3.3 cube root teaching reflection

3.3 cube root teaching reflection model one:

In this lesson, the teaching method mainly applies the creation situation--propose the problem--establish the model--the solution to the problem. In the actual teaching, the teaching method of intensive refinement and student self-learning is mainly adopted.
When introducing a new lesson, it created a problem that students often encounter in life, let students start from practical problems, feel the roots of the cube in the life of a wide range of applications, experience the necessity of learning the cube root, stimulate students' interest in learning, and then design The problem, a problem that is easy for a student to solve, guides the student's attention from the open cubic operation to the cubic operation, and gives the students a preliminary understanding of the reciprocal relationship between the cubic operation and the open cubic operation. Explore new knowledge and be prepared.
In the first two sections of this chapter, there are many similarities in the content between the square root and the cube root. Therefore, in the teaching, the analogy method is used to let the students learn new knowledge through analogy with the old knowledge. The comparison between the cube root and the square root is emphasized in the teaching. The connection and difference between them, so that the old and new knowledge are linked, is conducive to reviewing and consolidating the square root, but also conducive to the understanding and mastery of the cube root. The summed up "one two one" helps students to understand vividly. Through independent thinking, group discussion, and cooperative learning, students can give full play to their subjective initiative, feel the reciprocal relationship between cubic operations and open cube operations, and learn ways to find solutions from cube root and cube inverse operations.
It reflects the intensive and refined teaching in the present teaching, and the subjectivity of the students is best presented. In the process, the teacher plays the role of guiding and inducting, asking questions, letting the students think, the teacher no longer speaks, or speaks very much. Less, but if you want to be a good "director" teacher really wants a lot of time to prepare lessons, students need to prepare lessons in advance, the workload is really big under the class, but the students got the performance, and the enthusiasm in the class was confirmed by the teacher.

3.3 cube root teaching reflection model two:

According to the requirements of the curriculum reform, students will experience the process of exploring, discussing, communicating, and applying mathematical knowledge to explain related problems through the study of mathematics teaching in the middle school. From the experience of applying mathematics, developing their own mathematical thinking ability, and obtaining some research problems, Experience and methods to solve problems, so as to cultivate students' interest in mathematics learning and experience the success of learning.
In the "Real Numbers" in the eighth grade mathematics, we encountered the teaching task of "Cubic Roots". The contents of the first two sections of this chapter, "square root" and "cube root", have many similarities in content arrangement. Therefore, the analogy method is used in teaching to let students learn new knowledge through analogy with old knowledge. The teaching highlights the contrast between the cube root and the square root, and analyzes the connection and difference between them, so that the relationship between old and new knowledge is beneficial to review and consolidate the square root, and is conducive to the learning and mastering of the cube root. Through independent thinking, group discussion, cooperation and exchange, students have exerted their subjective initiative in "independent exploration, cooperation and exchange", and felt the reciprocity of cubic operation and open cubic operation, and learned from the cube root and cube are mutual Find the way to solve the problem information in the inverse operation.
The teaching design of this lesson is based on the textbook and curriculum standards of the PEP. The teaching method highlights the “Creating a Situation----Proposing a Problem----Building a Model-----Solving a Problem” The idea is to adopt the teaching method of students' self-learning in the actual teaching.
When introducing a new lesson, I created a problem that is often seen in the actual life of students. “To make a box with a square shape of volume, what should be the length of the box?” Let the students feel from the actual problem situation. The calculation of the cube root has a wide range of applications in life, and the need to learn the cube roots is stimulated to stimulate students' interest in learning. Then design question 1: Calculate a number of cubes. A step is laid here, and a problem that is easy for students to solve is set up. The student's attention is guided from the open cubic operation to the cubic operation, so that students can reciprocate the cubic operation and the open cubic operation. The relationship has a preliminary understanding and is ready to further explore new knowledge.
In the teaching, the problem 2 is arranged: the characteristics of the cube root of the discussion number, let the students calculate the cube root of the positive number, 0, and negative number, find their respective characteristics, and through the students exchange discussion activities, it is concluded that the positive cube root is a positive number, 0 The conclusion that the cube root is 0 and the cube root of the negative number is a negative number allows students to go through a special-to-general cognitive process through inquiry activities. Attention should be paid to the students to provide a certain space for exploration and cooperation, and to explore the students' thinking ability in the process of inquiry activities, effectively changing the way students learn.
In the question of question 3, a fill-in-the-blank question was designed: Can you find the values ​​of the following formulas and fill in the blanks with " " or " "? Because Therefore __
Because Therefore
What can you draw from the above calculations? Let the students explore the relationship between the cube root of a number and the cube root of its opposite number, so that the problem of finding the cube root of the negative number can be transformed into the problem of finding the cube root of the positive number, let the students understand the thought of transformation, and use the expression to express it. That is, the impression of the students is profound.
Through the teaching of "Cubic Roots", I have a deeper understanding of the teaching design and teaching practice of the concept class. In the implementation of the new curriculum, we are delighted to see that the traditional acceptance teaching model has been replaced by lively independent learning, exchange and cooperation mathematics activities. The class has lived up, the students have moved, dare to think, dare to ask, dare to say, dare to do, dare to argue, full of curiosity and expression. Communication allows students to share happiness and share resources. Teaching from life allows students to feel the joy of learning.

