Reflections on Tree Planting Teaching 1 Tree Planting is the material of "Mathematics Wide Angle" in the second volume of the fourth grade experimental textbook of the new curriculum standard of People's Education Press, which is derived from many classic lessons before. Therefore, in the preparation stage of teaching, I have carefully studied many lesson examples, and found that many lesson examples have such a * * * feature: all teachers pay attention to distinguish three different types of "planting trees", namely, planting two heads, planting only one head and not planting two heads. The teaching mode of "students' independent inquiry (or group inquiry), feedback exchange and teacher's summary" is widely adopted. The distinction between "three situations" and the corresponding calculation rules ("plus one", "no increase, no decrease" and "minus one") are regarded as a kind of "law", which needs students to grasp firmly so that they can apply it directly without thinking when dealing with new similar problems. At the same time, in the reflection of these lessons, I found another feature of * * *. Many students can find the rules but can't skillfully use them, and can't relate the solution to the problem of planting trees with similar phenomena in life.
Through in-depth interpretation of teaching materials and various related teaching materials, I think the problem of "planting trees" can be divided into two different teaching objectives in teaching:
First, clearly introduce the relationship between the number of intervals and the number of trees, highlight the idea of "one-to-one correspondence", and analyze three different situations of planting trees on this basis, namely, "planting at both ends", "planting at only one end" and "planting at both ends", so that students can truly understand the relationship between the number of trees and the number of intervals.
2. Summarize the relevant calculation formula "total length ÷ spacing = number of intervals", and help students better master this problem-solving mode through the formula.
Reflecting on the whole teaching process, I think this course has been handled well in the following aspects:
1, the main line of this lesson is very clear, which is to extract the phenomenon of tree planting from life, and then establish a mathematical model through guessing and verification, and then apply this mathematical model to real life.
2. I pay attention to the overall processing of teaching materials and integrate and reconstruct them. Design examples are an open topic. The open design makes the classroom a dynamic and free space, which stimulates students' thinking, makes students explore attentively, and makes students fully experience the practical activities of "planting trees". It is systematically recognized that there are three situations of planting trees in a straight line, namely, planting trees at two ends; Do not plant at both ends; Only plant one head.
3. The thinking of planting trees has the necessary complexity, which is even more difficult for the fourth-grade students who are new to planting trees. So, I asked the students to use a formula to represent the number of trees planted according to the schematic diagram. In the process of column calculation, students initially perceive three situations through intuitive observation: planting "tree = interval number+1" at both ends, planting "tree = interval number" at only one end, and not planting "tree = interval number-1" at both ends. Then, guide the students to use the idea of "one-to-one correspondence" and raise their right hands to analyze three different situations of planting trees, that is, "planting at both ends", "planting at only one end" and "planting at both ends", so as to truly understand the relationship between the number of trees and the number of intervals in these three situations.
4. After the students have continuously calculated the number of trees in three planting methods, I guide the students to think: In these three cases, when we calculate the number of trees in succession, the first step is what we want first and how to get it. Through students' group discussion, we can get the number of requirement trees. First, we should calculate the number of intervals, and clearly summarize the relevant calculation formula "total length ÷ interval = interval", which can help students better master this problem-solving model.
5, pay attention to reflect the close relationship between mathematics and human life. After the consolidation exercise, I let the children know the phenomenon similar to the problem of planting trees in the form of pictures, so that students can further understand that many different events in real life contain the same quantitative relationship as the problem of planting trees, which can be solved by planting trees, and realize the important benefits of mathematical modeling.
I feel that the shortcomings of this class are as follows:
1, the thinking method of mathematics is the soul of mathematics. One of the purposes of arranging "planting trees" in this book is to infiltrate students with the idea of starting with simple problems. This lesson does not let students experience the problem-solving process of "simplifying complex problems"
2. After a class, I feel that I still firmly support the students, and I haven't completely put them down, so there are still many shortcomings in the class. Looking forward to future adjustments and improvements.
3. The problems generated in the classroom are not flexible enough to be used well.
In the future teaching, I hope that through my own accumulation and improvement, I can improve my professional level and standardize the potential of classroom generation, and I can see a better myself in the near future.
