How to carry out the exploration of teaching mode?

(a) Construct a scientific and effective teaching mode of elementary school mathematics classroom.

1. Constructing the general mode of primary mathematics classroom teaching:

The primary mathematics textbook of the Su Zue version pays attention to the selection of teaching content, and the textbook provides a large number of content conducive to students to carry out observation, manipulation, experimentation, reasoning, and other activities and the form of the activities that students like to be conducive to cause students to learn effectively, so that students can complete the "real-world problems". --mathematical problems - mathematical models - mathematical knowledge and methods - application of knowledge to solve problems "

(1) Create a situation, put forward mathematical problems:

Teachers do a good job of teaching pre-testing: what life experience have students accumulated? What real-life examples and experiences can be used as a pretext? What practical activities can students engage in to strengthen their mastery of what they have learned? How can we combine mathematics and life better? Then through the language portrayal, physical demonstration, multimedia computer demonstration and other means to create a vivid and interesting, intuitive image of the situation. Make students feel the close connection between mathematics and real life, enhance the confidence of learning and applying mathematics, and then mobilize students' enthusiasm and interest in learning, and develop students' abstract thinking. This link in the practical application of the situation should pay attention to let the context of service to the teaching content and teaching objectives, to try to exclude other factors outside of mathematics, to minimize the interference of students' thinking.

(2) Independent exploration, the establishment of mathematical models:

Teaching, the use of the Su Zue version of the textbook for students to provide students with a wealth of learning materials, to provide students with the appropriate time and space, to create opportunities for students to independently find mathematical problems, mathematical problems, prompting students to maximize their participation in the learning process. Through observation, experimentation, speculation and other activities, students experience the mathematical process of "experience - model - symbol", establish mathematical models, and gradually form their own understanding of mathematical knowledge and effective learning strategies. They will gradually develop their own understanding of mathematical knowledge and effective learning strategies. It also helps students to develop a sense of problem solving and a spirit of independent exploration.

(3) Consolidation exercises, practical application and expansion:

Based on the novel and creative design of the exercises in the Su-Teaching Edition of the elementary school mathematics textbooks, we make full use of a variety of interesting exercises that are combined with real life and practical experience to create opportunities for the students to apply the relevant knowledge and methods, so that the students can understand the value of the practical application of such knowledge and methods. It is also important to guide students to recognize themselves in self-evaluation and others' evaluation, to build self-confidence, and to develop themselves.

(4) Summarize and Reflect, Perfect Knowledge Structure:

Summarizing is the process of summarizing and generalizing what has been learned in this lesson, and it is the process of helping students organize fragmented and dispersed knowledge into organized and systematic knowledge, and it is also the process of students internalizing the new knowledge they have learned, and integrating it with their original knowledge to form a new knowledge structure. In the student group discussion and exchange on the basis of the whole class discussion and exchange, so as to guide the students will reflect and knowledge comb, learn self-evaluation and self-summarization, improve the students' learning ability.

2. Initially formed an elementary school math teaching "number and algebra", "space and graphics", "statistics and probability", "practice and integrated application" and so on. Practice and comprehensive application" and other areas of scientific and effective teaching model.

(1) The teaching mode of 'number and algebra' in the context of the new curriculum

①Create a situation to stimulate interest

According to the Su-Teaching Edition of the textbook emphasizes the cultivation of the students' sense of number, and by means of verbal depictions, physical demonstrations, slideshows, paintings and drawings, music rendering, and multimedia presentations, etc. The students can experience and understand the meaning of numbers by providing them with realistic scenarios and organizing operational activities. Closely related to the reality of life, focusing on the application of numbers in life. So that students appreciate the life of mathematics everywhere, enhance the learning and application of mathematics confidence, and then mobilize students to learn enthusiasm and interest, the development of students' abstract thinking.

② independent inquiry, cooperative exchange

On the front of the students put forward the problem of organizing, selecting the content of the class teaching, teaching objectives closely related to the problem as the object of study of the students in this class. By organizing students to participate in a variety of games, conversation, operation, cooperation and other mathematical activities, to experience the diversity of problem-solving methods, independent exploration in mathematical activities, construct new knowledge, new information, and promote the development of students' thinking.

③Practical application, expanding innovation

Designing situations or exercises that are more applied, comprehensive and open based on basic knowledge, deepening the understanding of new knowledge in application, thus consolidating new knowledge and forming skills. At the same time, it exposes the contradictions and differences in students' understanding and application of new knowledge, so that teachers can adjust their teaching in a targeted way to reduce mistakes and improve classroom efficiency.

