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What are the gains and losses of classroom teaching and effective learning research?
Selection and Practice of Effective Learning Methods of Mathematics for Primary and Middle School Students in Classroom Teaching

Keywords: learning style Effective learning style

I. Introduction

Questions raised:

(A) the needs of curriculum reform

The new curriculum standard points out that mathematics teaching is the teaching of students' mathematical activities. Effective mathematics learning methods cannot rely solely on imitation and memory. Hands-on operation, independent inquiry and cooperative communication are important ways for students to learn mathematics. Our aim is to change students' mathematics learning methods and advocate meaningful learning methods through curriculum reform according to their age characteristics and learning psychology. Highlight students' cognitive activities such as discovery, inquiry and research in the learning process, so that the learning process is more of a process in which students discover, ask, analyze and solve problems. Through practice, the process of changing learning methods and cultivating students' innovative spirit and practical ability.

(B) the needs of student development

The traditional learning method bases learning on human objectivity, passivity and dependence, which leads to the continuous erosion of human subjectivity, initiative and independence. Friedenthal believes that students' learning mathematics is a process of "re-creation". Students do not passively accept knowledge, but create and re-create the mathematical knowledge that their predecessors have created. Therefore, we must advocate autonomous, cooperative and inquiry learning methods in the teaching process, so as to change this passive learning state that ignores human spirituality and creativity, and turn the learning process into a process in which human initiative, initiative, independence and creativity are constantly generated, promoted, developed and promoted. Enable students to acquire the basic mathematical knowledge and skills necessary as modern citizens, and at the same time fully develop their emotions, attitudes, values and general abilities.

(C) the needs of teacher development

With the in-depth development of curriculum reform, the study, thinking and practice of new curriculum ideas have contributed to our self-reflection consciousness, and we have a new look and insight into some phenomena in the new curriculum reform. However, in practice, our teachers try to study their learning methods from the perspective of students and explore scientific and efficient teaching methods. However, they encountered a lot of confusion in the guidance and operation points of learning methods, which made the learning method of "autonomy, cooperation and inquiry" a mere formality. Through project research, they really change the way students learn mathematics, so that students can master knowledge, acquire skills, develop intelligence and form corresponding quality through classroom teaching.

(2) Research basis

One is based on Bruner's cognitive discovery learning theory.

Bruner carried out a large number of mathematics learning experiments, from which he summed up four learning principles: ① construction principle; ② Symbolic principle; ③ The principle of comparison and variation; ④ Relevance principle. The so-called construction principle means that students should construct their representatives in the most appropriate way when they begin to learn mathematical concepts, principles or rules. The symbol principle means that if students master the symbols suitable for their intellectual development, they can form an early structure in cognition. The principle of comparative variation shows that the transition from concept to abstract form needs comparative variation, and mathematical concepts should be learned through comparative variation. Relevance principle means that various concepts and principles should be studied in a unified system.

The second is constructivism theory and its influence.

Constructivism theory has three guiding meanings for mathematics learning: (1) knowledge is a process of construction, and learners' main role must be highlighted; (2) We must pay attention to the constraints and influences of the external environment. In order to gain something from mathematics learning and truly form an excellent cognitive structure, there must be a process of reflection, communication, criticism, experience, improvement and development. Because mathematics always repeats the main process of history to a certain extent, it attaches importance to the construction of mathematics by human beings. (3) Learning is development and a change of ideas.

(iii) Research objectives

Through research, the effective learning methods of mathematics suitable for primary school students, teachers' guidance and students' operation are summarized and refined.

(4) Research content

1. Through practice, study the psychological process of primary school students' mathematics learning and extract effective learning methods suitable for primary school students.

2. Sort out the key points of teachers' guidance and students' operation for effective learning and gain relevant experience.

3. Through practice, summarize the basic characteristics, operational requirements, applicable situational conditions and adaptive objects of diversified learning methods;

4. Through practical research, the benefit evaluation scheme of effective learning methods is formed.

(v) The purpose and significance of the research.

1. Explore effective learning methods for primary school students in concept teaching, calculation teaching, application problem teaching, geometry knowledge, etc., and accumulate some effective learning methods to form a series of effective learning methods for teachers of math group to continue to explore and learn.