Reflection on the Teaching of Tree Planting 2 In this course, I not only pay attention to the cultivation of students' practical potential, but also make students feel that mathematics comes from life and is also applied to life. For example, the relationship between the number of trees and the interval is abstracted from the relationship between the number of people waiting in line and the interval, which is both funny and close to students' life.
When writing textbooks, we always give the length of the way out and find the number of intervals or trees, but in practice, many questions give the number of intervals and trees and find the length of the way out. While avoiding the problem of last class, I also ask students questions about the problem of last class, so that students can evaluate each other or teachers and students can evaluate each other, focusing on praising most students who learn well, giving each student the opportunity to participate, cultivating students' sense of success in exploring spiritual experience, enhancing students' self-confidence and sense of honor, and making them love mathematics more. The main goal of this lesson is to instill in students the idea of starting with simple questions. Make students have more opportunities to learn and understand mathematics from the surrounding things, realize that mathematics is around and experience the charm of mathematics. Therefore, in designing this class, my main teaching philosophy is: taking the problem situation as the carrier, taking the cognitive conflict as the inducement, and taking the form of mathematical activities, let students experience the whole process of mathematization of life, and learn the thinking method of solving problems from it. On this basis, according to students' cognitive rules, I designed the following links:
First, through pre-class activities, with planting trees in spring as the material, let students understand the relationship between interval and planting trees.
Second, take a tree planting as a carrier to create a climax that breaks through the key and difficult points of the whole class teaching.
Third, take the application of tree planting in life as the research object, and guide students to understand the essence of tree planting.
Fourth, consolidate multi-angle application exercises and expand students' understanding of tree planting.
Reflecting on the whole teaching process, I find it a little difficult for students to solve the problem of planting trees in real life simply by laws, so I pay more attention to laws, methods and students' experience of acquiring knowledge in class.
Experience is the process that students transfer from old knowledge to implicit new knowledge. In teaching, I created situations, brought many opportunities for students to experience, created a democratic, relaxed and harmonious learning atmosphere for students, and gave them sufficient time and space. If life experience is the basis of learning and cooperation and communication between students is the driving force of learning, then helping students understand with graphics is a crutch for students to construct knowledge. With this crutch, students can walk more steadily and better. Therefore, in the teaching process, I pay attention to the infiltration of the consciousness of combining numbers with shapes. Direct examples can guide students to draw pictures that simulate actual tree planting. Through the demonstration of line graph, let students fully understand the relationship between "interval number" and "planting trees", so as to infiltrate the idea of simplifying the complex into students, and let students choose the short-distance road drawing method independently to get the result. In this way, the initiative of learning is given to students, the potential of students is developed, and the practical potential and innovative consciousness of students are cultivated.
However, I feel that in the teaching activities of this course, the communication between teachers and students needs to be further strengthened, and sometimes students' learning foundation and understanding potential are overestimated, leading to high status. In the future teaching, we should have a comprehensive and in-depth understanding of students and make full preparations for more aspects.
Thoughts on Tree Planting Teaching 3 "Tree Planting Problem" is the material in the second volume of the fourth grade experimental textbook of the new curriculum standard. The purpose of arranging "planting trees" in this lesson is to infiltrate students with the idea of starting with simple problems for complex problems.
The textbook divides the problem of planting trees into several levels: planting at both ends, not planting at both ends, environmental situation and phalanx problem. The main point is: in the process of solving the problem of planting trees, students are infiltrated with a very important mathematical thinking method in mathematics learning and research, and at the same time, students are aware of the convenience brought by applying mathematical models to solve problems. The teaching of this course is not only to make students skillfully solve practical problems similar to planting trees, but also to infiltrate mathematical thinking methods with solving the problem of planting trees as the learning fulcrum. Develop students' thinking with the help of teaching materials and improve their necessary thinking potential.
I teach two kinds of trees in this class. The main goal of this course is to infiltrate students with the idea of starting with simple and complex problems, so that students have more opportunities to learn and understand mathematics from the surrounding things, realize that mathematics is around them and experience the charm of mathematics. I only came into contact with primary school mathematics teaching for one year more than ten years ago. Now I am taking part in the competition class, and I feel good about myself. I think the whole teaching process is successful.
