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Mathematical wide-angle template
As a teacher, on-the-spot class evaluation is our essential basic skill, and it is also a difficult technical work. As the saying goes, "laymen watch the excitement, while experts watch the doorway." As long as you make a move, you will know if there is one. " So, how to analyze it is a high-quality evaluation? In my opinion, the person who evaluates a "refreshing" class is justified, the person who attends the class suddenly realizes, and the person who lectures is convinced. How to do this, we must grasp at least three principles.

First, the principle of high focus

Classroom evaluation is not about telling stories and chatting, but based on objective description and diagnostic analysis of classroom facts. Some teachers don't know what to say when commenting on the class, because his observation points are not concentrated and he doesn't add his own thinking, which leads to boring lectures and no clue.

In order to avoid this situation, we can make some reforms in our attendance record, adding sections such as important and difficult points, improving ideas, teaching highlights, classroom observation points, etc., so that we can pay more attention when listening to lectures. The key and difficult points are the contents that you know well in advance before class. The observation point in the classroom depends on the research topic or the content you are interested in, with students' speech, the use of learning tools, group cooperative learning, design creativity and so on as a certain starting point. For example, the following lecture record table:

Second, the principle of promoting improvement.

The ultimate goal of class evaluation is to improve the classroom teaching level of lecturers. Therefore, the evaluation of classes should be stimulating, developing, targeted and guiding, and guiding is particularly critical.

On the morning of September 23rd, I pushed the door to attend classes and walked into the classroom of Fan Hu, a teacher in our school. Her teaching content is to understand three-dimensional graphics.

Mr Hu is a new teacher who has just arrived in our primary school this year. He is a young teacher, with good image and temperament, full of energy and always smiling.

It can be seen that Mr. Hu is very attentive to teaching. Let each student prepare school tools, and the teaching process is relatively smooth. I can predict that she will be an elite teacher in the future.

However, due to the unreasonable use of learning tools, the classroom failed to achieve our expected results.

Many students are fiddling with cubes, cuboids, spheres and cylinders. Teacher Hu was a little impatient and repeatedly reminded: "Don't play any more, and I will pay away the school tools if I play again!"

It's valid for one minute. After that, students go their own way and are still full of "curiosity" about their learning tools. Looking at these unruly children, I guess Mr. Hu is already Ma Benteng in his heart.

Perhaps because the principal was listening to the class, Mr. Hu didn't dare to lose his temper easily, so he had to finish the class in torment.

After class, we discuss: Why? What should we do?

First of all, I'm sure Mr. Hu asks students to prepare learning tools. Students fully experience and perceive the characteristics of three-dimensional graphics in the process of touching. You know, many teachers are afraid of trouble and chaos, so they can handle it by talking about it themselves.

Then I told her that we can take some tips to avoid the problem that students don't attend classes when playing with school tools:

1. Let the students put their learning tools in the drawer first. The teacher put the prepared teaching AIDS in a big box with a hole in the middle, let the lucky star take out three-dimensional figures (pretending to be mysterious), and let everyone say the characteristics one by one (take out one and say one, don't take it out at once). In this way, all students' attention will be focused on teaching AIDS, and their characteristics will be carefully observed. Remember to write it on the blackboard.

2. Look for the prototype of life in the group. Each group represents a graph. Tell me which objects in life are also such graphs. See which group finds more. (For example, a group represents a sphere. Tell me which items are spherical, too. )

3. Let the students take out their schoolbags, touch and play, and divide them into four piles according to four types of graphics.

When the teacher said a chart, the students quickly took out a chart. Understand the students' mastery.

5. Let the graphics go home (put them in the drawer).

6. Discriminatory practice to further strengthen the characteristics.

How to improve the concentration of junior students can be done from these four aspects:

1. Combination of lectures and exercises: use study sheets or workbooks;

2. Efficient explanation: The teacher does not speak for more than 20 minutes, and all students are required to keep their eyes on the teacher when talking about the key points;

3. Incentive evaluation: organizing teaching activities in the form of group competition;

4. Teaching traces: there should be a blackboard to present the core knowledge to help students remember and understand.

When I was evaluating the class, I first affirmed her advantages, and then gave constructive suggestions around two outstanding problems in her class. This kind of classroom evaluation provides the lecturer with specific strategies to improve her practice, which is of great significance to her future teaching work.

If you are listening to a demonstration class or a high-quality class, you should be good at finding new ideas, new methods and new strategies from the class when evaluating the class, and then extract them for other teachers to learn from.