2. Excellent teaching plans are compiled into a book, and excellent papers on effective learning methods are bound into a book, which provides reference experience for subsequent teachers who teach similar knowledge.

research method

The choice of effective ways and practical research must be carried out through classroom teaching, so we first understand the types of learning styles of primary and secondary school students in classroom teaching through literature research. Find the basis for choosing learning methods through consultation. (1) The purpose of mathematics teaching in primary schools. The purpose of primary school mathematics teaching is to enable students to master basic knowledge, form teaching skills and cultivate students' various abilities. According to different purposes, you can choose different learning methods. (2) Teaching content. Different teaching contents, when choosing learning methods, should be combined with specific content to determine the appropriate learning methods. (3) the actual situation of students. Students of different grades and levels of development have different acceptance and dependence on intuition. Therefore, there are some differences in the choice of teaching methods. (4) objective conditions. The material conditions and teaching equipment of the school also restrict the choice of teaching methods. At the same time of literature research, action research method is also carried out, which is constantly improved in practice and supplemented by case study method in the research process.

Specific operation:

1. According to the actual situation of the school, the stage plan is made at the beginning of each semester, and the sub-topics of each semester's research content are established. Teachers choose the teaching content of each grade according to sub-topics. Teachers of this grade try the same teaching content and choose learning methods to design teaching plans according to the characteristics of students of different ages.

2. Design multimedia teaching courseware.

3. Practice reflection, twice and thrice teaching and research, and then practice reflection.

(1) Action research:

A, prepare lessons in class, and communicate collectively in the teaching and research group before class.

B, according to the plan for teaching practice, two or three times of teaching and research, practice, and reflection.

C. summarize and reflect on the teaching practice.

(2) Summary and improvement: Through a stage of practice, I have certain feelings, and make a case analysis with the grade group as the unit.

(2) Research process

This topic has been studied for more than two years. During this period, members of our research group have made some achievements through "practice-reflection-practice-reflection-improvement".

The first stage: collecting information and research results about "learning style" teaching. Initially establish the theme of school research

Through the scattered collection and centralized communication of all math teachers, many math learning methods have been found and sorted out. The most important thing is how to guide students to actively participate, explore independently, experience and practice in classroom teaching. And in each paragraph, summarize and sort out the ways suitable for students to carry out activities.

In the study of mathematics learning style in senior high school, we take students' effective participation in learning in the interaction of independent inquiry and group cooperative learning as the main learning style. The purpose of summing up this learning method is to let every student participate in the whole process of learning, to provide every student with a display space, to let students fully express their views, and to let students constantly improve their views and generate new ideas through group communication and discussion. At the same time, it also puts forward other activities such as observation, self-study, practice, consulting materials and operation.

Junior high school mathematics learning activities include: image learning, inductive learning, questioning learning, practical exploration learning and so on.

We choose students' favorite math learning methods in the lower grades, because children in the lower grades are young and tend to think intuitively. So we take operation, games, experience and guessing as the main learning methods.

The first stage; We have taught geometry;

For example, understanding the "hands-on" teaching cases of cuboids and cubes.

The first part:

(1) Make bold guesses and stimulate the desire for action. Let the students observe and understand cuboids and cubes, and guess how many sticks are needed to make a cuboid. Write down your guess? Fill in the form below:

A * * * What are the length and number of joints of each group of root array?

guess

result

(2) Hands-on operation and adjustment of thinking.

I announced the official start of cuboid construction and recorded the final data of cuboid construction. The students began to operate, enthusiastic, free to fight and enjoy themselves in a relaxed environment. I found that some students realized that the number of sticks and contacts was wrong through hands-on, and began to readjust their original ideas, adjusted all the data filled in the form, and finally built a cuboid. Explain that only by letting students act can they have their own thoughts.

Teaching reflection:

(1) Mr. is responsible for teaching students to learn;

(2) Teacher Wang's teaching methods must be based on learning methods;

A, guide students to have the desire to act and introduce new knowledge.

B, display and analyze, and develop the concept of space.

Reveal the law of mathematics in action

(3) Teachers must learn while teaching.

This is the first round of case reflection after each teacher's geometry class, according to the sub-topic "Selection and practice of effective learning methods in geometry learning for primary and secondary school students in classroom teaching" determined by the Mathematics Group. It is found that teachers can determine the learning method chosen by their class according to the age characteristics of students in different grades and other learning methods. It is found that the learning method of operation is more suitable for students in geometry teaching. Through hands-on operation, abstraction can be turned into intuition. Once the students have established the representation in their minds, they can imagine it in their minds, which can improve their spatial concept. However, it is found that if the teacher's operation requirements are not clear, the students' operation in class will be more chaotic. Through reflection, we usually have requirements for operation, and the requirements should not be for adults, but for children.