First of all, the design is smooth and easy to understand.
The design of the whole class is based on the actual situation of the students in our class. Create a situation before class to let students know what they want to learn, and then discuss the problem of planting trees with examples. No spacing is specified, the data is changed to a small size and the length is changed to 20 meters. The purpose is to make students highlight the starting point of knowledge in an open situation, so that students can understand the reasons for exceeding 1 and less than 1 with one-on-one thinking method, establish a profound overall appearance, and refine the methods to solve the problem of tree planting. Changing small data there is conducive to students' thinking, mainly to take care of the last 20% of students. Then use an example, let students use their brains and hands to verify it repeatedly, and finally sum it up: the number of segments+1= the number of trees. The design of this lesson is based on the cognitive law: through the perception interval of examples, taking examples as the carrier, breaking through the key and difficult points of teaching, taking the application of tree planting in life as the discussion object, and understanding the essence of tree planting through multi-angle application, expanding the understanding of tree planting. The whole class is clear in thinking, rigorous in structure, easy to understand, and always makes difficult breakthroughs around key materials.
Secondly, pay attention to practical experience exploration.
In teaching, I create situations, give students many opportunities to experience, and pay attention to helping students understand and construct knowledge with the help of graphics. In the process of teaching, I have always been permeated with the consciousness of combining numbers with shapes. In teaching, I first encourage students to make their own designs and try to design tree planting schemes. In the process of students' independent exploration, many students use the method of drawing line segments, and reproduce the line segments with multimedia in communication, so that students can see that a line segment is divided into four segments on average, plus two endpoints, and a * * * has five points, that is, five trees are to be planted. Let students find that the problem of preparing saplings when planting trees can not be solved by simple division. After changing the spacing, the number of line segments and trees also changes accordingly, and then ask: "What rules can be found?" Inspire students to discover the law through phenomena, that is, the number of trees is more than the number of sections (intervals) 1. Finally, according to the requirements of the textbook, the problems of planting trees designed by ourselves are solved by applying the discovered rules: the spacing is 2m, 4m, 1 0m, and the number of trees planted is more than the number of segments (spacing)1. This shows the whole process of analyzing, thinking and solving problems, so that students can experience this process and learn some methods and strategies to solve problems.
Third, contact life and expand thinking.
Beneficial learning is that students experience self-construction in specific situations, and experience and construction are the key to students' learning. Experience is the foundation of construction. Without experience, construction is not good. Experience is a process in which students transfer from old knowledge to implied new knowledge. In the design, although the scene was created, the experience could not reach the level of continuing to construct learning. So in this class, I gave students many opportunities to experience and created a situation that can inspire students to sing. From the familiar things around us, such as ourselves, classrooms, exercises, architecture, etc. , stimulate interest in learning, stimulate the desire to explore.
Although this class is practical, there are still problems.
1. In order to solve the problem that students can find a simple law of "number of trees = number of intervals+1", they can't use this law to find the path length, because the cognitive starting point of students is different from the logical starting point of knowledge structure. It is believed that students can solve the problem as long as they find "the number of trees = the number of intervals+1". In fact, this only shows that some students have the potential to continue their studies, which leads them to find the rules but not to apply them. In other words, there is a missing link between the discovery of law and the application of law. I want to strengthen the teaching of law communication. For example, when drawing rules, I can talk about knowledge diffusion such as "interval number = tree number-1, road length = interval number x interval length".
Second, grasp every detail, solve the problem immediately, and think from the perspective of students.
For example, students' questions, the difference between interval length and interval number, and the difference between two ends and two sides should be considered. Students' knowledge cognition is generally constructed independently through the activity experience in a specific situation. Without experience, architecture will be very abstract. In this teaching design, although I created the situation, it is impossible for students to continue to construct the learning theme with only one experience. I can use line diagrams or examples to help students learn. Let students have the tools they can rely on, and combine the written information with the learning foundation with the combination of numbers and shapes, so that learning can continue, students' thinking development can rely on it, and the thinking method of mathematics learning can really penetrate.
