Reflection on the teaching of fractional multiplication

Part 1: Reflection on the teaching of fractional multiplication

Time passed quickly, and one month passed in the blink of an eye. The teaching of the first unit was basically completed. Looking back at the teaching of fractional multiplication, I have been confused about how to deal with the meaning of fractional multiplication during the lesson preparation. Later, I thought that if we can judge from the specific practical problems that there is a multiplication relationship between the two data, the multiplication relationship has a new one in this unit. Expansion, that is, "seeking the sum of several identical addends", "how many times is a number", and "how many fractions of a number are used".
When the teaching score and the integer are multiplied, according to the student's existing knowledge base, the student is guided to recall the meaning of the method of reviewing the integer multiplication and the addition of the denominator score. In addition, scientific learning methods can improve learning efficiency and enable students' wisdom to be fully utilized. In the calculation of the multiplication of the teaching score and the integer, the fractional multiplication is introduced starting from the meaning of the integer and fractional multiplication that the student is familiar with.
In addition, at the beginning of the preparation of the unit, the master prompts himself to add a class to compare the difference between the score addition and the score multiplication after the score is multiplied by the integer and a multiplier, and then the fractional multiplication and simple calculation are performed. teaching. At that time, I was listening to the fog and I didn’t understand the intention of the master. It was not until the beginning of the teaching score multiplication hybrid operation that the master’s good intentions were understood. Although at the reminder of the master, I have a comparative teaching of fractional addition and multiplication. However, at night, some students calculate the score addition method according to the rules of fractional multiplication. At this time, they know why the master had to compare the score multiplication and addition at that time. When I saw the student's homework, I explained the difference between fractional multiplication and addition again during the class review before the class. Let students have a clearer understanding when calculating. Although this problem is solved, students encounter another problem in the fractional multiplication mixing operation. Some students calculate the addition and multiplication first when calculating the multiplication and multiplication operation, especially when the addition is preceded and the multiplication is later. Calculating the multiplication, under the guidance of the teacher, suddenly realized. Explain that students are not proficient in the order of operations of the four arithmetic operations. In the future teaching, I should also emphasize the order of operation of the four arithmetic operations.
The teaching of this unit, score multiplication and solving problems is also a key content. When helping students analyze the meaning of the question, if the student will draw a line drawing, it will be of great help to understand the meaning of the question. However, it may be due to the fact that in the fifth grade, students are required to draw line segments and understand the meaning of the questions according to the line segments. Therefore, when the sixth grade clearly requires that the line drawing be drawn according to the meaning of the question, the students are not used to it at the beginning, and the line drawing drawn does not reflect the meaning of the question very well. For this aspect, the teaching needs to be strengthened again, because this The ability to improve students' problem analysis and problem solving will be greatly improved. The teaching of the next unit, if the student can draw a suitable line segment map according to the meaning of the question, will be of great help to answer the question correctly.
In addition, in the teaching, pay attention to the understanding of the unit "1", the focus is on finding the quantity of the unit "1" in the application question and how to find the above - first find the rate sentence in the question and then from the rate sentence Find out the unit "1" and make a supplementary pad for the teaching of the later application. Before the teaching, I would like to deepen the teaching materials, grasp the degree of textbooks, ask other teachers, and learn from each other. Inspire more interest in the classroom, communicate with students after class, and learn about their learning dynamics. Teaching according to the actual situation to improve the quality of teaching.

Part 2: Reflection on the teaching of fractional multiplication

In the teaching of a multiplication of the meaning of the score and the score multiplication score, through the operation, demonstration, observation, comparison and other activities, that is, first image specific, then abstract summary, to help students understand the meaning and arithmetic of fractional multiplication. In teaching, teachers should guide students to operate, intuitively understand, make students participate in teaching, give full play to students' initiative, and mobilize students' enthusiasm.
Based on the knowledge that has been learned, we use the migration and expansion of knowledge to understand the meaning of fractional multiplication. Through the review of integer multiplication, the students first make clear the meaning of integer multiplication, and then make full use of the visual map, so that students can clearly see that they can be calculated by addition or multiplication.
Guide students to combine intuitive operations with abstract reasoning and understand the derivation of the calculation of fractional multiplication.
Because the calculation of fractional multiplication is more abstract, students have some difficulty in understanding. When teaching, I try to strengthen the intuition, become abstraction into the image, give students the opportunity to create opponents, stimulate the interest of students to learn, and let them actively participate in the teaching process. Based on the intuitive operation, the calculation method of the score multiplication score is derived, and then the rule of fractional multiplication is summarized.
Develop students' good calculation habits and serious learning attitudes. It is not difficult for students to master this part of the content. However, through the study and practice of this part of content, it is necessary to cultivate good calculation habits and rigorous and serious learning attitudes such as careful examination, attention to the order of calculation, observation of digital features, and selection of simple methods. They will lay the foundation for future study.
In the process of teaching, teachers should be the mainstay, students as the main body, students to create the participation in teaching activities, through the operation, demonstration, observation, comparative training of students' abstract summary ability, through analysis and discussion, to cultivate students' analytical ability. At the same time, in the teaching process, we must pay attention to grasping the internal relationship between old and new knowledge, so that students can understand the horizontal connection between knowledge. Students find the connection between knowledge and knowledge in contact and comparison, and gain an experience of exploring knowledge.
We must also pay attention to the guidance of learning and training, and cultivate the internal thrust of students.