For example, the fifth-grade teacher in the "trapezoidal area" put forward the following requirements for students before letting them operate:

(1) Cut or spell to transform the trapezoid into a learned figure.

(2) Draw a picture, test and mark the data you need.

(3) Calculate the area of the trapezoid.

(4) Tell me about your method.

Under the guidance of teachers, organizing students' independent inquiry and cooperative learning, cooperative learning will not be a formalism.

stage Ⅱ

In the first round of practice, everyone felt that the research scope was not wide and the knowledge points involved were only five grades. The teacher in the same grade only tried one lesson plan and only one lesson example. We summed up the gains and losses in the first stage, and changed the strategy in the second round of practice. The sub-topic was determined as "Selection and practical research on effective learning methods of computational learning for primary and secondary school students in classroom teaching", from centralization to decentralization, and each math teacher determined the teaching content according to his own grade. Make the choice of learning methods and reflect on practice again.

※ Case: "Explore the algorithm by operation, explain the algorithm and increase the ability"

The first paragraph: try to divide the sticks and understand the arithmetic.

1, 49 game sticks, distributed to 4 people on average, how many sticks each? 49÷4=

Please take out your sticks to score and say it.

Can you use an expression to express the process he just divided?

Whole bundle demonstration: formula: 40 ÷ 4 = 10.

Demo items: formula: 9 ÷ 4 = 2... 1.

So: 49 sticks are distributed to 4 people on average, each with 12 sticks, and the remaining 1 stick. Formula: 49 ÷ 4 = 12... 1.

The activity mode of middle-grade mathematics learning is suitable for learning with the help of operated images, and language is a tool of thinking. Thinking in operation not only makes the purpose and procedure of operation more clear, but also provides content for language expression. Training students to combine operation with language from the order of operation, and then expressing it with formulas can train students' language order and accuracy.

Throughout this lesson, students can understand arithmetic through operation, but operation is only a crutch to help students understand arithmetic. When students understand arithmetic, they can think about the process of division, talk about the process of calculation, and then write the process of horizontal calculation by themselves. It does pave the way for vertical computing to understand logic, rather than letting operations go through the motions as a form.

As the leader of preparing lessons for the lower grades, he summed up in the calculation teaching of the new textbook: the first semester of senior one arranges the addition and subtraction of numbers within 10, the second semester of senior two arranges the addition and subtraction of numbers within 100, and the second semester of senior two arranges the addition and subtraction of three digits. The arrangement of teaching materials follows the age characteristics and cognitive rules of students. ※. The new textbook has made a great breakthrough in guiding students to study law. For example, when teaching the addition and subtraction of numbers within 10, the textbook not only lets students know the meaning of addition and subtraction, but also arranges several floors-the game of numbers and fractions, 10 and other activities. Through these activities, we can not only guide students to master relevant knowledge, but also infiltrate orderly thinking. For another example, when teaching addition and subtraction of numbers within 20, "rounding ten" is the key to calculating carry addition, and "breaking ten" is the key to calculating abdication subtraction. It can not only cultivate students' mathematical qualities such as observation, comparison, reasoning and induction, but also make full preparations for cultivating students' migration ability.

From 10 to 10, we can see the potential of students and their innovative thinking. Of course, these innovative thinking are produced by students' re-creation on the basis of accumulating a large number of mathematical thinking methods. For example, there are three basic methods for addition within 20, namely, counting up, division and combination, and adding to ten. When calculating 23+35, students have the following 10 algorithms.

20+30=50,3+5=8,50+8=58

3+5=8,20+30=50,50+8=58

(Calculated according to the digital value table, converted into integer plus integer, number plus number, integer plus number)

23+5 = 28, 28+30 = 58 or 23+30 = 53, 53+5 = 58.

35+20 = 55, 55+3 = 58 or 35+3 = 38, 38+20 = 58.

20+30=50,50+3+5=58

(Divide the number into two digits plus integer ten digits and one digit)

23+7 = 30, 30+28 = 58 or 35+5 = 40, 40+ 18 = 58.

(For the transfer of the complement method, first add it to the whole ten and convert it into the whole ten plus two digits)

20+35=55,55+3=58

23+30=53,53+5=58

23+40=63,635=58

With these learning methods as crutches, students will use the transfer law to learn new knowledge when they study the two-digit addition and subtraction within 100 in the second semester of senior one, without your teacher saying much. Of course, at this time, we are not satisfied with the students' calculation results. Teachers should further guide students to observe classification and further cultivate students' mathematical thinking quality of classification, conjecture, reasoning and induction.