3.3 cube root teaching reflection model three:

"Cubic Roots" Eighth grade mathematics The last semester of the "real number" in the second section of the "Cubic Roots" first lesson. The content of the cube root is based on the concept of square root and square root of arithmetic. This section is basically parallel to the content of the square root of the previous section. It mainly studies the concept and method of cube root. It is basically the same from the order of knowledge expansion. This section also starts from the specific calculation and summarizes the concept of giving the cube root, and then discusses The reciprocal relationship between cubic and open cubes, studying the characteristics of the cubic root.
When I introduced the new lesson, I used a new method to understand the new method, so that students can start with the following questions: 1. What is the square root and the square root of the arithmetic? How to symbolize the square root and arithmetic square root of the number a? 2. There are several square roots for positive numbers? What is the relationship between them? Is there a square root for negative numbers? What is the square root of 0? By reviewing the analogy of old knowledge, it paves the way for new knowledge.
After that, I created a problem situation that is common in student life. “1. Observe and think: a square box is 2 cm long. Can you find its volume?”
On this basis, another problem has been set up that is challenging and can be solved by students. "2. Xiao Ming wants to make a box with a square shape of 27cm3. What is the length of the box? How much can you help? Help him?” Helping friends solve problems, the enthusiasm of the students is mobilized. At the same time, the students’ attention is guided towards the idea of ​​cubic computing and cubic computing, in preparation for further study. The teacher gives a solution to the problem based on the student’s full discussion
In the exploration of new knowledge, I mainly adopt the analogy learning method in teaching. First, let students recall the concept and representation of square root, and contact the above questions, and ask students to summarize the concept and representation of the cube root. Later, a student can't wait to give the concept of a cubic root. "Generally, if a cube of number x is equal to a, ie x3 = a, then the number x is called the cube root of a." "It's awesome. Can you give me an example to illustrate?" For example, "23=6, 2 is the cube root of 6, 33=9, 3 is the cube root of 9." He waited for my answer with the questioning "The children of our class." It’s not the same. She understands the concept of cube roots very well, just?” “Teacher, I know where her problem is, he equals the multiplication with multiplication” and she says the correct answer. "It seems that this classmate is very careful, everyone cheers for her. Can we give other examples?" The students sneaked a few words below, some of them quietly calculated, and some students began to lift Grabbing an example, the classroom atmosphere was mobilized.

3.3 cube root teaching reflection model four:

