students are "red-faced, with glowing eyes, small hands held straight and their mouths always open". Although it makes people feel lively and noisy, it rarely makes people feel heartache. The reason is that the classroom lacks the power of thinking and the spiritual pleasure that touches the depths of the soul.

In some classrooms, cooperation is formal, but not substantive. Under the background of lack of problem consciousness and communication desire, students "discuss" in a reactive and passive way, lacking equal communication and communication, especially deep communication and collision.

4. In some classes, inquiry is tangible. Students just go through the procedures and steps of inquiry process mechanically, lacking curiosity, exploratory thinking and critical questions, which leads to formalization and mechanization of inquiry and becomes an "empty shell" without connotation and spirit.

5. In some classes, some mathematical contents are mechanically put into the situation, which is far-fetched to connect with reality and overemphasizes the source of life. Thus wasting valuable time and hindering students' real understanding of mathematics knowledge.

6. Some classrooms, preset transition, occupy the generated time and space. On the surface, teaching is orderly. In essence, this is the embodiment of the traditional teaching idea of taking teaching as the center and knowledge as the standard. Due to the lack of independent thinking, positive interaction and personalized interpretation, students can only obtain superficial or even false knowledge, lack of activity, and can not be transformed into students' wisdom and quality, so this is inefficient teaching.

7. Some classrooms generate too many classes, which will inevitably affect the practice of preset goals and lead to the implementation of teaching plans, thus leading to arbitrariness and inefficiency of teaching; Excessive generation will make teaching lose its center and direction, and at the same time, it will also lead to generalities and superficial, and eventually deviate from the purpose of generation.

Second, to improve the effectiveness of decimal mathematics classroom teaching issues that need attention

The first question: classroom quality.

Quality and efficiency are the lifeblood of constructing primary school mathematics classroom teaching. An effective classroom must be a process that emphasizes high-quality teaching and learning. Otherwise, no matter how wonderful and vivid your classroom teaching design is, the final result will be that the classroom quality will not be achieved, which is equal to the failure of classroom teaching. How can we improve the classroom quality? I think, first of all, teachers should teach effectively. In order to teach effectively, we must set practical teaching goals, and to achieve the teaching goals, we must (1) create effective learning situations. (2) Integrate various teaching methods and carefully organize learning activities. ③ Effectively capture, utilize and organize teaching resources. ④ Multilayer feedback, effective regulation and proper evaluation. Secondly, students study effectively. How to judge students' learning effectiveness? It should be formulated from the following aspects: ① Whether students have mastered the basic knowledge learned in this class and whether their learning skills have been improved. (2) Did students go through the process of "mathematization" in this class, that is, the process of mathematical discovery, abstraction, generalization, reasoning, modeling and application, and gained mathematical ideas, methods and strategies in this process? (3) Whether the students have experienced the fun of learning in this class, whether they have the desire to explore knowledge, and whether they show confidence and success. (4) Whether the students have achieved all-round development.

The second question: classroom efficiency

Classroom efficiency refers to the efficient completion of teaching tasks by teachers in unit time. A class lasts only 40 minutes. At the end of this class, you haven't even finished the basic teaching tasks. Can you talk about classroom efficiency? Obviously not. Therefore, as a teacher, we must be cost-conscious, handle the relationship between input and output, long-term and short-term, sustainable development and temporary benefits, and not gain temporary benefits at the expense of students' physical and mental health and extended class hours.

The third concern: effective teachers.

Effective teachers are the key to improve the effectiveness of classroom teaching, otherwise everything is empty talk. So what should a practical teacher look like? We think it should be as follows: ① Understand the textbook deeply, set a good position for the basic knowledge that students should master in this class, and lay a good foundation; Imagine how to form a knowledge network in students' minds, endow them with mathematical ideas and methods, infiltrate the history and culture of the subject and improve their mathematical literacy. ② Fully understand students, respect their differences and teach students in accordance with their aptitude. ③ Effectively organize teaching materials, optimize learning resources, and provide valuable and energetic mathematics education for students. (4) full of enthusiasm, passion, longing, knowing how to love, sincerity, friendliness, tolerance and fairness, knowing how to respect students and how to gain their respect, and giving them understanding and trust. ⑤ Have educational wisdom and teaching wit.

