Reflection on the Teaching of Fractional Division

Part 1: Teaching Reflection on Fractional Division

The short 40-minute class was over, but there were a lot of problems exposed. This also shows that I am still immature as a new teacher. There are still many places to improve.
First of all, this class is not complete enough. A lesson should be introduced by the problem - the exploration of new lessons - the consolidation of exercises - the summary of the class - the arrangement of assignments. But my class ended in a hurry after the conclusion, and the summary was quite rushed. Obviously, there is still a need to strengthen the overall layout and time allocation.
Secondly, in this class, perhaps the tension of the students, perhaps the students did not master enough, leading to many unforeseen problems. For these problems, my ability to respond is very weak. I don't understand how to deal with some problems. Therefore, I can only let other students report the correct answers and take them. And this problem is precisely the need to solve it yourself. Students have problems. This is the time to show the level of the teacher. For the wrong answer, the students can discuss the "cause of the error", "what is the right thing", etc.; in the wording should also try to avoid "right?" ", "Is it correct?" and so on, if the "question" is negative, but should take "other answers?" and other sentences, let other students think. Therefore, more detailed preparations are needed for this issue, and more solid considerations are needed.
Moreover, in fact, I only used one example before the concept was introduced. But in fact, an example is not representative. Instead, more examples, positive examples, counterexamples, etc. should be used. If necessary, the teacher can also create some wrong questions for the students to judge. The ultimate goal is to make the students understand the concept more clearly and more thoroughly, so that students can finally summarize the concepts themselves. Therefore, Teacher Zhang Bo also suggested that the consolidation exercise behind the concept should be put forward and placed before the concept is formed as an analysis.
In addition, in the classroom, students should be the main body, and teachers only serve as a guide. We need to give more time to the students, let them think, discuss, let the students find out through the teacher-designed hierarchical steps step by step, solve the problem themselves, and let the students really "do mathematics." Instead of the teacher instilling the student acceptance.
This is a very educational lesson, and there are quite a few problems exposed in the classroom. Other teachers have also pointed out various effective improvement methods. I believe that I will make great progress through this opportunity.

Part 2: Reflection on the Teaching of Fractional Division

"Mathematics teaching should start from the student's life experience and the existing knowledge background, so that students feel that mathematics is in their own right, and they are in middle school mathematics. Make students understand the importance of learning mathematics and improve their interest in learning mathematics." Division, for primary school students, is a relatively abstract content. The reason why mathematics knowledge can be understood and mastered by students in the national ministry is not only the result of knowledge deduction, but the result of interaction of specific models, graphs and scenarios. So when I was designing the lesson and division, I considered the following two aspects:
1. Start by solving the problem and feel the value of the score.
Introduced from the problem of dividing the cake, let the students in the process of solving the problem, feel that when the business can not be represented by an integer, the score can be used to represent the quotient. This course is mainly carried out from two levels. One is to use the original knowledge of the students to solve the problem of dividing the average score of one cake into several parts, which is represented by commercial scores. The second is to understand the average share of several cakes by means of physical operations. A number of shares can also be expressed in terms of scores. These two levels are developed from the perspective of problem solving.
2. The expansion of the meaning of the score is synchronized with the understanding of the relationship between divisions.
When the fraction is used to represent the quotient of the integer division, the divisor is used as the denominator and the dividend is used as the numerator. Conversely, a score can also be seen as dividing two numbers. It can be understood that dividing "1" equally into 4 parts means such 3 parts; it can also be understood that dividing "3" equally into 4 parts means such one part. That is to say, the understanding and establishment process of the relationship between score and division is essentially synchronized with the extension of the meaning of the score.
After teaching, I will reflect on my own teaching and find that in terms of the state in which the mathematics knowledge of the national stage is stored in the minds of the students, in addition to the abstraction, it should be abstract and concrete mathematical knowledge that can be transformed. The whole course teaching has the following characteristics:
1. Provide rich materials and experience the process of “mathematicalization”.
The understanding of the relationship between scores and divisions is based on the concrete sensible objects and pictures, and the hands-on operation is used to generate mathematical knowledge under the support of rich representations. It is a continuous accumulation of perceptual accumulation, and gradually abstracts and models. process. In this process, we pay attention to the following aspects: First, provide rich mathematics learning materials, and second, on the basis of making full use of these materials, students gradually improve their own conclusions, from text expression to text representation. To the process of using letters, the process from complexity to conciseness, from life language to mathematical language, has also undergone a process of concrete to abstraction.
2. The problem lies in the method, and the content carries the idea.
Mathematical learning is a process of problem solving, and the method is naturally contained in it; the learning content carries mathematical ideas. In other words, mathematics knowledge itself is only one aspect of our study of mathematics. More importantly, we use knowledge as a carrier to infiltrate mathematics thinking methods.
As far as scores and divisions are concerned, the author thinks that if you only teach for a relationship, you just grab the tip of the iceberg. In fact, with the help of this knowledge carrier, we should also pay attention to the methods of inductive and comparative thoughts, and how to use existing knowledge to solve problems, so as to improve students' mathematical literacy.