According to their own disciplines and students' characteristics, the math group also carried out extracurricular activities in mathematics, and designed and carried out a special learning activity of "Looking at Development from Digital Changes". The object of this activity is all the fifth grade pupils. ※. Students in this grade have learned some statistical knowledge and mastered certain statistical ability. With the help of this ability, students can take community teams as units, and each team has its own name. Under the leadership of the team leader, all team members can make online inquiries, observe and interview their parents, neighborhood committees, principals' offices, general affairs offices, etc. Understand Shanghai and China since the reform and opening up.

The enthusiasm of the students is very high, and they all conducted serious investigations and interviews. Just looking at the door of the principal's office and the general affairs office, there are always students with papers and pens. Getting students out of the classroom and into the community, the principal's office, the general affairs office and other places is actually a kind of cultivation of students' ability. It is a good way for students to review the past and learn new things by summarizing the statistical data of group members with what they have learned, and it is also conducive to improving students' interest in learning and feeling that they are learning useful mathematics. In the third stage, let students draw their own statistical tables into bar charts, so as to show the great changes in Shanghai more intuitively and clearly since China's reform and opening up. And choose a good statistical chart to show. It not only achieves the goal of making students skillfully draw statistical charts, but also enables students to give full play to the role of designers. At the same time, let all students feel the great changes in China since the reform and opening up through digital charts of familiar things around them, stimulate the patriotic enthusiasm and national self-esteem of all teachers and students, and strive for a better tomorrow for the motherland.

Mathematics comes from and serves life. This is not only the goal of learning useful mathematics, but also the goal of new curriculum reform, and it is also the best embodiment of this study.

The third round of exercises

On the basis of a large number of exercises in the first two rounds, we started more in-depth exercises. On the basis of the last round of practice, the members of the research group summed up the gains and losses, found out the shortcomings and improved the methods. Later, we also formulated "Selection and Practice Research on Effective Learning Methods of Concept Learning for Primary and Secondary School Students in Classroom Teaching" and "Selection and Practice Research on Effective Learning Methods of Problem-based Learning for Primary and Secondary School Students in Classroom Teaching". Our math teacher explored the knowledge characteristics of the grades he taught, and combined with the topics, carried out the second application problem of the fourth grade, the average application problem of the fifth grade and the second grade of primary school. The concept of axisymmetric figure, the classification of secondary angles, acute triangle, right triangle and hypotenuse triangle, common divisor and maximum common divisor are also studied.

Such as an axisymmetric figure.

● Case description

"Symmetrical beauty" gives people a sense of symmetry, balance, coherence and smoothness, thus reflecting a kind of demure, steady and solemn. But in math class, how to make students feel and experience the beauty of mathematics in "doing math" activities, so as to become interested in mathematics and take the initiative to learn mathematics?

Fragment 1: 1. Perceive symmetry in "doing" and construct concepts.

1. Media presentation: scenes of various butterfly and dragonfly pictures.

2. Show students' works and exchange works.

3. What are these symmetrical figures called when reading a book? Read 126

Reveal the concept: when folded in half along a straight line, the figures on both sides of the straight line can completely overlap, and we call such figures axes.

Section 2: Applying concepts and discovering laws in "doing".

1, judge whether the following plane figures are axisymmetric, and why?

2, display plane graphics:

Rectangle, rhombus, parallelogram, trapezoid, circle, equilateral triangle, isosceles triangle,

Right triangle, square (in pairs)

3. Practical operation and communication report

The third part: expanding space and thinking in "doing"

1, physical projection shows:

● Case reflection

For a long time, teachers have been pursuing inquiry learning to guide students' learning, especially their understanding of "doing mathematics" is clear, and they have tried some specific contents in the textbook according to their own students' reality, but why have they failed in practice? I think the following aspects deserve our consideration:

1. When students really participate in learning activities in class, everyone becomes the main body of learning, and classroom teaching time will become the resistance that restricts teaching to let go. Fundamentally speaking, a meaningful inquiry class, meaningful acceptance and active inquiry are organically combined. In class, "doing mathematics" needs more time, and unnecessary exercises will inevitably be simplified. However, because some teachers still have the teaching concept of focusing on results, when the teaching of explicit knowledge conflicts with the activities of "doing mathematics", they would rather give up the process and ensure the time for practice.