④Reflective summarization, self-construction

Can be based on students' group discussions and exchanges, whole-class discussions and exchanges, and summarize in the discussion and exchanges. It is worth noting here that it is not the teacher who summarizes, but the teacher who guides and organizes the whole class to summarize themselves.

E.g.: teaching "with the letter of the number" a lesson, the teacher set the problem situation: students, we all know that the 2008 Olympic Games will be held in our country, in order to meet the 2008 Olympic Games, I envisioned (with the projection) in this form from left to right to build 2008 squares, who can tell the teacher in 10 seconds how many matchsticks are needed? At this point the teacher took the opportunity to tell the students a basic idea of mathematics: from simple to start, in-depth problem solving!

First, let the students use matchsticks to build a match, count and fill in the following table: (given to the students in advance)

Number of squares to build

1

2

3

10

100

Number of matchsticks to be used

During this process, the students are actively doing their hands, and the teacher makes a round trip, and finds that the students are able to write the number of matchsticks quickly. Instead, the teacher asked the students, "Which cells in the table can be counted out directly by building and assembling?" "The number of matchsticks to build 100 squares can't be counted out, so what should we do?" Then let go and let students discuss in groups before answering. And ask students to give reasons.

Student 1: Because 4 matchsticks are used for the first square and 3 are added for each additional square, the number of matchsticks needed to build 100 squares is 4+3×99=301 (根).

Student 2: First one, then three for each square, so for 100 squares you need 1+3×100=301 matchsticks

......

Then ask: If you use X to represent the number of squares you are building, how many matchsticks are needed to build X number of these squares? How many matchsticks are needed? Through discussion and exchange, students got different five answers: [4+3(X-1)] sticks, (3X+1) sticks, [4X-(X-1)] sticks, [X/X+(X+1)] sticks, and [X+2 X+1] sticks. And ask students to choose one of these methods to calculate how many matchsticks are needed to build 2008 squares? Tell how the math was done.

Finally, discuss what the X in 4+3(X+1), X+X+(X+1), 3X+1, 4X-(X-1) stands for?

Putting aside the matchstick problem, what can X represent? The students realize that X can mean "the number of squares", "integer", "positive integer" can also mean "the length of the rectangle is X centimeters "The length of the rectangle is X centimeters", "There are X students in the class", "The temperature is X degrees Celsius" and so on. In short, letters can stand for any number, length, number, etc. And ask students to write down the perimeter or area formulas, and the arithmetic laws represented by letters, that they know for shapes represented by letters (projected). And point out the number represented by the letter.

Through hands-on learning, independent exploration, cooperation and exchange of learning methods, so that the students themselves to complete the general law from the special case, and the letter of the general law of the process of cultivating students to analyze, generalize the ability to initially form a sense of symbols, and appreciate the need to explore the general law.

(2) The teaching mode of "solving practical problems" in the context of the new curriculum.

①Situation introduction

To emotion, situation, doubt, and interest in the design of a lively and interesting situation, creating cognitive conflict thinking situation,

The vivid life into the classroom.

② question

Let the classroom teaching start from the students' questioning, so that the question becomes the natural main line of the classroom. Such as what information do you know? Who can use their own language to put this information together and raise a question? The problem of students, teachers should be good at guiding, selecting effective questions, pay attention to the protection of students' enthusiasm and the generation of effective questions.

⑧ Try to explore

Let students consciously and actively experience and find the necessary quantitative relationships, so that the students' minds to form a clear idea of the solution. Give the initiative of learning to the students, pay attention to the effective participation of individual students, combine the operation and thinking, guide students to speak the problem of reasoning, teach students the method of expression, cultivate the habit of saying. Promote the synchronization of students' language development and thinking development.

④Consolidation of the use of

Thematic scenarios or tabular groups of questions are good forms of practice, they can not only train students to the quantitative relationship in the question of the sense, but also conducive to the training of the students to analyze the information, extract the information, the ability to synthesize the information.

For example, "two-step calculation application problems" can be used to carry out the training of the following "thematic scenario map" group of questions:

According to the information above, can you solve the following problems? What other questions can you ask?

Uncle Zhang took 200 yuan and bought a volleyball and a pair of sneakers, how many yuan are left?

How many yuan were used to buy 3 basketballs and 5 soccer balls for one **** at school

The school bought 8 sets of clothes, how many more yuan was spent on the tops than on the pants?

