Heterogeneity in the same class is a new teaching and research method, which gives full play to our teachers' innovative ability, makes classroom teaching unique, has different teaching ideas and different teaching methods, and makes our audience really feel the charm of mathematics teaching art. I hope you will like the model essay on cone volume I brought below.
The volume of the cone is a part of the field of "space and graphics" in the mathematics curriculum standard. The main task of this lesson is to explore the calculation formula of cone volume. Students learn on the basis of mastering the characteristics of cone and the volume formula of cylinder.
Students have mastered the following knowledge and skills: mastered the meaning and calculation method of surface area and volume of cuboid and cube, mastered the calculation method of surface area and volume of cylinder, and understood the characteristics of cylinder and cone. Initially experienced the exploration process of "analogy conjecture-verification explanation". Be able to work in groups and finish some simple practical activities. In teaching, we should not only let students know why, but also let them know why, that is, dig deep into the internal relationship between knowledge.
The success of this lesson lies in:
1, can review the teaching content of this lesson purposefully and pertinently, and pave the way for the calculation of cone volume later. For example, this lesson uses courseware to show the figure of cylinder. Q: What is this number? How to find the volume of a cylinder? The student answers: the volume of a cylinder = the area of the bottom × the height (V = SH). The teacher skillfully shows the cone with the same height as the cylinder (both the bottom and the height appear). Q: What is this number? Import: The volume of the cylinder will be found. Shall we learn the volume of a cone today? Do a good job of paving the cylinder and cone with equal bottom and equal height.
2. In the teaching process, teachers pay attention to let students observe, calculate, guess, estimate, verify, discuss, induce and other mathematical activities in specific situations, and explore and master the volume formula of the cone. In this process, teachers pay attention to guiding students. And some simple practical problems can be solved by using the volume formula of cone.
Through demonstration, observation and verification, the volume relationship between cylinder and cone is compared first. Comparing a cylinder with a cone, whose volume is larger and whose volume is smaller? what do you think? Their bottoms are equal, their heights are equal, and the top of the cone is pointed, so the volume is small and the volume of the cylinder is large. So, is the bottom area × height the volume of a cone? Imagine and guess: What are the characteristics of this cylinder and cone? Observation: the area of a triangle is half that of a rectangle. Question: So what is the volume of a cone that might be a cylinder? 1/2 or 1/3. Finally, through the experimental verification, through the process of studying the problem, it is concluded that the volume of cylinder and cone is V = 1/3SH under the condition of equal bottom and equal height. Teachers also instruct students to do experiments in groups. It is not the relationship between a cylinder and a cone with equal bottom and equal height, which further proves that the cylinder and the cone are equal bottom and equal height, and the volume of the cylinder is three times that of the cone with equal bottom and equal height, or the volume of the cone is 1/3 of that of the cylinder with equal bottom and equal height. Blackboard: V= 1/3Sh.
3. By observing the changes of students' expressions, answering questions, practicing, testing and giving feedback on the accuracy of hands-on operation, we can know whether students have a solid grasp of new knowledge and skills. We can see from them that the teaching task is better.
Teaching suggestions:
When students are allowed to use teaching AIDS for verification, as long as they are given more time, especially cooperation time, they can not only explore the volume relationship between cylinders and cones with equal bottom and equal height, but also deduce their own formulas according to their own knowledge and experience. In this link, the degree of teachers' letting go is not enough.
Today, in the teaching and research class of our school, we listened to Professor Guo Xiaoqing's lesson "The volume of a cone".
The content of this lesson is mathematics in the sixth grade of primary school. In the classroom, the clear design of teacher Liu's teaching links, coupled with the teachers' neat language, has brought good results to the teaching and added a little luster to the classroom. Success:
1. In teaching, teachers pay attention to let students experience mathematical activities such as operation, conjecture, estimation, verification, discussion and induction in specific situations, and explore and master the volume formula of cones.
2. We can use the volume formula of the cone to solve some simple practical problems and cultivate the ability of preliminary analysis, synthesis, comparison, abstraction and simple judgment and reasoning.
3. In the process of combining guessing, experiment and verification, students can further realize the value of "transforming" thinking methods, enhance their confidence in learning mathematics and develop the concept of space.
4. The tutorial plan is used properly. Teaching suggestions:
After listening to the lesson "The Volume of a Cone" by Mr. Guo Xiaoqing, the third volume of grade six gained a lot. As a young teacher, it is not easy to take part in this teaching activity bravely and make careful preparations, and it is even more difficult to complete the teaching task naturally and smoothly. Next, I want to focus on two successes of this class, hoping to discuss them with you.