Part 3: Rethinking the Teaching of Fractional Multiplication

First, let the students understand in the process of exploration.
In the teaching objectives of this module, “exploration” is a keyword – “combining specific situations, exploring and understanding the meaning of fractional multiplication in operational activities”, “exploring and mastering the calculation method of fractional multiplication, and correcting Calculation". This is determined by the two dimensions of “mathematical process” and “problem solving” in mathematics goals; at the same time, the process of “exploration” is also an important way to achieve the goals of “emotion, attitude and values”.
In the teaching process, students are organized to explore mathematics knowledge, and different strategies should be adopted according to different materials and backgrounds in order to achieve the goal of effective activities. For example, in the fractional multiplication of this unit, since students have a solid foundation for the meaning of integer multiplication, the exploration of the meaning of the fractional multiplication integer and the calculation of the algorithm can be carried out independently. In the fractional multiplication, because the students just know the meaning of the score multiplication of "how many fractions of a number is", and the process of using graphs to represent the score multiplier is more complicated, so use "help one to put, put one put The strategy is more appropriate. Specifically speaking, the teacher conducts collective guidance through simple specific cases. This is the “helping one to help”. Then through specific exploration requirements to help students try to explore more complex examples, this is "put a release."
Second, reviewing the homework done by the students, the problems are concentrated in the following points;
1, the problem of off-calculation, many students blindly use the operating law to calculate.
Take countermeasures: Pay attention to the purpose of the students to understand the purpose of the simplified calculation. The calculation of the scores is basically the same as the integer and decimal calculations. The order of operations is changed without changing the results, and the cumbersomeness of the calculation is minimized. But the method is different. Integers and decimals are often rounded up to ten, and the score is for good scores.
2. In teaching, I paid attention to the understanding of the unit "1", analyzed the meaning of the question according to the meaning of the score, and ignored the review of the calculation method of the unitized poly, and how many fractions of the number of the two-step calculation The review of the set of questions.
Third, take countermeasures:
In the practice class, first review the number of words that are a few of the number, and combine the review questions to let students recall the meaning of a multiplication score, and further deepen the meaning of the score. Help students understand the difference between "a few parts of a number" and a few points of "one number to another", and lay the foundation for learning the corresponding scores.
When reviewing the score multiplication method, according to the mathematical model of the fractional multiplication method, the problem is said to be what is asked, and the quantitative relationship in the title is written. In the teaching, we should pay attention to the condition and problem of the title by using the line segment diagram, and strengthen the one-to-one correspondence between the rate and the quantity. This is helpful for the students to find out who is the standard and the relationship between the rate and the quantity.
Problems can lead to thinking, thinking about ways to promote change, and getting things to reverse the teaching situation. Explain that teachers are not afraid of problems in teaching, and having problems to solve them will minimize teaching losses. In the classroom, students' interest is stimulated. After class, they communicate with students, understand their learning dynamics, and teach according to the actual situation to improve the quality of teaching. Of course, the preparation before the teaching is meticulous and thoughtful, and the possibility of teaching mistakes will be smaller.