It is also possible to practice using a list-based set of questions: the unit prices of food in the food cupboard of the Carrefour supermarket are shown in the table below

Bread (bag)

Drink (listen)

Sugar (kg)

Slices $3

Coke 2 yuan 60 cents

Peanut sugar 20 yuan

Coconut 3 yuan 2 cents

Juice $1.50

Fructose $16

Jam $2.80

Coconut milk $3

Chocolate $25

Think about it: (1) What do you know from this information above?

(2) If you buy one serving of each of the three types of food, what is the most you can spend? What is the cheapest?

Fill in the blanks: Use 50 yuan to buy the above foods, according to their own ideas, fill in the shopping plan in the table below.

Category

Scheme

Bread (bag)

Drink (listen)

Sugar (kg)

Total ($)

Unit price

Quantity

Unit price

Quantity

Unit price

Quantity

(1)

(2)

(3)

(4)

Problem group training, the topic is not long, but it contains a lot of information. The application problem group not only trains students to perceive the quantitative relationship in the questions, but also trains students to analyze information, extract information, and synthesize information.

⑤ Summarize

Help and guide students to organize and internalize the new knowledge they have learned in a timely manner to form a new knowledge structure, such as what have you learned in this lesson? How to start to solve such a problem?

(3) The new curriculum background "calculation" teaching mode

①Review padding, context stimulates interest. In the learning of new knowledge before, and new knowledge is closely linked to the knowledge and skills, learning methods and thinking methods for distinctive targeted training, such as according to the content of the subject teachers to prepare a variety of oral training, questioning and the content of this lesson related to the definition, laws and so on. Through the premise of compensation and thinking orientation, to help students make good migration before the preparation of knowledge and skills.

② skillful use of migration, independent exploration.

To fully inspire the students to seize the same point of the old and new knowledge, to lead the students' thinking to the linkage of the old and new knowledge. At the same time to seize the essence of the old and new knowledge to compare and differentiate. When students find out the intrinsic connection between the old and new knowledge, guide students to compare, analyze, and seize the essence of the difference to prevent the occurrence of negative migration.

③ Guide the generalization and clarify the method.

Guiding students to experience the process of analyzing, synthesizing, abstracting, generalizing calculation methods and understanding arithmetic. Fully realize the diversity of algorithms. Strengthen the estimation, cultivate students' sense of estimation, but can not arbitrarily pull up the requirements, not to mention a handful. After all, the elementary school stage, the development level of logical thinking of the lower grades students and language expression ability is limited, a person said incomplete, can be supplemented by more than one person, the teacher and then on the basis of this inductive, summarize the correct and diverse methods of calculation.

④ Practice to deepen and optimize the method.

Teachers around the teaching objectives, carefully designed a variety of forms of exercises for students to try to calculate the use of the method, so that the teacher timely guidance, correction and make up for the shortcomings. The design of the practice should pay attention to: practice to be targeted, practice to have ladder, practice form diversity, practice to have a certain intensity.

⑤Summary review, self-evaluation.

Guiding students to systematically recall the whole lesson, further clarifying the key points of knowledge, difficulties and keys, and ensuring that students systematically master knowledge. At the same time, students should be taught to evaluate the method of "what I have learned", "what I still do not understand", and some details should be reminded to pay attention to, such as writing format, writing standardization. (4) the new curriculum background "statistics and probability 's teaching mode.

(4) The teaching mode of "statistics and probability" in the context of the new curriculum

① Trigger demand.

Creating certain problem situations, life situations, etc. to arouse students' curiosity, promote the need for students to collect data and statistics, experience learning activities and other learning interests. For a class of efficient learning to do a good job of psychological and ideological preparation.

② operation inquiry.

To guide students into the whole process of statistics, games and other learning activities: choose the statistical theme, collect data, organize data, analyze data, make decisions, communication, evaluation and improvement; so that in the feeling, experience and other specific learning activities to gain an understanding of mathematics, and gradually establish the concept of statistics and the application of awareness, thinking skills, emotional attitude, and values, etc. get The development and progress.

③ Application Expansion

In addition to using the statistical objects provided by the textbook, students are also guided to statistics on school classes, the number of students in each class, the weather and other real-life statistics, guided to obtain information through observation, watching TV and newspapers, asking questions, etc., supervising and checking the students' records, and finally summarizing the information, and cultivating the students' comprehensive ability in such practical activities.