First, build a reasonable platform for learning new knowledge. It is mainly reflected in Mr. Liu Can's use of the original knowledge to promote the study of new knowledge, and the design of prize-winning questions and answers and experiments, so that students can boldly learn from the previous methods of learning the cylindrical volume formula and explore the conical volume formula. By using the migration law, students can be inspired by the ideas and methods of calculating the volume of a cylinder, understand the methods of calculating the volume of a cone, and integrate old and new knowledge. This learning method of reference not only makes the teaching of this course easier, but also helps students to understand and master this learning strategy more deeply, which is conducive to students' further study and lifelong development.
Second, pay attention to cultivating students' practical ability. The focus of this lesson is to explore the origin of cone volume formula through experiments. Taking the experimental purpose as the main line, let students cooperate in groups, participate in activities with hands-on, eye observation, brain thinking and various senses, and explore the origin of the formula of cone volume from intuition to abstraction, so as to understand and master the formula of cone volume, cultivate students' observation ability, calculation ability and preliminary space concept, and overcome the emphasis on conclusions and preliminary space concept in the teaching of geometric formula calculation. This kind of learning, students learn vividly and remember firmly, which not only plays the leading role of teachers, but also embodies the students' dominant position. In the process of learning, students are explorers, researchers, collaborators and discoverers, and have gained rich learning experience.
However, there are some shortcomings in this course, such as improper connection between teaching links and time allocation, insufficient diversification of teaching methods and lack of reform and innovation. For example, in the new teaching class, as in the traditional teaching, the teaching AIDS of cylindrical containers and conical containers are directly taken out, so that students can carry out the sand dumping experiment according to the experimental requirements and purposes. I think before the experiment, we must create good problem scenes for students, such as (what do you think the size of the cone is related to? What do you think is the closest relationship between the volume of the cone and the volume of the figure? What does it matter to guess their volume? Do you want to know their relationship? ) through the communication between teachers and students, questions and answers, guessing and other forms, strengthen the awareness of questions, stimulate students' thinking, and make students have a strong thirst for knowledge. At this time, students are eager to prove their guesses through experiments, so they are interested in doing experiments. In this way, students' thinking is activated, their learning enthusiasm is improved, their interest becomes stronger, the classroom atmosphere becomes warm, and the teaching efficiency and teaching effect can be imagined.
Of course, I believe that through this exercise, Mr. Guo will be more and more broad in the future teaching road.
After listening to the lesson "The Volume of a Cone" by Mr. Guo, the fourth edition of the sixth grade, people feel that the concept of the new curriculum standard has been internalized into Mr. Guo's teaching behavior. The main highlights of this lesson are as follows:
(1) Attach importance to students' operational activities. Through hands-on activities, students can feel the formation process of knowledge and promote the effective improvement of students' thinking and the development of practical ability. In this way, students can not only truly understand and master knowledge, but also feel the joy of success and enhance their self-confidence in learning.
(2) All students actively participate, highlighting the main role of students. Teacher Guo boldly lets students explore independently in teaching. Under the guidance of the teacher, students actively discover the relationship between a cylinder with equal bottom and equal height and the volume of a cone through mathematical activities such as observation, experiment, guess, verification, reasoning and communication, and then derive the formula for calculating the volume of the cone. In particular, mathematical communication is fully reflected, including communication between students and teachers, communication between students and multi-directional communication between groups or large groups. Teacher Guo pays attention to creating a classroom atmosphere for students to debate and defend. In the process of students' argument, teachers participate equally as observers, making the classroom an arena for debate. This kind of teaching has really played a democratic role, making students feel that they are the masters of the classroom and truly become the masters of learning. In this class, every student has experienced the process of autonomous inquiry learning. Students get not only fresh mathematics knowledge, but also scientific inquiry learning methods and problem-solving methods. If they learn knowledge in such inquiry for a long time, they will become thoughtful, think, study and learn.
Insufficient:
The connection of teaching links and the allocation of time are somewhat inappropriate, the teaching methods are not diversified enough, and there is a lack of reform and innovation. For example, in the new teaching class, as in the traditional teaching, the teaching AIDS of cylindrical containers and conical containers are directly taken out, so that students can carry out the sand dumping experiment according to the experimental requirements and purposes. I think before the experiment, we must create good problem scenes for students, such as (what do you think the size of the cone is related to? What do you think is the closest relationship between the volume of the cone and the volume of the figure? What does it matter to guess their volume? Do you want to know their relationship? ) through the communication between teachers and students, questions and answers, guessing and other forms, strengthen the awareness of questions, stimulate students' thinking, and make students have a strong thirst for knowledge. At this time, students are eager to prove their guesses through experiments, so they are interested in doing experiments. In this way, students' thinking is activated, their learning enthusiasm is improved, their interest becomes stronger, the classroom atmosphere becomes warm, and the teaching efficiency and teaching effect can be imagined.
Today, I listened to the teacher's lesson about the volume of a mathematical cone and was deeply moved by the teacher's exquisite teaching art and profound teaching experience.
