Reflections on the teaching of fractional addition and subtraction 1

? The addition and subtraction of fractions with different denominators are taught on the basis that students have mastered the addition and subtraction of fractions with the same denominator, which has many similarities with last class. The key point is to help students understand and master the addition and subtraction of different denominator fractions.

The design of this lesson embodies the following characteristics:

1, let students learn mathematics in specific situations.

Computer teaching is boring. In the new curriculum, the activity situation of "planting land according to needs" is created, and students can paint 1/2 and 1/4 on a rectangular piece of paper, which not only reviews the old knowledge, but also paves the way for the teaching of new knowledge.

2, operating experience, guiding students to explore independently, cooperation and exchange.

3. Mathematical knowledge can only be transformed into students' own knowledge through students' active participation and independent exploration. In teaching, teachers can pay attention to leave enough time and space for students, and with the help of hands-on operation, understand the reason why 1/2 plus 1/4 needs to be divided. Thus, the calculation methods of different denominator scores are obtained. During the whole activity, students are always in the process of discovering, asking and solving problems, and their learning enthusiasm is fully mobilized. Through the efforts of themselves and their peers, students understand reasoning and master algorithms, and have experienced the whole process of knowledge formation. At the same time, it infiltrated the idea of transformation.

4. Combine fractional addition and subtraction with problem solving, and cultivate students' ability to solve practical problems.

Let students know the practical significance of fractional addition and subtraction, improve their interest in calculation and further understand the application value of fractional addition and subtraction.

Improvement:

Although the teaching language pays attention to enlightenment, it is not bright and concise enough. I'm always worried that students won't, or don't narrate properly, want to take the place of speaking, or repeat students' speeches, which will affect the teaching rhythm.

Reflections on the teaching of fractional addition and subtraction II

The addition and subtraction of fractions is one of the important basic knowledge of mathematical operation. Mastering the calculation method of fractional addition and subtraction is an important index to evaluate whether students have good computing ability and sense of numbers. The addition and subtraction of fractions with different denominators taught in this lesson plays a connecting role in the addition and subtraction of fractions.

Success:

Pay attention to guiding students to construct the internal relationship between fractional addition and subtraction and integer addition and subtraction. Fraction addition and subtraction have exactly the same meaning as integer addition and subtraction, and they also have the same meaning. Addition refers to the operation of combining two numbers into one number, and subtraction refers to the operation of finding the other addend by knowing the sum of two numbers and one of them. Their calculation methods seem different on the surface, but they are essentially the same. They are characterized in that only numbers of the same unit can be added or subtracted. In this sense, it is necessary to unify the calculation to the same unit. When teaching the example 1, through the elf's prompt: Can you solve it with what you have learned? In fact, it points out the direction of exploration for students: transforming it into learned knowledge to solve it. Through students' independent thinking, it is found that scores have different denominators and different units, so they cannot be added directly. We should use the knowledge we have learned before to divide the fractions with different denominators into fractions with the same denominator, so that we can work it out. In other words, numbers in the same unit can be added and subtracted.

2. Pay attention to the cultivation of transformation concept. In primary schools, teachers not only impart knowledge, but more importantly, let students master the key and soul to solve problems. In this lesson, the infiltration of transforming ideas is particularly important. The addition and subtraction of different denominator fractions is how to solve new problems into old ones. The key point is the process of changing new knowledge into old knowledge, that is, changing the addition and subtraction of different denominator fractions into the addition and subtraction of the same denominator fractions. Strengthening this concept is conducive to children's lifelong learning in the future.

Disadvantages:

In the calculation, it is found that individual students use common multiples instead of minimum common multiples; Second, the result of the calculation did not become the simplest score, especially the multiple score of 3, which many students did not see, leading to mistakes.

Re-instructional design:

Pay attention to the general scoring method, focusing on the targeted practice of scoring multiples of 3.

Reflections on the Teaching of Fraction Addition and Subtraction (Ⅲ)

? The addition and subtraction of fractions with different denominators is the second lesson of Unit 5 "Addition and subtraction of fractions" in Book 5 of the new curriculum standard of People's Education Press. It is the teaching content after learning the first lesson "addition and subtraction of fractions with the same denominator", so in the teaching process, I grasp the connection between the two parts and start teaching closely around the meaning of fractions.