Part 3: Reflection on the Teaching of Fractional Division

First, the problem shows:
In the unit of fractional division, the main methods are the calculation of the score divided by the integer, the integer divided by the score, and the score divided by the score. Among them, in the teaching process of the fraction divided by the integer, the students accept the comparison. Fast, the learning effect is also very good, but after the teaching integer is divided by the score, through the student's practice feedback, it is found that the students have more errors in the calculation, mainly in the following aspects:
1. In the synchronous change of the divisor and divisor, the student forgets to turn the divisor into a multiplication sign.
2. When the divisor becomes its reciprocal, the student mistakenly turns the divisor into a reciprocal.
3. There is no timely appointment of the points in the calculation, resulting in inaccurate answers.
Second, the cause analysis
Why are these error phenomena formed? Through comparative analysis, there may be some reasons:
1. Teaching methods: The examples explain that the components are not enough; the teaching speed is faster; the opportunities for learning difficulties are not enough; the words are much more, and the writing is less.
2. Student learning method: The influence of the score divided by the integer has formed a mindset, thinking that each time the score is to become a reciprocal, the integer does not change, resulting in a mistake in the synchronous change; secondly, the student does not during the course Being good at focusing on the points, in the fractional division method, the dividend can not be changed, the synchronous change refers to the change of the divisor and the divisor; finally, the student's learning attitude and study habits also directly affect the teaching effect of the undergraduate.
Third, the solution
1. Increase the chances of student boarding,
2. In the classroom, students are required to read the key words to deepen their impressions.
3. The auxiliary work requires students to conduct individual counseling on the same level.