Part 4: Rethinking the Teaching of Fractional Multiplication

Grasping the textbook is the foundation, and it is the key to handling the generation and presupposition. This is the biggest achievement after I finished this lesson.
Meaningful mathematics learning must be based on the students' subjective wishes and knowledge and experience. The mathematics practice class is based on the consolidation of basic knowledge of mathematics, the formation of problem-solving skills, skills and the cultivation of students' knowledge to solve practical problems. class. The common forms of practice classes are monotonous, straightforward, dull, and enthusiasm for students. It takes a lot of time to write and write. In order to improve students' interest in learning, they stimulate their curiosity and cultivate their ability to explore and think. In the teaching, I have effectively dealt with the teaching materials, and chose the exercises that are full of life, interesting, and diverse forms. They are introduced from the excitement of the conversation, the calculation method is highlighted by the mouth, and the calculations are made to the various variants. Computation, comprehensive application, let students understand the meaning of fractional multiplication in calculating, speaking, thinking, understanding the arithmetic of fractional multiplication, knowing that fractional multiplication comes from life, thus further recognizing that mathematics has in life. The wide application has inspired students to learn the confidence and positive emotions of mathematics, and undoubtedly make students become more and more eager to practice.
Teaching is a complex activity. It requires careful planning before the teacher's class. This is the presupposition of teaching. Accurately grasping the teaching materials, comprehensively understanding the students, and effectively developing resources are the key points for teaching presupposition, and also the logical starting point for dynamic generation. The differences between students and the openness of teaching make the classroom more versatile and complex. The development of teaching activities sometimes coincides with the teaching presets, and more often it is different from the pre-sets, and even completely different. When teaching is no longer carried out according to the presupposition, teachers will face severe tests and difficult choices. Teachers should flexibly choose, integrate, and even abandon teaching presupposition according to actual conditions, and wit to generate new teaching programs to make teaching spiritual and intelligent. Presupposition and generation are two factors that teach good lessons, and both are indispensable. In traditional teaching, teachers rely too much on pre-class presuppositions. Classroom teaching tends to be too rigorous and thorough, and has strong planning. This is a pre-set advantage and a presupposition. Although the presupposition is a necessary condition for teaching, it is by no means a decision condition for a good class, and it is not the only condition for a good class. In the process of teacher presupposition, I can't fully imagine what happened in the classroom. I must discover it at any time, even discover the internal dynamics of students in the classroom, and create conditions to promote the transformation of internal factors into improving mathematics literacy.
There are also many shortcomings in this lesson:
1. Because my understanding of the new course materials is not deep enough, there are three different graphic methods in the students' understanding of the score multiplication algorithm, and I only agree with the ones in my mind, which is obviously Not enough, the methods of mathematics learning are diverse, and the presentation of learning outcomes is also diverse and open.
2. In teaching, it relies too much on pre-class presuppositions, loses the timely generation of teaching resources in the classroom, misses the generation of internal factors dynamics in the classroom, and does not create conditions to promote the transformation of internal factors to improve mathematical literacy.
In the future teaching, we should learn more about educational theory, strengthen subject knowledge, profoundly comprehend teaching materials, use good teaching materials, handle good teaching materials, grasp the relationship between generation and presupposition, improve our classroom resilience, and continuously improve our business. Level. This will enable students to learn mathematics and love mathematics.

Chapter 5: Reflection on the Teaching of Fractional Multiplication

Today's teaching content is score multiplication scores, the focus is to consolidate and evolve understanding the meaning of fractional multiplication, and to explore the rules for calculating score multiplication scores.
In the teaching practice, I continue to use the mathematical method of “digital combination” to help students achieve the above two mathematical goals. There is no direct letting go of today's “inquiry activities”. This is because the students' understanding of the meaning of the multiplication of the scores of “how many fractions is a few” is not deep enough, so the whole teaching process is divided into three levels:
First, guide the students to graphically represent the meaning of the scores, and then use the formula to represent the graph, deepen the meaning of the score multiplication of "seeking how many fractions of a number is", and the process of calculating the score multiplication score.
Second, taking 3/4×1/4 as an example, let the students explain the meaning of the formula first, then use the graph to represent the meaning. Finally, in the calculation process based on the graph representation, the purpose of this is to The process of "and the number of forms" is the process of students consolidating the score multiplication and the calculation process of the score multiplication score.
Third, the students use the method of combination of numbers and forms to independently complete the “do one thing” in the textbook, further achieve the above goals, and accumulate knowledge for the calculation of summarizing scores and multipliers. It can be said that the overall teaching effect is good.
Through today's class, I have a deeper understanding of the idea of ​​combining numbers and shapes. Because the meaning of fractional multiplication and the principle of computational rules are more abstract, it is not easy for students to understand. Therefore, the use of graphics to visualize abstract problems is particularly important in the teaching of this unit. Throughout the textbooks, the infiltration of the combination of numbers and shapes also has different levels. For example, the fractional multiplication and fractional multiplication in the last semester use specific physical graphics to help students abstract mathematical problems from specific problems; scores in this semester The multiplier score uses intuitive geometry to help students understand the calculation of score multiplication scores; in the next score multiplication application, we will also use line segment diagrams to help students understand the problem of fractional multiplication; the graphics used are increasingly simple It embodies a process in which the textbook combines the idea of ​​number and shape.
The process of combining numbers and shapes is not a simple abstraction that becomes an intuitive process, but an abstraction becomes intuitive, then from intuitive to abstract, that is, two aspects of "the number of shapes" and "the number of forms" The organic combination, only the complete is the "interaction" between the number and shape of the students, in order to make them perceive the "digital combination", so that they can consciously apply the "digital combination" method when solving problems.