Third, the principle of efficient application.

Teachers often ask me, is there a fixed template for class evaluation? In fact, as long as it is reasonable and useful, you can comment whatever you want. But we can recommend some commonly used models to you.

1. critical classroom evaluation

If the evaluation is too complicated, many teachers will be afraid of difficulties and unwilling to participate in the evaluation, which will make it difficult to promote regular teaching and research activities. Therefore, teaching and research activities in a small scope need not pay too much attention to depth and height. Focusing on the content of the lecture, I will only talk about a few points. We can adopt the model of "3 1 1": 3 highlights, 1 suggestions, 1 thoughts. The three highlights can't be platitudes, we should find the "points" that are really worth learning, because this orientation is particularly important. 1 Suggestions are constructive suggestions for the deficiencies in the teaching of lecturers. In 1 thinking is the content of special concern. Analyze the phenomena you have observed and then put forward your opinions. For example, what you observe is the influence of the position of the lecturer station on the students' concentration. Take out your opinion that U-shaped walking is beneficial to improve the participation rate of all students, and explain the reasons.

2. Pass the class assessment

Judging from the first link, the evaluation from one link to another is particularly effective for teachers or new teachers who go out to give lectures. But also pay attention to a few points. First, you can't completely replace the lecturer's thinking with your own thinking. Only by understanding the lecturer's design concept can we come up with our own improvement plan instead of blindly overthrowing others' teaching design; Second, be grounded. Don't be too idealistic, but it should conform to the nearest development zone, so that the lecturer can feel that he can pick peaches in one jump; Third, we should also focus on praise where it should be praised. It can't be said that because of time, the advantages will not be mentioned. Instructors only talk about problems, which will lead to teachers' lack of self-confidence and thus lose their original intention of learning from others.

3. Thematic classroom evaluation

Thematic evaluation is very suitable for large-scale teaching and research activities. Piecewise analysis is not only like a complete paper, but also like a distinctive case. This puts higher demands on the professional quality and theoretical level of reviewers, and needs to do some homework in advance. Focusing on a special topic, choose teaching clips to clarify opinions, so that everyone can be promoted in practice and theory. For example, Xu, president of the Municipal Academy of Educational Sciences, wrote "Exploration and Practice of Mathematics Classroom Teaching Mode under Core Literacy —— A Brief Comment on the Mathematics Demonstration Class of Attached Primary School and Yangqiao Two Classes".

A philosopher once said: You have an apple and I have an apple. After exchanging with each other, everyone is still an apple; If you have an idea, so do I. After communicating with each other, everyone has two ideas. Today, on the platform we built, two math classes presented by two teachers, the Primary School Attached to Wushu Teacher and yangqiao Middle School, performed different wonderful performances on the same content. Although it is a heterogeneous exhibition activity in the same class, it is more an activity of exchange of ideas and collision of wisdom than an activity in which teachers from different regions learn from each other and help each other. I think this two-way interactive teaching and research form alone is commendable. It shows us whether our teachers are providing students with a well, a stage or a blue sky in the exploration of classroom teaching reform. ...

First, from the understanding of the intention of compiling textbooks, we can see the practice of teachers' concept of "using textbooks"

The problem of planting trees is the content of the seventh unit of mathematics wide angle in the fifth grade of primary school mathematics published by People's Education Publishing House. The two teachers have different ideas in dealing with textbooks:

Li Jie, a teacher in yangqiao, started from being sensible, from two kinds of cases, from one side of the road to two sides of the road, and finally expanded her understanding and analysis of three kinds of trees in life: visible fake trees, unimaginable trees that are not easy to see and invisible but audible trees.

Fan, a teacher attached to a primary school, takes the task of planting trees as an introduction to drive students to seek the conditions needed to complete the task, and then begins to explore the task in groups and sections. Almost at the same time, he began to study three different ways of planting trees: planting at both ends, planting only at one end and not planting at both ends. Expand and discover the "tree" in life through re-practice;

① Street lamp diagram ② Stone pier diagram ③ Beam column diagram ④ Queue diagram

Visible "tree": the age of sawing wood, the floor of climbing stairs ...