? This lesson focuses on students' understanding of arithmetic and mastering the addition and subtraction methods of different denominator fractions. After completing the teaching of this course, I think there are several aspects worthy of attention in the future teaching.

1, in the "knowledge review" session, students should be clear about the addition and subtraction of fractions with the same denominator.

Last class focused on the meaning of fractions, which is the key and foundation for us to learn the addition and subtraction of fractions with different denominators. Therefore, in the teaching of addition and subtraction of fractions with the same denominator, students must be required to fully understand the arithmetic and calculation methods of addition and subtraction of fractions with the same denominator.

2. In addition and subtraction teaching of different denominator fractions, don't stay in the natural state of students' learning.

As the organizer of learning, teachers should raise the teaching content to a higher level and let students enter an orderly, regular and mathematical thinking state from a natural state. For example, after students discuss the arithmetic of fractional addition with different denominators, teachers should promptly guide students to clarify the relationship between each step and previous knowledge.

3. Guide students to clarify the tasks of each step.

Through observation and discussion, students can clearly understand how to solve the problems encountered in the addition calculation of fractions with different denominators.

Different denominators become the same denominator-make the decimal units the same, which is the basis of calculation.

Common denominator (least common multiple of denominator)-general division-addition and subtraction into fractions with the same denominator.

Through the design of this teaching link, students can understand and master the algorithm and method of fractional addition with different denominators in independent inquiry, and it is more natural in the teaching of fractional subtraction with different denominators. So I want to make full use of the meaning of fractions in teaching to carry out comprehensive teaching.

Reflection on the Teaching of Fractional Addition and Subtraction (IV)

The addition and subtraction of fractions with different denominators is based on the addition and subtraction of fractions with the same denominator. Compared with the addition and subtraction of fractions with the same denominator, the difference in this part is that the total score is added in the calculation process. Therefore, the key of this course is to transform ideas, aiming at introducing new knowledge into the existing knowledge structure and allowing students to use existing knowledge to solve new problems.

When learning the addition of different denominator fractions, I guide students to think:+Can it be calculated directly like reviewing questions? Why not? Then can you find a way to calculate the sum of+with what you have learned? Students discuss in the form of group cooperation, and the conclusion is that the scores of different denominators are converted into the scores of the same denominator by the method of total score, and then calculated by the calculation method of adding the scores of the same denominator. Then the teacher once again leads the students to review what problems have been encountered in the addition calculation of fractions with different denominators, and how do we solve this problem? Importance of strengthening transformation thought in fractional addition calculation with different denominators. At the same time, in order to let students better understand why they need to transform, I showed a courseware to transform ""into "",which is more intuitive and clear. Students not only have a clear idea of transformation, but also have an understanding of arithmetic, and master the calculation methods of fractional addition with different denominators, thus forming operational skills. But in the subtraction teaching of different denominator fractions, students are allowed to practice independently.

After the whole class, I think there are several points worthy of attention in the future teaching:

First of all, teachers should use teaching materials flexibly. Example+teacher's transformation through courseware demonstration is vivid and intuitive, but it always feels that students understand under the influence of teachers and their autonomy is not strong. Because of the large amount of data in the examples, it is difficult for students to understand the idea of transformation by drawing or origami. Wouldn't it be better to change the data in the example to+,so that students can understand by drawing or origami without making courseware, and give full play to students' autonomy, creativity and hands-on ability? This makes me deeply realize that as a teacher, we should not only think from our own aspects, but also put ourselves in the other's shoes, prepare ourselves less and prepare more students, so as to give students more space and let them show their elegance on the small stage of the classroom!

Second, the teaching of calculation is rather boring. In practice, we should try our best to make it more interesting and competitive, and make students happy and willing to learn. We still have to work hard in this regard. Come on!

Reflection on the Teaching of Fraction Addition and Subtraction (5)

Today, I finished teaching the lesson "Addition and subtraction of fractions with different denominators", and my heart was filled with emotion. I was moved by these excellent students and a little depressed. The detailed analysis of the whole teaching process has given me a new understanding. Let's reflect on the success or failure of this class.

Overall evaluation:

First, use it flexibly and introduce situations appropriately.