We teachers should attach importance to our teaching materials: we should dig out the content matching with "doing mathematics" in the teaching materials to carry out inquiry activities. In the process of "doing mathematics" activities, we should create good conditions as much as possible, so that students can have more independent experiences and personal activities, give students enough time and space, and let every student be fully active.

2. "Doing Mathematics" requires every student to actively participate in classroom activities. However, teachers still play an important guiding role in the process of students' participation in activities. Without the correct guidance of the teacher, the classroom will be fragmented. Teachers preset teaching links in organizing students' "doing mathematics" activities, and students will certainly have new generation problems in each link. Therefore, in the process of strengthening students' experience and feelings, teachers' guidance is still indispensable, and even teachers' guidance at key points of activities will play a decisive role. In classroom information feedback, we should pay attention to students' thinking process and question quality. Achievement can be used as a standard to test students' mastery of what they have learned, but it is not the main standard. Students' thinking process and mathematical literacy are the most important.

Example: Feel the "demand" and construct a new example of statistics teaching. ※

Teaching fragment

1, creating situations and generating statistical needs.

(1) Teacher: Children's Day will be in more than two months. Every year, our school organizes parties for all classes! The teacher wants to prepare a wonderful cartoon for the children. What cartoons did the teacher choose for you? -Media display: Mickey Mouse, Donald Duck, Pikachu, Lion King and Garfield.

Teacher: Among these cartoons, the teacher likes watching Garfield best. I wonder which one you like best.

Students actively report

(2) Teacher: Oh, so many children say that the teacher really can't remember how many children like Mickey Mouse and Donald Duck and how many children like digital baby. Is there any good way to let the teacher know?

(Student Report: Raise your hand, stand up and call the roll one by one)

(3) Teacher: OK, let's ask you to raise your hands and try! Everyone can only choose one favorite cartoon, and can only raise their hands once!

(List the data on the blackboard in order)

2, preliminary feeling the need of statistical tables

(1) numbers are all here. Can you understand?

(2) How do children and teachers in other classes understand?

Student: Write down what cartoon it is at the top of each number.

(3) Show pictures of cartoon stars and stick them on the blackboard.

(4) In order to make people see more clearly, we can also make a table-teacher statistics.

3, a preliminary understanding of statistical concepts

(1) Just now, the children raised their hands and counted them to know the number of people who like all kinds of comics. This process is actually statistics. Blackboard: statistics

(2) The teacher made a table of the statistical results of the children just now, which we call a statistical table.

4. Be able to read statistics

What do we see in this statistical table?

Now, which cartoon do you think the teacher should show the children on June 1 day? Why?

Reflection:

"Statistics" is the content strengthened in the curriculum standard. The first phase requires "let students experience the process of data statistics" and "pay attention to let students experience the simple process of data statistics with the help of examples in daily life". In this lesson, I mainly start with stimulating students' cognitive needs, so that students can constantly construct new statistical knowledge in solving problems, initially experience the whole statistical process of data collection, collation, description and analysis, master basic statistical knowledge, learn some basic statistical methods, and appreciate the significance and value of statistics.

At the beginning of teaching activities, I created a situation to celebrate Children's Day on June 1st, which greatly attracted students' interest. When the students were in high spirits, they threw out a key question: which of the four cartoons should they choose? Let students feel the necessity of counting people and stimulate their strong interest in solving problems. In class, the students actively used their brains and offered suggestions, and successfully found a solution to the problem: by raising their hands to count the number of people, which cartoon has the largest number of people, they decided which one to watch. Since this is the first time that students really come into contact with statistics, I think it is necessary for students to understand and feel its role. In class, I deliberately listed the number of cartoons on the blackboard irregularly, and raised such a question: How can others understand which cartoon the children in our class like best? Students actively develop their thinking and can spontaneously construct reasonable cartoon statistics. Because it is self-demand that produces structured statistics, it is easy for students to understand all kinds of statistics instead of being mechanically instilled by teachers.

With interest, you have the motivation to learn; Only when there is demand can students explore independently and maintain a good learning attitude. This is teaching in the lower grades.

It can be seen that children in lower grades are younger and their thinking is more intuitive. So we take experiential games, guessing and so on. As the main learning method, it can also be supplemented by operation.

Summary stage

Summarizing the work does not mean the end of practice. We sum up while practicing, and practice serves for summing up. There is no end to research. Today's report is only a summary of our practice in the past two years, and it is also the starting point of our future research.