Invisible "tree": the next number in the bell, the moment in time …

All roads lead to the same goal, and both teachers have a concept of "using teaching materials"; Because the problem of planting trees is a general term for a mathematical phenomenon or law. It does not refer specifically to the activity of "planting trees", but to this problem or phenomenon. In teaching, teachers don't stick to the phenomenon of planting trees, but combine real life to saw wood, install street lamps and set up celebration baskets. Let students realize that there is mathematics everywhere in life. Therefore, with the problem of tree planting as the background, through appropriate teaching methods, students can clearly understand that street lamp problems, queuing problems, sawing problems, climbing problems and so on have the same mathematical structure as tree planting problems, so that students can build corresponding mathematical models.

Secondly, from the ingenious design of the teaching process, we can see the construction of mathematics classroom teaching mode under teachers' core literacy.

1. Introduction from life cases

Starting with the pictures of all kinds of trees on campus, Miss Li asked her classmates: Are they arranged neatly? This requires us to plant trees evenly and orderly. So, let's learn about planting trees together today.

Teacher Fan introduced the method: I hope the primary school will plant trees on the side of the path leading to the library, and the school decided to give this task to our class. Students, how many seedlings should we prepare?

Through this design, students can fully feel the life prototype of mathematical problems and better practice the new curriculum concept of mathematicization of life problems.

2. Build through analysis and comparison.

It is a general rule to find laws from simple examples. Simplify complex problems, study laws from the overall situation, and then find solutions.

For example, two teachers instructed students to study three different ways of planting trees, all of which started from planting trees at both ends, and found that the total length, spacing and number of trees changed during the process of change and invariability, only the relationship between the number of trees and the number of intervals did not change, and the number of trees = interval number+1. This is the structural relationship between interval number and tree.

3. Speaking from experience.

With the basic model of planting trees at both ends, there is a foundation when guiding students to find three different ways of planting trees. The difference is that Mr. Li took a slow and steady approach.

Teacher Fan's class, on the other hand, analogizes the migration among three tree planting methods, and is carried out in sections and groups in the same task, with a broad vision, which is conducive to students' understanding of variants in experience and experience.

Therefore, I appreciate several ideas that Teacher Fan extracted from the final combing and integration: 1. Mathematicization of life problems; 2. The core of mathematical problems; 3. Construct the core issues; 4. Math problems are life-oriented. This paper explains the research results of mathematics classroom teaching mode in the middle school attached to Wushu Normal University, and recommends that you seriously study the teaching design of a model student teacher.

Third, from the students' learning experience and sentiment, we can see the manifestation and return of the essence of mathematics learning.

"Wide Angle of Primary School Mathematics" is a special section in the textbook of mathematics experiment published by People's Education Press. It presents the problems with rich mathematical ideas in a lively and interesting way, which enables students to achieve the purpose of solving problems through observation, guessing, experiment, operation and verification, and at the same time improve their quality of solving problems. There are two main lines running through the content of "wide angle of mathematics": mathematical knowledge and mathematical thought. Mathematical knowledge is a "bright line", which is intuitively reflected in teaching materials in the form of words and charts, while mathematical thought is a hidden line behind mathematical knowledge, which cannot be taught as a separate content and needs teachers to infiltrate into teaching activities.

The problem of planting trees is a classic problem of "wide-angle mathematics", which carries the most basic mathematical ideas: "simplifying the complex", "combining numbers with shapes", "one-to-one correspondence" and "mathematical modeling". Starting with simple problems, exploring laws, establishing models and applying models are the basic modes of wide-angle mathematics teaching.

1. Understand the idea of "simplifying the complex"

Some mathematical problems are complicated and the solving process is tedious. When the results are similar and the quantitative relationship is similar, starting with a simple problem, looking for a solution to the problem or building a model is called "simplifying the complex". In mathematics teaching, the thinking method of "simplifying the complex" is widely used, which can save time, improve efficiency, make thinking faster and the result more obvious. In the process of teaching the example 1, guide students to ask "how many trees can be planted on both sides of a 100-meter path?" Explore, if students find that the data is too large to fully express when drawing, they can change the data to "? Rice ",at the same time, the problem is simplified, and the" two sides "are simplified as" one side "on the premise that there are as many small trees on both sides. After simplification, students quickly draw a figure to guess and verify, and get the law. "Simplifying the complexity" makes it easy for students to gain operational experience and get rules, and also fully cultivates students' interest in learning. This is also the embodiment of the idea of mathematical reduction.

