Reflection on the mathematics after the small class

Part 1: Reflections on mathematics teaching in the country _ the lowest common multiple

The "Last Common Multiple" lesson has made students' enthusiasm for learning higher, and the knowledge is more natural and solid. The students' thinking is also spiraling upward and has achieved good teaching results. I am doing it from the following aspects:
First, create a situation to stimulate interest, so that students take the initiative to participate in learning.
The “public multiple” and “least common multiple” singles are used to understand the students from the perspective of pure mathematics, which is obviously boring and boring. I start from the student's experience and existing knowledge, stimulate students' interest in learning, provide students with opportunities to fully engage in mathematics activities, and enhance students' confidence in learning mathematics. Make these boring knowledge become fresh and agile mathematics, so that students can learn both the knowledge and the joy of learning mathematics in the process of solving problems.
Second, to develop students' ability to explore independently.
In teaching, we should not teach students the ready-made mathematics, but let the students observe, think, and explore mathematics. In the study of the significance of the lowest common multiple, the author designed the method to find the lowest common multiple, the lowest common multiple conjecture, the decomposition of the quality factor, a series of open mathematical problems, so that students have enough space for thinking activities to solve problems, and independently explore. Activities, so that students are thinking about mathematics and mathematics is around us.
Third, the lack of mining needs to be improved
1. The situational creation at the beginning of the class takes into account the connection with the example, but the transition is not good enough.
2. How to stimulate students' interest is not only a temporary effect, how to design the plan from the perspective of students, and to keep students' learning enthusiasm in the classroom is a question worth considering.

Part 2: Reflections on mathematics teaching in small and medium schools _ common factors and the greatest common factor

The Standard states that “student is the master of mathematics learning, and teachers are the organizers, guides, and collaborators of mathematics learning.” This philosophy requires that the role of our teachers must change. I think the role of teachers must be reflected in the following aspects. First, we must guide students to think about and find the relationship between the immediate problems and their existing knowledge experiences. Second, we must provide opportunities for students to be placed in problem situations. Third, we must create an atmosphere that encourages exploration and understanding. Provide students with an instructive discussion mode; Fourth, encourage students to express and discuss different answers based on deepening understanding; fifth, guide students to share their thoughts and results, and re-examine their own ideas .
In contrast to the concept of the "course standard", I made a little attempt on the teaching of "the common factor and the greatest common factor".
First, guide students to think about and find the connection between the problem at hand and their existing knowledge experience.
"The common factor and the greatest common factor" is a content that is learned after the "public multiple and the lowest common multiple". If we analyze the content of this lesson, we will find that these two parts have similarities in both the presentation of the textbook and the way of thinking. Based on this understanding, at the beginning of the lesson I made the following design:
“Today we study the common factor and the greatest common factor. What are your guesses about what you are learning today?”
Students have already learned the public multiple and the lowest common multiple. These two parts have similarities. The students began to let the students freely guess. The students will give birth to some ideas through the retrieval of existing knowledge. In view of it, satisfactory results have also been achieved. What is the common factor and the greatest common factor? How to find the common factor and the greatest common factor? Why is the largest common factor surface not the smallest common factor? These problems have been better generated in the collision of students' thinking and thinking. Undoubtedly such a design is close to the student's recent development zone, laying the foundation for the effectiveness of the classroom.
2. Provide an opportunity to place students in problem situations and create an atmosphere that encourages exploration and understanding.
“Do you have any guesses about what you are learning today?” The question is more inclusive. Different students can tell their own different guesses in the face of this problem. Students’ differences and personalities are better respected. Really reflects the thoughts facing the whole. Different students have their own opinions when thinking about this problem. They have generated the content of this lesson in mutual complementation and mutual inspiration, so that students can fully appreciate the charm of cooperation and build a harmonious classroom life. In this process, students deeply understand that mathematics knowledge is not so inscrutable, respectable and incomprehensible. Mathematics is not terrible. It actually breeds from the original knowledge and is rooted in life experience. Such teaching is undoubtedly conducive to cultivating students' self-confidence, and the cultivation of self-confidence is not the most meaningful and fundamental content of education?
Third, let students conduct independent thinking and independent exploration
Through the students’ guess, I sorted out the questions raised by the students:
What is the common factor and the greatest common factor?
How to find the common factor and the greatest common factor?
Why is the greatest common factor and not the smallest common factor?
What is the role of this part of knowledge?
Let me first let students think independently? Then organize communication and finally let students self-study textbooks
Such a design is challenging for students and gives full play to the subjectivity of students in the process of problem solving. In this process, students formed their own understanding and gradually improved their ideas in cooperation and communication with others. I think this is probably what the Standards advocates to provide students with the time and space to explore and communicate.