④ Summarize the extension

You can summarize the students' learning attitudes, results of learning, learning methods and so on. The direction of the extension can be the subsequent learning content, it can be the introduction of related knowledge and so on.

such as the teaching of the first grade book P98-99 pages of statistics, we first create a life scene of the animal games, triggering interest in learning, the production of the classroom will demonstrate the graphics appear faster, so that it is difficult for students to independently count the number of various graphics know the number of such a break in the cognitive structure of the balance of the students, so that the students naturally seek to simple and fast records of This breaks the balance of students' cognitive structure and makes them naturally seek for a simple and fast way to record data, which triggers their need for statistics.

Then we guide the students to discuss how to record the number of various shapes, and after the students record the data on their own, we show them different ways of recording, and again guide them to make comparisons, and to find out simple and fast ways of recording data. This allows students to explore and optimize statistical methods in the process of experiencing statistics, which effectively promotes and develops students' concept of statistics. It stimulates students' enthusiasm for independent exploration and their sense of innovation. In the subsequent session of statistical application, it was arranged to buy a buy fruits for each student in the class, which fruits to buy? How much of each kind of fruit to buy more appropriate statistics and discussion questions, students in the thinking and discussion after the formation of **** knowledge: first use the method of drawing a √ to investigate the class's favorite fruits, and then discuss if the class reunion, which fruits to buy more, which to buy less. So that students appreciate the role of statistics in the service of life.

(5) The teaching mode of "space and graphics" in the context of the new curriculum.

①Observation and accumulation

The main tasks in this stage include (1) reviewing the old knowledge, preparing for the learning of new knowledge, and building a sensible bridge between the new knowledge and the old knowledge; (2) stimulating interest and motivating the learning of some objects and interesting phenomena; (3) accumulating representations, and building up representations in the minds of the students through observing a large number of geometric forms. to pave the way for the formation of concepts or the discovery of laws later on. This is the core task of this stage.

For example, in the teaching of the understanding of the circle, first recall what geometric shapes have been learned before? They are surrounded by what, then the teacher with a ball tied at one end of a thin rope, one end of the fixed in the hands of the forceful flinging demonstration, guiding the students to observe and think: what kind of shape is formed when the ball moves in the air? This is also a figure made of line segments? Starting from the recall of plane figures surrounded by segments, by observing the teacher's spinning ball rotation drawing circle demonstration, students get a curve closed into a circle visual image. This is from the circle formation process to recognize the circle, rather than a simple static presentation of a circular object. This treatment, not only can attract the attention of students, but also allows students from this demonstration process to find the circle and previously learned the difference between plane shapes, but also conducive to the following more comprehensive and deeper understanding of the circle.

②Operation discovery

Teachers according to different teaching content, choose different operating materials (models, objects or teaching aids, etc.), so that the students in the process of cutting, spelling, folding, measuring, folding, drawing, moving a process, through the eyes, ears, fingers, and other sensory cooperation and other students to cooperate to discover the characteristics of geometric shapes, put the The preliminary perceptual understanding gained from observation is pushed to a deeper level. The main task of this stage is to discover the rules through the operation, and in the process of discovery to learn to cooperate and experience the joy of learning.

such as the trapezoidal area formula derivation, we can use the idea of transformation, in the operation of the discovery stage to guide the students in groups, focusing on the wisdom of the trapezoid to transform it into a familiar geometric shape, and then asked to find out the area, and then derive the trapezoidal area of the formula. In the process of concrete operation students found several successful and feasible ways: (1) use two identical trapezoids to put together a parallelogram; (2) cut the trapezoid into a parallelogram and a triangle; (3) cut the trapezoid into two triangles (two triangles of the height of the trapezoid is the height of the trapezoid); (4) cut the trapezoid into a rectangle and two triangles (if it is a right-angled trapezoid is a triangle)...... In this teaching process, students through the cut and put together operation, they discovered and summarized the formula for the calculation of the area of the trapezoid, compared with the teacher's direct lecture for students to accept, this method allows students to personally experience the process of discovery of knowledge, which not only deepens their understanding of the formula, but also strengthens their confidence in independent inquiry

③These are the first time that students have been able to find out about the formula.

③ Practice application.

The main thing is to use the knowledge they have just learned and the laws they have discovered to solve some practical problems, and in the process of solving problems, let the students master the knowledge they have learned, form mathematical skills, and cultivate and develop their good thinking qualities.