There are many things worth learning in this course:
1, the introduction of creative scenes can greatly stimulate students' desire to learn.
The scene comes from life, not only related to the activities of students building houses, but also related to the children of two teachers. The students are full of interest. Among them, mathematics problems are closely related to the teaching objectives of this lesson. Play a good import effect.
2. Learning guidance is detailed, which is suitable for students to carry out activities freely, and is truly reflected in the teaching concept of doing middle school mathematics.
The teacher prepared learning tools for each group, and the students were all impressed.
3. The presentation stage still reflects the students' dominant position.
After the homework, students report and clearly explain the experimental process and findings. In this link, students can also arouse deeper thinking, question and supplement the teacher's blackboard writing, and fully reflect the democratization of the teacher-student relationship in teaching.
For example, the derivation of the premise of equal base and equal height. Then the teacher naturally asked the students to observe the relationship between cylinder and cone and compare their bottom area and height. In this link, students have a deeper understanding of the conditions of equal bottom and equal height.
4. After summarizing the formula of experiments and small exercises, the arrangement is reasonable.
At the end of the experiment, after the students found the volume relationship between a cylinder with equal bottom and equal height and a cone, the teacher designed a small exercise to fill in the blanks with pictures, and calculated the volume of the cone according to the volume of the cylinder. This unique design is convenient for more students to summarize the calculation formula of cone volume.
5. The practice forms are diverse, emphasizing the guidance of algorithm diversity.
The arrangement of exercises is from easy to difficult. Independent column calculation first, I will evaluate the reasoning, and then non-calculation in the row. Pay attention to listening to different methods in the process of column, and broaden students' thinking. Later, exercises such as fill-in-the-blank judgment appeared, which were more comprehensive. In addition, the exercises randomly compiled by the teacher link the division of knowledge scores, so as to achieve mastery, so that students can better master the knowledge in this section. Promotion exercises provide a good resource for students to understand the value of mathematics knowledge in life with real life.
Suggestion: Create more independent exercises to give students with learning difficulties a space to think, and also facilitate teachers to examine students' mastery in class.
The evaluation draft of the sixth grade paper of Mathematics Cone Teacher Gao had a wonderful math class, which made me appreciate the elegance of Teacher Gao and my friends in Class 6 (2) and benefited me a lot.
Highlights of this lesson:
1. This lesson introduces the object (vertical hammer), so that students can initially perceive its volume and measure it with a cup; Then, it conflicts with the fact that we can't measure the volume of conical roof in life with cups, and introduces the exploration of conical volume to expose students' thinking.
2. The derivation of the cone volume formula makes students deeply understand: every time water is poured in the experiment, students can experience the relationship between the cone and the cylinder volume with equal bottom, and gradually perceive the multiple relationship between them. This is the biggest highlight of this class.
……
At the same time, there are some regrets:
The data in the example of 1. is not ideal, which is not convenient for calculation; The calculation method is relatively simple; Calculation skills lack guidance. For example, ×3 1 can be divided by the data in the question before calculation, which can facilitate calculation and improve accuracy.
2. The practice level needs to be adjusted.
Grade 6 Mathematical Cone 7 Volume II Review Draft 1, delve into the teaching materials and use them creatively.
On the basis of fully understanding the students, grasping the curriculum standards, teaching objectives and the intention of compiling teaching materials, Teacher Fan purposefully adapted and processed the teaching materials according to the students' living and learning reality. For example, in pencil sharpening activities, students experience the connection between cylinder and cone in the process of pencil sharpening; Another example is the design of hands-on experiments, so that students can understand and master new knowledge in observation, comparison, hands-on operation and cooperation and exchange. Creative integration of some life materials has strengthened the close relationship between mathematics and life.
2. In teaching, teachers pay attention to let students experience mathematical activities such as operation, conjecture, estimation, verification, discussion and induction in specific situations, and explore and master the volume formula of the cone.
3. On the breakthrough of the difficulty, through guessing, questions are raised, and experiments are carried out with questions. Through the cooperation of students in groups, the empty cone is filled with water and poured into a cylinder with equal bottom and equal height, and it is concluded that the volume of the cone is equal to one third of that of a cylinder with equal bottom and equal height.
It not only serves as a bridge and inspiration for deriving the volume formula of the cone, but also helps to develop students' spatial concept, cultivate students' observation ability, thinking ability and hands-on operation ability, and provide rich perceptual materials for further study, thus gradually transitioning from concrete operation to internal language.
Mathematics curriculum should pay attention to students' life experience and existing knowledge experience. When teachers introduce new knowledge, they create interesting fairy tale situations, which turn boring math problems into living reality and make math classes full of vitality. Create a certain situation, let students dare to guess, want to guess, enjoy guessing, exchange ideas in guessing, and naturally put forward a challenging math problem, thus arousing students' strong desire for further exploration.