Third, the actual effect.

(A) students have changed their learning methods and improved their learning efficiency.

Under the guidance of the new curriculum concept, using different learning methods to let students learn can improve the efficiency of classroom teaching. The learning styles of junior students are mainly operation, games, experience and guessing. When using these learning methods, we should be good at cultivating students' observation ability and language expression ability. Junior high school mathematics learning activities include: image learning, inductive learning, questioning learning, practical exploration learning and so on.

For example, when students study multiple application problems, they can draw line segments and combine numbers and shapes. With the help of images, they can accurately find out one or more copies.

The main learning method of high school mathematics is to let students participate in learning effectively in the interaction of independent exploration and group cooperative learning. In particular, the study of geometry knowledge is very suitable for this learning method, which provides a space for each student to show. Through autonomous learning and communication, students can constantly improve their views and generate new ideas.

(2) Encourage teachers to accumulate experience and improve their professional level in practice.

Every semester, math teachers should choose the knowledge points of practical lessons according to the topics determined by the math group, and around the central topic of learning style, force the math group teachers to study or read books online, read the theoretical knowledge about learning style, determine the teaching content according to their own students' reality, and reflect on whether the learning style they adopt is suitable for students of this grade. Because teachers' teaching concepts and teaching behaviors are changing, the quality of case analysis is getting better every year.

(3) A large number of classroom teaching practice courseware has been made, and a large number of teaching designs, lectures and cases have been accumulated. We regard these materials as school textbooks and resources enjoyed by teachers, so that teachers can use them repeatedly and adjust them constantly, which really optimizes the teaching resource environment.

Fourth, analysis and thinking.

Through a lot of practice, we believe that it is the common pursuit of mathematics teachers to choose and practice effective learning methods suitable for primary and secondary school students in classroom teaching. Effective learning methods aim at students' progress and development. Teachers should have all the ideas for students' development and use scientific teaching strategies to make students enjoy learning, learn and learn, and promote students' all-round development, active development and personality development.

(1) Teachers pay attention to the introduction of situations and guide students to experience and observe.

Teachers can give full play to the role of teaching situation map and use modern educational technology to change static into dynamic. We can use good scenes to guide students' observation, provide them with enough observation and thinking, let them understand pictures and ideas, get information about choice and handsome selection, and highlight the characteristics of mathematics. Our teachers are good at thinking, and they are also the direct creators of teaching situations. Teachers are good at selecting materials from the things and phenomena around students and creating new teaching situations, so that students can not only feel that there is mathematics everywhere in their lives, but also stimulate their thirst for knowledge and desire to explore new knowledge.

(2) Teachers pay attention to students' activities and guide students to study and explore independently.

The cognitive law of students is "vivid, intuitive and abstract thinking", and teachers can design and organize operation activities according to this law, playing the role of organizer and guide. First of all, there are requirements for operation, so that every student must communicate in groups; There is communication when there is operation, and students are guided to combine intuitive images with abstract generalizations, so that their hands, brains and mouths can be used together. Students' independent inquiry is actually a kind of "re-creation". Teachers should choose these repeated or reproduced teaching contents purposefully, provide students with space and time for independent exploration, let students actively carry out mathematical activities such as observation, experiment, guess and verification, and pay attention to the process and methods of students' exploration. Teachers should carefully handle the dialectical relationship between autonomy and guidance, release and collection, and process and result.

Independent exploration and cooperative communication are both ways for students to learn, and there is no difference. Teachers should make them penetrate each other and complement each other in teaching, so that students can form their own understanding of mathematics in the process of exploration and gradually improve their own ideas in the process of communication with others, which will certainly enable students to play both the role of individuals and the role of groups in learning activities, thus improving the effectiveness of teaching.

(C) Pay attention to the evaluation mechanism

Evaluation can be a multi-angle evaluation, which can discover the bright spots in students and explore their potential. In teaching, teachers should provide different opportunities for different students to show themselves, and make appropriate evaluations in a timely and targeted manner, so that students can experience success and build self-confidence; The evaluation of students in classroom teaching should not only look at the results, but also pay attention to students' learning process, problem-solving thinking process and students' participation. Encourage students to evaluate themselves and others; We should not be stingy with praise, nor should we praise too much. We should pay attention to students with learning difficulties and middle and lower students, be kind to students' mistakes, be good at finding good places among them and protect students' self-esteem.