Third, ways, methods and strategies to improve the effectiveness of mathematics classroom teaching in primary schools

1. Facing students' mathematical reality-accurately grasping teaching objectives

Instructors should design teaching from students' existing knowledge base, life experience, cognitive rules and psychological characteristics, find the breakthrough point of teaching, highlight the key points of mathematics, break through the difficulties of mathematics, capture the growing point of teaching, and make the teaching objectives conform to the teaching reality.

There is such a teaching design case. In a math class, in order to explain the concept of "symmetry" to students, the teacher prepared a large number of Peking Opera masks after class. In class, the teacher showed the students one by one with slides, telling them that this is the "quintessence of Chinese culture". Finally, the teacher asked the students "What is the quintessence of Chinese culture"? Some students shook their heads, and some students said loudly, "The quintessence of Chinese culture is a grimace."

Here we have to think.

Why are students speechless and uninterested in the questions carefully designed by the teacher? Sometimes students turn a blind eye to "wonderful pictures" and have no interest? The fundamental reason is that the design of teachers' teaching objectives is divorced from students' mathematics reality. After thinking, the countermeasures we should take are:

① Understand students' existing knowledge base and life experience, and determine practical teaching objectives. As a teacher, you should do research before class.

The design of mathematics learning activities must be based on students' cognitive development level and existing experience. As a teacher, we should grasp the starting point.

③ In teaching practice, students should pay attention to the process of abstracting practical problems into mathematical models and explaining and applying them. As instructors, we should let students experience this process.

2. Create a good mathematics learning situation-stimulate students' learning needs.

Creating a good learning situation according to the cognitive law, psychological characteristics and teaching content of primary school students is helpful to stimulate students' interest in learning and generate the need to explore new knowledge. Therefore, this learning situation should be realistic, meaningful, valuable and challenging.

Since the curriculum reform, "creating situations" has become a beautiful landscape in the primary school mathematics classroom. Some interesting, novel, thoughtful and challenging classroom learning situations have opened teachers' eyes.

However, some seemingly vivid and far-fetched learning situations lack the value of mathematical thinking, which is really disturbing and worrying. For example, there is a second-grade math class "Understanding Multiplication". At the beginning of the class, the instructor showed you a wonderful picture like a cartoon-"A Corner of the Zoo". The teacher asked the students to observe the pictures and asked, "What did you find?" After observation, the students spoke in succession.

Health 1: I find it really interesting here! There are small animals, houses, trees, white clouds, rivers and bridges.

Health 2: I found that the water in the river is still flowing!

Health 3: I found fish swimming in the river!

Health 4: I found the rabbits jumping happily.

Health 5: I found the chicken's head still moving. Are they pecking at rice or eating insects?

Health 6: I found two white rabbits on the bridge. Are they going to cross the bridge or not?

Health 7: Which of the two houses over there is chicken's and which is rabbit's?

Health 8: White clouds are fluttering in the distance, as if welcoming our children!

……

At this time, more than ten minutes passed, and the students made new discoveries. The teacher kept asking "What else did you find" in affirmation, so the students made new discoveries. Hearing this, we can't help asking, is this a math class or a picture reading and speaking class? A lot of energy is devoted to the design of the situation, and a lot of classroom time slips away in "non-mathematical activities"

We have to reflect on what this learning situation can bring to students' mathematics learning. We must think:

① What is an effective learning situation? ② Why should we pay attention to the creation of learning situations? (3) What kind of learning situation does mathematics learning need? ④ How to create a mathematics learning situation?

The previous examples tell us that the creation of learning situations has left the specific teaching objectives, so we should have countermeasures to create learning situations:

(1) Create a learning situation in which mathematics is closely related to life; (2) Creating a mathematical activity situation with thinking value; ③ Creating a beautiful fairy tale situation; (4) Creating problem situations of conflict between thinking and cognition; ⑤ Create problem situations from mathematical knowledge itself.

The correct use of countermeasures in teaching, I have a case here: when teaching, a teacher arranges his teaching process like this.

(1) Calculate the perimeter of the following two figures (one is a rectangle and the other is a square), and explain what tools and methods are used.