After the lesson of the eighth volume of the sixth grade mathematical cone, I reflected on the teaching of the whole class. Generally speaking, ups and downs are ok. Through students' bold speculation about what shape the volume of a cone may be related to, scientific verification is introduced. However, in the process of pouring water twice, students found the relationship between a cylinder with equal bottom and equal height and the volume of the cone, and thus obtained the volume formula of the cone V = sh÷ 3. In the whole teaching process, at the same time, guide students to treat this experiment with a scientific attitude and verify their guesses. The whole process pays attention to seeking truth from facts and carefully analyzes our own experimental conclusions, thus cultivating students' scientific experimental view. I didn't design the link that "the volume of cones is cylindrical 1/3, and their bases and heights must be equal" in teaching. It is randomly produced in class, but it increases the knowledge of students. Through students' examples, students can find that when the bottom area and height of a cylinder and a cone are equal, the volume of a cone is also one-third of that of a cylinder, so this sentence is wrong. In a word, every student in this class has experienced the link of "guess-experiment-discovery", which not only makes students gain new knowledge, but also makes them feel the pleasure of exploring success.
However, according to the homework after class, students basically understand the volume of the cone, but they often forget to divide it by 3 when calculating. Some students with learning difficulties still can't master the topics that need flexible judgment, which shows that their understanding of the volume formula is still at a relatively simple and low level, and the formula can't be used flexibly.
In this lesson, it is not only troublesome to measure the volume of a cone (such as a plumb hammer) by drainage method, but sometimes it can't be used (such as measuring the volume of wheat piles). I realized that this method has some limitations, so I introduced a new lesson. From the similarity on the surface, we know that the volume of the cone may be related to the volume of the cylinder, and then through bold speculation, experimental verification and analysis of the experimental results, the volume formula is obtained. Then consolidate the formula with appropriate exercises to achieve the teaching purpose of this lesson. The overall feeling of this class is smooth and the students' thinking is active. In class, students can be better guided to think and summarize the relationship between cylinders and cones with equal bottom and height, highlight key points and break through difficulties.
"Mathematics Curriculum Standard" clearly points out that students should "learn to observe and analyze the real society by using mathematical thinking mode, solve problems in daily life and other disciplines, and enhance their awareness of applied mathematics." The design of this lesson fully embodies this concept. In class, let students use cones and cylinders to hold sand, so that students can feel the close connection between mathematics and life. Through their own exploration, we can use mathematical thinking to solve problems, and we can also use our own knowledge to study and solve other mathematical problems in life, thus cultivating students' application consciousness. At the same time, classroom teaching pays attention to students' autonomous learning and cooperative inquiry, which gives full play to students' learning initiative and cultivates students' innovative ability.
Although this course has achieved the teaching purpose and achieved good teaching results, there are still some shortcomings. Due to the limitation of conditions, the preparation of learning tools is not sufficient. Classroom language is not concise enough; Students don't pay attention to the generation when they report; There is no serious study on the volume relationship between unequal base and unequal height. I will pay attention to these problems in the future teaching process, so that I can make continuous progress.
The evaluation draft of the second volume of the sixth grade mathematical cone 10 makes students truly become the initiative of the activities. Only in this way can students truly feel that they are the masters of learning. In graphics teaching, according to the characteristics of learning content, paying attention to operation and practice can make teaching achieve the highest efficiency.
The teaching objectives of the lesson "Cone" are:
1), know the cone, and know the bottom, edge and height of the cone;
2), master the measurement method of cone height;
3) Derivation of cone volume formula;
4), through an example, students can use the conic formula for simple calculation.
In teaching, the first three teaching objectives are successfully accomplished in a relaxed and pleasant atmosphere through actual touch, hands-on measurement, exploration and deduction. In the application of the formula, considering that the students have previewed the example, the teaching of example 2 is changed and a conical wheat pile is given. The bottom diameter is 20 decimeters, the height is 14 decimeter, and the weight of wheat per cubic meter is 0.375 kg. How much does this pile weigh? Let students practice independently. I thought it was a problem that could be solved quickly by applying formulas, but the students didn't finish it for a long time. It turns out that I didn't consider 1/3 and 3 of the cone volume formula when I changed the numbers. The given diameter and height of 14 can't be reduced to 1/3, which complicates the application of the formula in decimal calculation and wastes a lot of time. The class ended in a hurry before the after-class exercises were finished. Rethinking mathematics after class is vivid and rigorous, and it needs careful planning to produce a seemingly simple number. A simple and fluent good class is not handed in casually, as long as you think hard, make overall arrangements and pay attention to every detail.
Teaching needs learning, teaching needs reflection, progress in reflection and improvement in reflection.