First, the status of teaching materials
"Cubic Roots" Eighth grade mathematics The last semester of the "real number" in the second section of the "Cubic Roots" first lesson. The content of the cube root is based on the concept of square root and square root of arithmetic. This section is basically parallel to the content of the square root of the previous section. It mainly studies the concept and method of cube root. It is basically the same from the order of knowledge expansion. This section also starts from the specific calculation and summarizes the concept of giving the cube root, and then discusses The reciprocal relationship between cubic and open cubes, studying the characteristics of the cubic root.
Second, a good place
1. In this lesson, I can successfully complete the teaching of this lesson, master the whole classroom, use some inspiring language, and make the whole classroom move more active. Students are more motivated to answer questions and can show themselves in front, and The performance is very good, and the successful experience, which also gives students confidence, is more active in the later learning, but also wants to express themselves.
2. The class of this lesson has a large capacity. On the basis of guiding students' concept of square root, through the introduction of practical problems, they can sum up the concept of cube root. After the teaching of example 1, students further understand the concept; through two explorations, Obtaining the nature of the cube root and the range of values ​​of the square root and the cube root are 1, -1 and 0. Based on the concept and nature of the cube root, the students have done a lot of exercises and completed the book. 1, 2, and 3 of after-school exercises and after-school exercises.
3. Through my observation and understanding in the classroom, through the performance of the students doing exercises and the problem of doing the exercises, through the observation feedback of the teacher in charge of the back of the class teacher, know that the students mastered this lesson is good, reached Scheduled teaching objectives. The next day, I asked some students how they feel about the lessons of Cube Root. Will they? Students also reflect the city, listening very clearly, I feel very simple. The exercises done by the latter students are also quite good. They are all written correctly. They have answered several questions in class and they are very good.
4. In the teaching, I specified three points for the requirements of Example 2: first read the following formulas, explain the meaning of the representation, and then evaluate. It not only exercises the language of the students, but also strengthens the concept of the cube root, and finally completes the evaluation and completes the answer. From this, it also infiltrates a learning method for students, strengthens the importance of reading questions, and clarifies the meaning of the questions in order to solve them. In fact, this is also learned through the lessons of the instructor Lu Chun during this time, thanks to Teacher Lu.
5. When I explain the value range of a, I am getting the nature of the cube root: a positive number has a positive cube root; a negative number has a negative cube root, and the zero cube root is zero, let the students think about a What is the value range? Students have a cubic root based on positive, negative, and zero nature. Naturally, the range of values ​​of a can be obtained. This is natural, and students can easily understand that there is a sense of being natural.
Second, the inadequacies
1. In teaching, I always use my consciousness as the transfer. In the classroom, I follow the route I designed. I can't play the initiative of students' learning. I can't let the students out, always in my own hands. I think Students should be able to talk less easily, and if they feel that they are not understanding well, they should be based on the actual situation of the students, release the students, control them, and finally take them back.
2, I am influenced by my own consciousness in teaching, lack of principled things, lack of excavation of definitions, some places do not grasp definitions to further explain, lack of time processes for students to think, think, let students know the essential things Conducive to students' understanding.
3. The knowledge of the square root is not listed in the teaching, so the analogy of the cube root and the square root is not full and vivid. I use the language to express it. I will write it on the blackboard later in this lesson. better.
4. In the teaching, the pair of cubes and open cubes are not enough to reflect the reciprocal operation. Students should be further aware that the result of the cubic operation is power, and the result of opening the cube is the cube root.
Third, the place of doubt
In teaching, I always think that there is no need to explain, explain, and explain things that students have. I think the place where students will go to explain, and then it is a waste of time, and students don’t want to listen any more.
Fourth, feelings and thinking:
1. The development of students' habits and the cultivation of learning methods are effective ways to cultivate self-learning ability.
2. The effect of student understanding depends on the appropriate inspiration and guidance of the teacher based on the student's experience, and the extent to which the student participates in the learning process, including initiative and procedurality.
3, the difficulty and speed of the classroom are often based on the mid-stream students as a ruler, how to cultivate eugenics, help the undergraduates? How to operate? Especially the number of people who are in the post-entry group is huge, and they have to face the test evaluation. What should the class do? This is a question worth considering

3.3 cube root teaching reflection model five:

The knowledge structure of “cube root” is similar to the knowledge structure of “square root”. Therefore, using the migration analogy to teach this lesson, the generation and preset of the classroom are basically the same, and it exceeds the preset learning content.
Review the definition of the square root, the representation method, the meaning of the square root, the relationship between the square operation and the square root, the characteristics of the square root of the positive negative number and zero, based on the student's preview, and soon compare the knowledge points of this lesson, the teacher at this time To sum up: open cubes and open squares are the new sixth operations we are learning now. From here to the second and third parties, we can also extend the knowledge and what new knowledge is there. What? The students have learned together, and got the knowledge of square root calculation, square root, etc., and grasped the addition, subtraction, multiplication, division, power, and square, and the corresponding operation results, sum, product, quotient, power, and square root. . Properly performing such extensions can help to increase the enthusiasm of students to learn.
Letting the students explore the knowledge and gaining beyond the expectation. For the nature, the students of Beibeier, Qian Zeyu and others have written the text: the cube root of the opposite number of a number is equal to the opposite of the cube root of the number, and the students To sum up, the cube roots of the two numbers that are opposite to each other are opposite to each other. In addition, Xu Wei Danqing combined his own data to conclude: , for this reason, under the appreciation of the teachers, the important nature of the square roots of the students to migrate: , , the induction of the latter formula, Xue Ruixiang made a wonderful answer.
The calculation requirements and error analysis of the 8th and 9th questions in the promotion study are the difficulties of this lesson. In the group discussion, the students can deeply understand: “Whether it is the simplest form of the number, when seeking the square root or the cube root of it, first of all They have to be reduced to the simplest form. Chen Ming, Zheng Ruijie, Xue Ruixiang, Liu Pengcheng, Shi Wuzhen, Jin Peipei and Wang Zhenyu and other students have done corresponding training on the blackboard, and the whole class has made a difficult breakthrough.