Students quickly come to the conclusion that the length and width of a rectangle and the side length of a square are measured with a ruler, and then the circumference is calculated according to the formula. At this point, the teacher said affirmatively, "Please take out the circular pieces of paper prepared by yourself and think about how to calculate its circumference?" Some students frowned and thought, others gestured with a ruler, and finally everyone shook their heads. Faced with this sudden new problem, they are uneasy and helpless, and all want to find a good way to solve the problem given by the teacher, so there is the first cognitive conflict and the first climax of thinking activities. Some students say they can roll on the ruler. Everyone agreed with them and measured the circumference of their circle, and the problem was solved.

(2) Just as the students were proud to come up with a good way to measure the circumference of round paper, the teacher asked the second question: "Who can calculate the circumference of round flower beds on campus?" In the face of new contradictions, the old methods are at their wit's end, thus causing a second cognitive conflict. Finally, the students have to wrap a line around the circumference of the flower bed and measure the length of a circle line, which is the circumference of the garden.

The teacher said, "Everyone is smart and uses different methods to calculate the circumference of a circle, but who can calculate the circumference of this circle?" The teacher said, and drew a circle on the blackboard with a compass. Students look at the circle drawn on the blackboard, but they don't roll or encircle it. What should they do? So the third cognitive conflict appeared in the classroom, which aroused a strong thirst for knowledge. Then the teacher drew several circles of different sizes and asked the students: What changed when drawing a circle, and the circumference also changed? What does circumference have to do with it? Through practice, it was quickly found that the diameter of the circumference is = π, and then the formula for calculating the circumference was successfully obtained, and the students tasted the joy of success.

(3) After the students got the formula for calculating the circumference of a circle, the teacher made the students understand that knowing the diameter of a circle can calculate its circumference. Then the teacher did not stop there, but created the fourth cognitive conflict for the students, which further deepened and consolidated the teaching objectives of this class.

She said: "Students all know that there is a thousand-year-old tree in front of the teaching building of our school. It is a key cultural relic in our city, but I want to know the trunk diameter of this ancient tree. What should I do? "

Immediately, a student said, "Cut down the tree and measure it with a ruler." Another student immediately stood up and retorted, "This is a cultural relic. How can you saw it?"

Teacher: "Yes, what should I do?"

Finally, it is concluded that the circumference of the trunk is measured by thread first, and then the diameter is obtained by circumference ? π.

The whole class is full of energy and active in thinking. In the teaching process, according to the characteristics of contradictions and conflicts in the cognitive process, teachers properly display these contradictions and conflicts in front of students, resulting in problem situations and inspiring students to create good learning situations. This kind of learning situation is helpful to stimulate students' interest in learning and create a demand for new knowledge exploration. Therefore, this learning situation is realistic, meaningful, valuable and challenging.

3. Choose appropriate teaching methods-pay attention to students' experience in the process of mathematicization, find the right starting point and grasp the growing point.

The effectiveness of primary school mathematics classroom teaching must give students the opportunity to truly experience "mathematization". Therefore, we should adopt a variety of teaching and learning methods, so that students can learn to learn mathematics in independent thinking, inquiry learning and cooperative communication, and creatively solve problems with mathematical ideas and methods. And try a variety of experiences in the process of mathematical experience.

think

① Is hands-on operation just inquiry learning?

② Is group discussion cooperative learning?

③ Only mathematical activities are experiential learning?

(4) Is it heuristic teaching?

⑤ Is it "integration" by using computer courseware?

Countermeasures

(1) Try every means to make students need to explore cooperative learning.

(2) Create an interpersonal atmosphere of inquiry and cooperative learning, encourage independent thinking, communication, questioning and discussion, and stimulate the enthusiasm of inquiry and cooperative learning.

(3) Creating a good situation for inquiry learning, with clear inquiry objectives, and exploring cooperative learning is challenging and valuable.