Part 4: Reflection on the Teaching of Fractional Division

The "New Curriculum Standard" states that students are the masters of mathematics learning, and teachers are the organizers, guides, and collaborators of mathematics learning. In the teaching, only the establishment of the student's subject status and the optimization of the learning process can promote the students' independent learning process. The method of simple division and application of score division is one of the important and difficult points in the teaching of the entire national stage. How to stimulate students to actively participate in the whole process of learning, to refrain from the cumbersome analysis and dogmatic memorization in traditional teaching, and to guide students to understand correctly The number of fractional divisions applied. I made some of the following teaching attempts:
First, learn mathematics from life.
In the beginning, I changed the traditional practice of introducing new knowledge by reviewing old knowledge, directly drawing on the actual life of the students, drawing the questions through the number of students in the class, and then letting the students introduce the situation of the class, triggering the enthusiasm of the students to participate, and making the students feel the mathematics. Just at your own side, in the middle of life, mathematics, let students learn valuable mathematics.
Second, pay attention to the process and let the students get hands-on experience.
In order to let students know what is the key to answering the score multiplication question, I deliberately do not make any explanation. By omitting a known condition in the question, let the students discover the problem and feel the connection between the quantity in the set problem. Find the law during the learning process. So that students can really understand and conclude: the key to answering the score multiplication problem is to find the equal relationship between the numbers from the key sentences of the topic.
In the teaching, we strive to reflect the learning style of "independence, cooperation and inquiry". In the past, the efficiency of teaching the score division method was not high. The reason was mainly the deviation of teacher teaching. Teachers like to analyze the keyword language trivially, and like to use rigorous language to carry out rigorous logical reasoning. Although the analysis is the head, it is easy to go to the extremes, or to make unnecessary analysis in places that students already understand; or Taking students as scholars and doing in-depth and succinct analysis of what is not understandable is a waste of valuable classroom time. In the teaching, I combine the score division method with the introduced score multiplication method to teach students, let the students feel the similarities and differences between them through discussion and exchange, and explore the internal relations and differences between them, thus enhancing students' analysis problems. The ability to solve problems saves a lot of cumbersome analysis and explanation.
Third, analyze problems from multiple angles and improve their capabilities.
When calculating the application questions, I encourage students to actively seek a variety of different solutions to the same problem, expand students' thinking, and guide students to learn to analyze problems from multiple angles, so as to cultivate students' inquiry ability and innovative spirit in the process of solving problems. In addition, the change in the past only from the example of the abstract summary of the quantitative relationship, and let the students memorize, such as "yes, account, ratio, the equivalent of the unit is 1"; "Knowledge 1 to find a few multiplication, know how to ask 1 With the practice of division and so on, students can fully experience the experience, so that students can deepen their understanding of the quantitative relationship and solution of such application questions, improve their ability, and prepare students for deeper learning.
Throughout the teaching process, I was the organizer, helper, and facilitator of student learning. In this way, not only the students' full potential can be fully utilized, the students' exploration ability can be cultivated, and the students' interest in learning can be stimulated. Students learn easily and teachers teach happiness.

Part V: Reflection on the Teaching of Fractional Division

Effective teaching design needs to be carried out around three basic problems: effectively grasping the cognitive basis of students, effectively positioning teaching objectives, and effectively designing the teaching process. The main purpose of this lesson is to divide the learning score by an integer, let the students understand the meaning of the fraction divided by the integer, and master the calculation method of the fraction divided by the integer.
Accurately grasping the cognitive basis of students is the basis for teaching design. With the learning foundation of fractional multiplication, students can quickly adapt to the learning style of this lesson. The logical starting point of this lesson is the meaning of integer division, the meaning and calculation method of fractional multiplication, and the method of finding the reciprocal of a number. Therefore, I introduce the problem of fractional multiplication in reality and find the reciprocal of a number to help the children review the predecessors. When the students realize the reciprocal relationship between multiplication and division, they propose a practical problem in life and lead to fractional division. The necessity of calculations sets the ladder for subsequent learning.
After accurately grasping the cognitive basis of students, how to accurately target the target is the key to instructional design. If this class only pays attention to whether the students will count, it is not enough. In the design, we should also pay attention to the deeper elements after the appearance, such as: Do the students understand the arithmetic? Have their thinking been substantially improved? Are their learning methods improved? Do they have a positive attitude towards learning? and many more. Therefore, in the formulation of the teaching objectives of this lesson, my focus is not only on the students' calculations, but also on understanding the meanings, so that the students can deeply understand the truth of such calculations and highlight the "procedural goals." Let students experience the process of painting, painting, calculating, and speaking. In the process of inquiry, let the children form a learning attitude of “knowing that they must know why” and acquire a kind of learning. Ability to lay the foundation for students' sustainable development.
The teaching process is a direct reflection of the teaching objectives in the classroom. In teaching, I pay attention to the process of students' experience in discovering mathematics, providing students with hands-on opportunities, making full use of graphical language to make abstraction intuitive, helping students to understand the meaning of dividing a fraction by an integer, and "divide by an integer equal to multiply this. The rationality of the inverse of integers method. Then transform the angle of exploration, present a set of calculations, and in the process of calculation and comparison, let the students verify the rules found in the operation activities again. Give students a space to experience and feel in the learning process, such as: Who is talking about this algorithm? What is your idea? Students gradually accumulate the original experience in the process of self-expression, and then improve the students' mathematical thinking through the appropriate point of the teacher.