Reflections on Tree Planting Teaching The purpose of this course is to let students discover mathematical laws, establish mathematical models of tree planting problems and understand the relationship between "number of trees" and "number of intervals", so as to cultivate students' awareness of mathematical application, cultivate their spirit of active inquiry and cooperative learning, and finally master the solutions to problems related to tree planting.
Generally speaking, the students in this class have a wide range of participation, their enthusiasm and initiative are fully exerted, and the classroom efficiency is also high, which better reflects the advantages of hands-on operation and cooperative learning, mainly reflected in the following points:
First, hands-on, cooperation and exchanges, and explore the law:
In this class, students use the learning tools in their hands to design different tree planting schemes in groups, which is helpful for students to give full play to the advantages of group communication and cooperation, make students think clearly in mutual expression and listening, promote the formation of knowledge structure, improve their thinking level and improve their cognitive structure.
Second, the design of the exercise is unique, novel and gradual:
I pay attention to both the teaching process and the teaching effect in this course. In the practice session, I designed a gradient exercise, which reflected the teaching in different times. At the same time, I also guide students to use what they have learned to solve some common problems related to tree planting in life from different angles, so as to effectively realize the purpose of mathematization of life problems and life-oriented mathematics problems.
Because the answers to the exercises are in the form of competitions, the enthusiasm of students is fully mobilized, the classroom teaching effect is optimized, and the classroom teaching efficiency is greatly improved.
Third, fully reflect the main role of students and the leading role of teachers;
In this class, I fully reflected the students' main role by guiding students to operate, exchange and discuss, draw conclusions and apply conclusions, and the teacher only gave timely guidance.
Reflection on Tree Planting Teaching 5. In the teaching of this class, I arranged hands-on operation when exploring the law of planting at both ends according to the characteristics of teaching materials and the actual situation of students, hoping to deepen students' understanding and understanding of the relationship between the number of trees and the number of intervals in various forms of teaching activities by guiding students to participate attentively.
The activity design is like this: Show an open topic: A road is () meters long, plant a tree every 5 meters (both ends should be planted), how many trees do you need? Let the students decide the length of the road by themselves, so as to explore the relationship between the number of intervals and the number of trees when planting at both ends. The requirements are as follows: Design: the total length is () meters, with () intervals every 5 meters. Plant () trees, let students think independently, draw line segments, fill in forms and report. I thought that the teaching plan I designed considered the students' life experience, combined with the actual life, and attached importance to the cultivation of mathematical thinking. The infiltration of methods is feasible and students should be able to master it.
However, in the actual teaching process, students who are still eager to "plant trees" are like defeated cocks when "exploring the law", and have no fighting spirit and response. Usually, the students who get excellent grades are always those who don't want to participate. It seems that this design can't take into account the development of all students. Without students' subjective participation, how to cultivate thinking and construct themes? I began to reflect: Why can't students find simple tree planting rules? Why lack of participation? The students looked blank. After repeated thinking, I think there are some necessary problems in the inquiry activities I designed, which are too abstract and difficult for students. When you set your own length, you should think that the average score should be divided and only give students a line segment. They don't know where to start. I consulted an experienced teacher, pondered and adjusted my teaching process repeatedly, and made the main line of this lesson clearer from a simple idea, that is, extracting the phenomenon of planting trees from life, refining it, then establishing a mathematical model through guessing and verification, and then applying this mathematical model to real life.
At the same time, we can flexibly construct the knowledge system and pay attention to the overall processing of teaching materials. Be able to use teaching materials flexibly, integrate and reconstruct teaching materials, and let resources inspire exploration. Stimulate students' desire to explore. The example of design is an open topic, which is realistic, beneficial and challenging for students. The open design makes the classroom a dynamic space of its own, thus stimulating students' thinking, making them explore attentively and making students fully experience the practical activity of "planting trees". Let the students systematically establish three situations of planting trees, that is, planting at both ends; Do not plant at both ends; The problem of planting trees under closed conditions (one kind is planted and the other is not planted).