Part 3: Reflections on Mathematics Teaching in Elementary Schools_Combination and Prime Numbers

In the teaching of "combination and prime number", I jumped out of the shackles of the textbooks, embodying the new curriculum teaching philosophy of "people-oriented development", respecting students, trusting students, and dare to let the students learn by themselves. Throughout the teaching process, students can start from the actual state of the existing knowledge and experience, through the operation, discussion, induction, experienced the process of knowledge discovery and inquiry, and experience the joy of solving the problem or the feeling of failure.
First, students have a wide range of participation and a strong interest in learning.
The new curriculum teaching standards require us to “make students experience the process of forming and applying mathematics knowledge.” Therefore, in teaching, I pay attention to all students, so that students can learn in a pleasant atmosphere and arouse students' strong desire for knowledge. For example, let students use the learning tools to fight and use "2, 3, 4...12 small squares to spell several different rectangles to experience the difference between prime numbers and composite numbers, and to replace the teacher's explanation. It stimulated students' interest in learning and curiosity, so that all the students participated in the “activities”. The classroom atmosphere was pleasant and enthusiastic, and the students learned easily and learned firmly, which greatly improved the efficiency of classroom teaching.
Second, from the student's point of view, return the initiative of the classroom to the students.
Classroom teaching, students are the "protagonists", teachers are only "supporting roles", teaching should leave a lot of time and space to students, so that each student has the opportunity to learn, discuss, observe and think. In addition to giving students the opportunity to work together, I also let students classify several numbers. Although students may have different classification criteria, they can classify numbers with only two factors into one class and put together numbers with more than two factors. In this way, the teacher can guide the students to tell what is called prime number and what is called a combination number. Let the students summarize the numbers and prime numbers in their own language. In this process, guiding students to participate in the process of knowledge formation is conducive to cultivating and improving students' ability to acquire knowledge.
Third, ignite the spark of student wisdom, let the students really live.
Einstein said: "It is more important to ask a question than to solve a problem." I designed such a link after the class in this lesson. You also want to study what kind of knowledge about the prime number and the number. This learning task is not only a task for students to explore in the classroom, but also to leave a space for students to expand outside the classroom. Each student can explore their own mathematical space according to their own different levels, so that different students have different developments in mathematics.

Part 4: Reflections on Mathematics Teaching in Elementary Schools_Axisymmetric Graphics