A. Formation of skills. Intellectual skills mainly refer to the calculation of the product, which includes the calculation of the perimeter and area of plane shapes, the calculation of the surface area and volume of three-dimensional shapes and so on. In the process of calculation, it involves a series of factors such as the understanding and application of concepts and formulas, the formation of spatial concepts and oral and written arithmetic, and problem solving. Operational skills mainly refer to drawing, such as drawing certain geometric shapes with tools (ruler, triangle board, compass), or using tools to measure angles, measuring the length and weight of objects.

B. Development of thinking. In the teaching of space and figures, we should focus on developing students' image thinking. In practice, we should strengthen the training of expressive thinking, not only let the students make the final answer, but also let them say their own ideas and analyze the process of solving the problem. Through the exercises, the cultivation of students' thinking qualities, such as agility, simplicity, criticality and profundity, etc., should be strengthened.

4 Evaluation and Motivation

Evaluation and motivation is not an independent stage, it runs through the above three stages. Evaluation should not only focus on students' academic performance, but also discover and develop students' potential in many aspects, and help them recognize, affirm and accept themselves.

(6) The teaching mode of "practice and comprehensive application" in the context of the new curriculum.

①Pre-course preparation.

First of all, we should determine the topic of inquiry. Think about what students care about, what they are interested in, and then guide students to find the topic of inquiry. At the same time, it is necessary to do a good job of pre-course investigation or pre-course production, and arrange for students to do pre-course investigation or pre-course production. According to the characteristics of the teaching materials, the lower grades are mainly based on the activity scenes of students' study, life and games, so that students can ask questions and solve problems from the activity scenes. Middle grades to students in the actual operation of the main, so that students in the operation of practical activities in the study of new issues.

② Inquiry in the lesson

By guiding students to sort and summarize the many problems raised, develop activity plans, participate in practice, independent experience, cooperative problem solving, expression and communication, so as to obtain a general method and strategy for understanding society and solving problems.

③ Post-course extension

Students are guided to carry out post-course verification, observation and application, writing math diaries, and helping parents to solve practical problems.

Taking the tangram lesson as an example, we collected information to make the online courseware "Colorful Dreams", combined with physical learning aids, guided students to understand the origin of tangrams, learn the production method of tangrams, and explore spelling through activities such as guessing what it looks like, copying without going out of shape, dexterity challenge, and creativity ring, etc., which is multi-perspective, multi-level, and effectively improves both the quantity and quality of the information, and successfully provides the possibility of the student's Self-construction provides the possibility.

(2) Stimulating learning interest, changing learning styles, and improving students' comprehensive literacy

The above teaching model focuses on both the implementation of the curriculum in the teacher's classroom (the teaching level) and the development of mathematics in the students' mathematical learning process (the learning level), and is based on promoting the students' comprehensive, harmonious and sustainable development, so the promotion and application of the above model makes it easy for the teachers to teach, effective to teach, and enjoyable for the students to learn. Therefore, the promotion and application of the above model makes teachers teach easily and effectively, and students learn happily and actively. The traditional way of learning has been transformed and students' comprehensive literacy has been enhanced.

1. Students can find their own problems in the learning context provided by the teacher, inspired and guided by the teacher, explore their own ways to solve problems, and in the process of solving problems learn to communicate with their classmates, evaluate and reflect on their own activities and the results of other people's processes, choose the best way to solve the problem and methods, and then realize the self-construction of knowledge.

2. Changes in the learning process and learning styles of students. It is manifested in the fact that many students' learning styles such as reading, homework, gathering information, and cooperating and communicating with others have changed or are undergoing positive changes, and their learning habits are more favorable. Students have gradually developed their own methods of reading, manipulating, discussing, calculating, thinking, presenting, evaluating, etc., and their learning abilities of observing, thinking, calculating, writing, summarizing, applying, etc. have been significantly enhanced. Many students have developed a good learning style of pre-study and self-study.

3. As teachers changed the traditional evaluation methods, focusing on providing students with opportunities for self-evaluation, the students' awareness of self-evaluation greatly enhanced, in addition to students in the cooperation, communication, but also learned to objectively evaluate others, to find the strengths of others, to make up for their own shortcomings, and learned to correctly accept the opinions of their classmates.