④ On the basis of the grouping principle of "heterogeneity within groups, homogeneity among groups", the dynamic arrangement of groups is implemented, which breaks the long-standing situation that some people play a controlling role and some people are in a subordinate position, so that every student has the opportunity to establish an image and provide everyone with opportunities for development, progress and self-change. The correct use of countermeasures in teaching, I have a case here:

The content is to find the "average" in primary school mathematics teaching. The first process of students' experience is: Why should we learn to average? In this way, we can design a situation: let three people clap the ball in groups to compare the results, and then use the total. But if there are four people in a certain group patting the ball, the students will immediately say "it's unfair to stop using the total"-this is the growing point.

"Cut-in" is not a direct "cut-in" of "Today, let's learn the average, which can better represent the average level of a group of numbers", but a process of finding a suitable cut-in point from the realistic background of life and then letting students cut in. For example, a student said to me after a racket match, "Teacher, I really shot 12, and now it's eight." I immediately asked him, "Where are the four you are missing?" The student looked at the classmate next to him and said, "I gave it to him."

Give more, give less, add more, and then gradually level off. Is this a mathematical process? Have you found the starting point and growth point of your life? This lesson pinpoints the starting point of teaching, highlights the key points of teaching, breaks through the difficulties of teaching and grasps the growing point of teaching. Students can easily understand the average and essential meaning and connotation of mathematical concepts.

Fourth, do a good job of double basics and moderate training-promote the internalization of mathematical knowledge.

Grasping the essence of mathematical concepts is an eternal topic in mathematics education. Paying attention to the effectiveness of classroom teaching is undoubtedly paying attention to students' basic knowledge and skills of mathematics. Mathematical concept is the foundation of supporting mathematical architecture, and basic mathematical ability is the guarantee of building a good building. Therefore, knowledge must be in place and ability must be trained. It is our unshirkable responsibility to do a good job of "two basics".

5. Carefully design teaching activities, capture and skillfully use teaching resources-presupposition and generation.

Classroom teaching activities are faced with different personalities of life, which should be a dynamic generation process. Teaching activities are the process of "dynamic generation" of "static presupposition" in the classroom.

The wonderful generation comes from this high-quality careful presupposition. Therefore, to improve the effectiveness of classroom teaching, we should pay attention to both careful presupposition and generation. In this way, in the implementation of classroom teaching, students' generation can be tolerated, and classroom generation can be screened wisely, so as to achieve the purpose of skillfully using generation to promote students' development.

So, where do the generated resources come from?

First, teachers carefully presuppose;

Second, it is naturally generated in classroom learning.

No default classroom is an irresponsible classroom!

A classroom that is not generated is not a wonderful classroom!

think

Have you carefully designed every class? Is every design and activity of teaching effective?

Is there room for generation in the preset? Have you used a generation effectively?

Does the teaching form you adopt contribute to the development of students? How to get out of the teaching misunderstanding of classroom surface prosperity and essence inefficiency?

Countermeasures

Careful presupposition-accurately grasp the teaching materials, fully understand the students, effectively develop resources, and evaluate them timely and accurately.

Pay attention to generation-accept generation with tolerance, understand generation rationally, choose generation wisely and use generation skillfully.

Six, the implementation of three-dimensional goals to promote the sustainable development of students.

The effectiveness of classroom teaching first depends on the effectiveness of classroom teaching objectives. The goal of classroom teaching restricts the process and development of classroom teaching and directly affects the quality of teaching. To this end, as educators, we should do the following work:

(1) Keep pace with the times, choose good teaching content, and consolidate students' basic knowledge and skills. (knowledge and skills)

Pay attention to students' learning process and results with enthusiasm, smart mind and keen tentacles. Stimulate students' wisdom, enlighten students' thinking, and make students consciously or unconsciously use mathematical ideas and methods to solve problems creatively. (process method)

(3) Carefully care for children's enthusiasm for learning, do everything possible to mobilize students' enthusiasm and initiative, go all out to protect children's self-esteem and self-confidence, let students experience the value of mathematics in learning, and constantly establish correct values. (Emotions, attitudes, values)

To sum up, in order to improve the effectiveness of primary school mathematics classroom teaching, we should: determine the starting point of teaching, highlight the key points of teaching, break through the difficulties of teaching, and capture the generating points of classroom. Simple teaching style, solid double-base training, thick teaching capacity, active thinking of students and flexible teaching methods.