Symmetry is a basic transformation of the basics. It is the necessary foundation for learning space and graphic knowledge. It can not be ignored to help students build space concepts and cultivate students' spatial imagination.
The first teaching of this book is axisymmetric graphics. The teaching materials are arranged in various forms of operation activities. In the teaching of this class, I designed three operation activities in combination with the characteristics of the teaching materials, allowing students to gradually experience axisymmetric graphics in hands-on operation. The basic characteristics.
First, create a situational teaching, please classmates who fold clothes to show off the method of folding clothes. This leads to the subject. Next, show the axisymmetric objects: Tiananmen, airplanes, trophies, and let students observe what they have in common? Students observed that they are the same on both sides. 2 Cut the small tree: Through the different evaluations of the teachers and students, the figures are the same on both sides, so fold the paper in half, then cut it, cut it and then expand it. This is the small tree.
This is the first operation of this lesson, arranged after the students observe the symmetry in life, the purpose is to let students initially sense the axisymmetric phenomenon in the operation. The student's operation activity seems to be a purposeless operation, but it is very difficult to find a small tree or even a beautiful window grille. It is very difficult to find the law. Through the communication of the students, it can be initially perceived that the same graphic on both sides can be folded up. Again, this is the initial perception of the axisymmetric graphic features.
Second, draw a picture, fold a fold, draw the objects seen by the students to get the following graphics to discuss the grouping operation, and draw the conclusion - after the graphics are symmetrical, the two sides completely coincide, and thus what kind of The graphic is an axisymmetric graphic.
This is the second operational activity of this lesson, arranged after the students have a preliminary perception of the features of the axisymmetric graphics. The student's operation is a purposeful and guided operation. The purpose is to explore the basic characteristics of the two sides of the crease after the folding of the figure in the process of the operation. On this basis, the concept of the axisymmetric figure is explained. .
Third, find ways to make a symmetrical pattern of each axis, and group their own works.
This is the three-time operation of this lesson, and after the students have a more correct system of understanding of the axisymmetric figure, it is intended to consolidate and deepen the understanding of the axisymmetric figure in the operation activities. The students' activities are diverse and the works are also rich and colorful.
The purpose of the three operational activities is different, and the results are also very different. In this activity, the students have deeper understanding of the axisymmetric graphic features through orderly and hierarchical operations, and the basic features of the fully conceptual axisymmetric graphics.
The biggest feeling of this lesson is that due to the pre-class preparation, all the exercises and operation activities are more natural in the series of visits, the classroom structure is compact, the students are interested, and the students can experience the axisymmetric figures in different ways and at different angles. Characteristics.

Chapter 5: Reflections on Mathematics Teaching in Elementary Schools_Median and Moderate

In this lesson, I mainly use the group cooperation learning method, through the heterogeneous group of two people, is also the most common cooperation method we usually use to achieve one-on-one mutual assistance and full participation in the common development. The relationship between teachers and students, the relationship between students and students has become a rich and unified "learning community" of mutual learning and learning. At the same time, this kind of cooperation means that every student has the opportunity to express and make different people get different Development, so that students who do not like to speak have a certain amount of performance space, the difference will not be regarded as a headache in education, but as a kind of wealth and heritage of education. In this process, I extend my hand when they need help, and give them rational and fair judgments when they are arguing, helping them to construct the knowledge structure over and over again, maximizing the potential of students and demonstrating their talents. At the same time, I attach importance to the evaluation of students' ability to find problems and solve problems, pay attention to the self-evaluation and mutual evaluation in the process of group report and exchange, free defense, and give the initiative to the students, which will make the students truly become evaluation. The main body.
For example, after knowing the median and the majority, students are required to cooperate with each other. This cooperation, which sets a set of data to find the median and the majority, can better reflect the effectiveness of the group cooperation. Originally, the teacher had two questions. Why should I let the students do the questions here? On the one hand, in the cooperation, the students can be tested for the degree of understanding and mastery of the knowledge. In the activity, one person makes another judgment, and can explain the reason reasonably. The small problem is solved before the large group report, which stimulates the students to speak out. The problem and the desire to solve the problem. On the other hand, we can make full use of the students' resources to give full play to the students' huge potential and trigger the presentation of special situations. The group can not solve the problem and feedback to the large group, which can make students pay great attention and help solve special problems. In the case that the students can't say it, I also made advance preparations, which is a complement between teachers and students, so that the teacher's timely appointment, and the students' independent inquiry will be played in the group cooperative learning.
In addition, the content of "Median and Modes" is not in the traditional textbooks. It was not originally the content of the textbooks. It is not only for me, but also for all the mathematics teachers of the country. It is new. of. In order to be able to control the teaching materials, I repeatedly read the textbooks and teachers' teaching books, comprehend the teaching materials, and read a lot of materials, and strive to ponder thoroughly, but unfortunately, their understanding and grasp of the teaching materials is still not in place, so this class There are many shortcomings in teaching. For example, in the classroom teaching, there are some valuable problems in the report of the students that I did not expect. Due to lack of experience and failure to respond in time, I missed the wonderful experience of not making an appointment.
In short, “Classroom should be a journey into the unknown. At any time, it is possible to discover unexpected passages and beautiful scenes, rather than everything that must follow a fixed and unrelenting journey.” This is what I saw in a magazine. In a word, as the end of my case, I hope to bring further thinking to myself, so that I can better capture the "accidents" in the classroom, make it a bright spot, and create wonderful things for my math class. .