The characteristics of this class:
First, through independent exploration activities, students can gain successful learning experience and enhance their confidence in learning mathematics well.
This course is designed from this point of view. A model with a fixed total length of 30 meters and trees is designed for students to "plant trees", which can fully mobilize students' hands, brains, mouths and other senses to participate in mathematics learning activities and improve the effectiveness of students' participation in learning to a greater extent. It is very simple for students to find the rules in the group simulation of tree planting activities. This kind of activity is not only a rare platform to fully show students' individual thinking and understand their original life experience, but also a model of planting trees in the activity, which lays an intuitive foundation for students in their next study.
Second, infiltrate the mathematical thinking method of "seeing the big from the small" to cultivate students' mathematical thinking potential and problem-solving potential.
"It is better to teach people to fish than to teach them to fish", and the new curriculum concept has a more remarkable feature of "keeping pace with the times", which is the concern about infiltrating mathematical thinking methods. In the teaching process of this course, we should make full use of the difficulties that students encounter when they want to test large numbers. We can guide them to find laws to verify by "seeing the big from the small", so that students can observe, guess, experiment, reason and communicate. So as to lose no time in infiltrating common mathematical thinking methods into students, and accumulate richer and more practical ideological experience for future follow-up study.
The teaching process is like this: after students master the inquiry method of the law of two-headed planting, let them find the law of two-headed planting in groups. By drawing their own pictures and arranging their own forms, students will soon find the laws contained in them, thus generating a strong sense of success and self-confidence, which greatly mobilized students' intentions.
Third, pay attention to the expansion and application of tree planting problem model, and pay attention to the close relationship between mathematics and human life.
The model of planting trees originates from reality and is higher than life. Therefore, it has a wide range of application values in reality. In order to make students understand the benefits of this modeling, we have strengthened the practice of model application function. After the students independently discovered the first two laws of tree planting, I timely asked whether there was anything similar to tree planting in our life. Through students' examples, let them further understand that many different events in real life contain the same quantitative relationship as the problem of planting trees, and all of them can be solved by planting trees, and realize the important benefits of mathematical modeling. I didn't stop there, but let students look for similar phenomena in their lives, such as planting telephone poles, arranging seats, installing street lamps, inserting colorful flags and so on. After students abstract mathematical phenomena from concrete life, once again, let students solve different life problems with laws, let mathematical knowledge be applied to life, and let students deeply understand the value and charm of mathematics. In the whole class, most students are active in thinking.
4. Infiltrate the idea of combining numbers and shapes to cultivate students' consciousness of solving problems with graphics.
The combination of numbers and shapes is a common way of thinking to solve mathematical problems. The combination of numbers and shapes can make some abstract mathematical problems intuitive and vivid, change abstract thinking into image thinking, and help to grasp the essence of mathematical problems. Based on this idea, when I reached a teaching goal of this course: to understand the law between the number of intervals and the number of trees, I adopted the method of combining numbers and shapes-drawing to solve problems, thus gradually improving the potential of students to solve problems. After showing the example, we arranged such a practical activity: grouping to make way for the small tree model on a segment to simulate tree planting. While increasing students' interest in learning, due to the combination of numbers and shapes, the relationship between trees and spaces in tree planting is also easy to understand.
The shortcomings of this lesson:
1, that is, I overestimated the students. I thought it would be no big problem to solve the problem of planting trees as long as the students understood the relationship between the number of trees and the number of intervals, but the fact was beyond my expectation, because some students understood that the total length and interval did not require the number of intervals. I thought this was something that students had learned and often used, so I didn't review my personality, which made students with poor foundation unable to start.
2. In terms of time allocation, I relaxed first and then tightened, and spent a little time in finding the rules and simple application, so that the later exercises were hasty.
3. In the teaching process, because of the fear of endless lectures, when students "answer irrelevant questions", they are impatient and can't calm down and listen carefully to the students' speeches; Teaching is an art of regret. Although this course has left many regrets, it is my own product and a bold attempt of new teaching methods. And in the process of preparing lessons, I learned a lot and gained a lot. In order to make every class less regrettable, I will continue to work hard. I wish I could go further on this road.