(C) Innovative ways of teachers' professional development, promoting the improvement of teachers' professionalism

1. Routine construction, focusing on the overall development of teachers.

In routine construction, we encourage teachers to use teaching materials creatively, develop resources of students' life scenes appropriately, improve students' learning styles under the guidance of the new curriculum concepts, advocate diversified learning styles such as hands-on practice, self-directed exploration, and cooperative exchanges, and make math learning activities a lively, active, and personalized process. And give full play to the power of the teaching and research group, the normal group teaching and research activities, activities concerned about the teachers of the above classroom teaching mode in practice, the reasonable use of pre-setting and classroom generation of the interrelationship between the pre-setting of the classroom, we also according to the characteristics of the teaching and research groups, tapping into the research and training power of the teaching and research group, to carry out targeted application of the classroom teaching mode of training, to help teachers to correctly understand and flexibly apply the relevant teaching mode. Promote teachers to shift the focus of teaching work to the direction of promoting the comprehensive, harmonious and sustainable development of students. Teachers not only pay attention to the content of the teaching, the process of predetermined, but also pay more attention to the dynamic generation of students in the learning process.

2. Tracking service, pay attention to the development of teachers.

The object of tracking service is the young teachers with "plasticity". The method we adopt for this part of the teachers is "targeting, intensive training". For young teachers in need of help to set up a support group, by the leadership and his master together, specifically for classroom teaching to give him a "tracking" menu: weekly listening to each other to evaluate each other a class, each semester to make a classroom teaching mode of application of the debriefing class.

3. Twinning activities, focusing on the mutual assistance of teachers

Through the form of "mentor and friend" twinning, the master is required to train from the basic skills, classroom teaching and educational research in three aspects. At the end of the school year, new teachers are given a comprehensive evaluation. Older teachers are more experienced in teaching, have a wide range of practical experience, have a better command of teaching materials, and have a better understanding and application of the above teaching models, and the twinning training enables new teachers to get started faster. At the same time, young teachers have vivid ideas, are full of energy, are not bound by traditional teaching concepts, and dare to speak and act. This in a way also promotes the old teachers to reflect on their own teaching behavior.

4. Thematic research, focusing on the needs of teachers

Thematic research is teacher training in the form of topics. Our practice is: a clear theme, backbone first, extensive interaction, expert review, and strive to achieve a topic. Through listening to lectures, watching class examples, analyzing cases, promoting the transformation of teachers' educational concepts, for the implementation of the new curriculum, the promotion of the above teaching mode provides the ideological preparation. At the same time, we invite experts to the school to give special lectures; and teachers around **** the same topic to talk about their thoughts and views, to carry out salon forum activities, to stimulate the potential and wisdom of teachers. And the classroom teaching as one of the entry points to carry out thematic training.

The research of this topic promotes the group optimization of the quality of mathematics teachers in our school and the development of teacher specialization. In the past three years, our school math teachers in the city and county level teaching open class more than 20, to participate in the provincial and municipal teaching competitions have many times, a number of young teachers in the classroom teaching in the refinement of the strong growth. With the advancement of the subject of research, the practice of reflection, the practice of summarizing the writing of scientific research papers has become a conscious behavior of teachers. Over the past three years, teachers have written nearly a thousand cases, reflections, teachers' papers are frequently seen in newspapers and magazines, "Jiangsu Education Technology", "Primary School Teaching Reference" and other magazines published more than 30 articles of our math teachers, at all levels and types of excellent paper competitions at the provincial level or more than one hundred and sixty one or two prizes. So far, our school has formed a high-quality team of math teachers with three Yancheng City-level teaching masters, four Dafeng City-level subject leaders, six Dafeng City teaching masters.

Tenth, a few thoughts on the subject of research

In the "new curriculum background of elementary school mathematics classroom teaching mode exploration and research" under the leadership of the subject, our school's math classroom teaching outlook has changed a lot. However, we are pleased to see that there are many shortcomings that need to be improved and a lot of problems that need to be studied and solved:

1. The lack of theoretical knowledge, the weakness of the research force and the lack of exchange of information with the outside world have a direct impact on the subject of further in-depth research.

2. "Point" of the breakthrough is not enough. Between the sub-topics research efforts, level and level of uneven, a few sub-topics have a slapdash, the tendency to go through the motions.

3. Not enough research on the application of the above teaching mode of systematic scientific and effective evaluation.

4. Teachers teaching initiative, creativity to be improved. Teaching model itself only for the teacher's teaching to provide a framework for teaching activities, prompting a line of thought, and is not available for teachers to mechanically imitate or simulate the template. In the process of choosing and applying, it is still necessary for teachers to give full play to their creative talents, and be good at boldly transforming according to different teaching tasks, different classes of students and their own teaching strengths. Constitutes the teaching model of the various teaching variables, teaching procedures in the teaching process of the arrangement, combination and specific operation methods, is not fixed, all of which for us to further optimize the teaching model, to create a simple and effective mathematical classroom left a wide space.