2. Infiltrate the idea of "combination of numbers and shapes"

The combination of numbers and shapes is a mathematical thinking method to solve mathematical problems by using the mutual transformation of numbers and shapes. It is one of the important mathematical thinking methods for students to learn mathematics, and it has distinct mathematical characteristics. Mathematician Hua once said: "When the number is invisible, it is less intuitive, and when the number is small, it is difficult to be nuanced." It can be seen that the idea of "combination of numbers and shapes" is important for mathematics learning.

In the teaching of "planting trees", Mr. Li used students to represent trees and "planted one tree at a time" according to the conditions. It is easy for students to intuitively discover the law between "tree" and "interval". First of all, we make a preliminary modeling from simple and individual data research. On the basis of the preliminary discovery of the law, the complex and general data are explored again according to intuition, and the data are sorted out with tables, so as to deepen the law, that is, re-modeling. This is also the process of abstract reasoning. The "combination of numbers and shapes" effectively communicates the relationship between problem conditions, intuitive drawing and tabular data, and visualizes the abstract meaning and implied law of the problem. "The combination of numbers and shapes" further enhances students' understanding of topics, enhances students' experience in continuous operation, makes analysis and induction, and finally establishes a model, thus improving their learning ability.

3. Clear the concept of "correspondence"

In the teaching of "planting trees", there are generally two teaching ideas. One is to find the law by physical operation, drawing and other methods, and then verify the law by abstract reasoning with tabular data, and then apply the found law to real life. This teaching idea is simple in logic. However, how can students not only "remember" the law, but also truly understand the causes of the law, so as to flexibly solve the problems of "receiving, not receiving" and "planting at both ends, only planting at one end, not planting at both ends".

Teacher Fan adopted the vertical comparison of three types of trees. If students are further guided to analyze the characteristics of interval arrangement on this basis, there is a one-to-one relationship between trees and intervals. Planting at both ends: there is one more tree after one-to-one correspondence between trees and intervals, so "tree = interval number+1". Similarly, based on the idea of "one-to-one correspondence", this paper analyzes the relationship between trees and interval numbers in "two-planting and one-planting", and analyzes the causes of the law from a mathematical point of view. Teachers grasp the idea of one-to-one correspondence contained in the textbook, let students perceive the essence of interval arrangement, remove cognitive obstacles, successfully build models and realize deep learning.

4. Experience the concept of "model"

Mathematics curriculum standard puts forward that students should be guided to understand the modeling process and develop "model thinking" in mathematics teaching. "Mathematical model" is a description of the essence of mathematical symbols, mathematical formulas and prototype simplification through quantitative relations. Mathematical models are often used in various fields of mathematics teaching and have a wide range of applications. However, the teaching of mathematical model cannot be taught separately like other knowledge, and students need to be guided to experience the process of "problem situation-establishing model-using model-expanding and popularizing" and realize the idea of "model" in the process.

In the teaching of "planting trees", the textbook presents the problem situation of "planting trees in a small road", which enables students to initially discover the law through observation and thinking, explore the law in cooperation, infiltrate the combination of numbers and shapes to verify the law, establish a model, and use the model to solve the problem. Students experience the process of modeling. Experiencing mathematics originates from life and is higher than life, and ultimately serves the essence of life. In learning activities, students have experienced the process of physical operation, graphic representation and abstract generalization, which gradually deepened their learning and approached the essence of mathematics.

And the two teachers' "model" construction ideas, as long as you carefully look at their teaching design, it will be clear at a glance.

The infiltration of mathematical ideas is a long-term and repeated process, and students should be given enough time and space in the infiltration process. Only after sufficient observation and verification of reasoning can mathematical thoughts penetrate naturally, and finally achieve the purpose of deep learning and improving literacy.

Therefore, if language expresses emotions and exchanges ideas in an abstract way; Physical chemistry is a science based on observable facts. What about math? Mathematics is the description of structure and relationship (there is quantity in this structure and change in this relationship) to verify the method and process of structure and relationship. As for logic, it is more like the characteristics of structure and relationship, while abstraction is the means to find the process of structure and relationship. Therefore, mathematics is to strip all meaningless concrete by abstract methods, leaving only simple structures and relationships to explore the logic.

Of course, curriculum evaluation should follow the principles of honesty, respect for differences and correct attribution, so that it can truly become an activity of ideological convergence, practical improvement, multi-benefit and mutual benefit. Commentators should also learn from others to make up for their own shortcomings, enrich and improve their teaching theories, improve their theoretical literacy and discipline literacy, promote their professional development and get the pleasure of professional growth.