? Addition and subtraction of fractions with different denominators is a calculation course, which is very boring for students. Appropriate introduction of situations can not only stimulate students' interest in learning, but also inject more vitality into the boring classroom. So before the new class begins, I first show the addition and subtraction formulas of two fractions with the same denominator for students to calculate, and then I show the addition and subtraction formulas of two fractions with different denominators to guide students to find differences and introduce topics. In this way, students not only reviewed the addition and subtraction methods of fractions with the same denominator, but also paved the way for the study of new courses. The smooth and natural transition from problem situations to new knowledge learning stimulated students' desire for knowledge and greatly mobilized their learning enthusiasm.

Second, self-study navigation, focusing on thinking.

Self-study guidance is a road map for students' autonomous learning and a "crutch" to help students walk. Therefore, in the design, students are guided to experience the process of independent exploration from three aspects: thinking by looking at pictures, trying to solve problems and exploring and discovering. So I designed self-study guidance in two steps, that is, let students solve the calculation method of fractional addition with different denominators first, and then learn the calculation method of fractional subtraction with different denominators. The design of each problem is also from shallow to deep, from help to release. First, let the students know why they should change the same initial score and how to change it. When they understand these two problems, they basically understand the arithmetic of fractional addition with different denominators. On this basis, let the students solve the calculation of fractional subtraction with different denominators by themselves. Therefore, in the guidance of self-study, it is pointed out that the focus of self-study is the combination of pictures and texts and thinking, so that self-study can be effective.

Thirdly, interaction after teaching, internalization and popularization of new knowledge.

If the detection in "learning first" is the key to finding problems, then "teaching later" is an important part of summarizing and refining the way of thinking. "How to transform" and "Why to transform" are two aspects that students should understand in the later teaching of this course.

After students try to calculate the test questions, guide them to observe and discover the similarities in the calculation process in time, and form a thinking method of "changing differences into similarities" and "solving new problems with the old", that is, "transformation", so that students can get out of the examples and solve the problem of "how to transform". Later, through the teacher's question, "Can you add and subtract the denominator directly without conversion?" Let students notice that the essence of representation in the calculation process is "different decimal units", let students know the truth and solve the problem of "why change".

When calculating and testing, we should pay attention to understanding from practice, discovering from practice, summarizing students' problems and piecemeal gains in time, refining while practicing, so that students can master the addition and subtraction methods of different denominator fractions.

Existing problems:

1. The designed exercise was not completed and the training effect was not achieved.

Because of paying attention to the clarity of the classroom in the later teaching, a lot of time was delayed, which led to the design of the exercise questions not being completed. It seems a little impatient when practicing in the later class, and students are not allowed to talk about the calculation process and only pay attention to the calculation results.

2. Lack of trust in students, inability to completely let go of students and excessive guidance.

This place is mainly reflected in the student report after class. I am a little impatient, afraid that my classmates can't speak well and can't speak clearly. I always want to help students say that I can't completely let them go.

3. Classroom control ability needs to be improved.

When students taught themselves, I found that some students did not follow the instructions to teach themselves. At this time, I didn't regulate them in time, but only gave individual guidance to individual students. If the re-guidance of students is stopped at this time, the self-study effect of students will be better than now, and the time of post-teaching will be shortened.

4. Only a few students with learning difficulties are concerned in the classroom, while some middle school students are ignored.

Teaching reconstruction:

If I am allowed to take this course again, I will reasonably integrate the time, especially sort out the problems exposed by students in the later teaching process, seize the students' wrong resources to teach soldiers, and let students learn the addition and subtraction methods of different denominator scores in exchange and mutual assistance, so as to complete the learning objectives of this class. This will also make the classroom time allocation more reasonable, and the classroom practice will achieve the training effect, and the students' learning effect will definitely be better than this class.

Reflections on the Teaching of Fraction Addition and Subtraction (VI)

The learning content of addition and subtraction of fractions with different denominators is a knowledge point after students have learned the basic properties, simplification, general fractions, reciprocity of decimals and addition and subtraction of fractions with the same denominator.

Key points: master the basic methods of converting scores of different denominators into scores of the same denominator, summarize the calculation methods of adding and subtracting scores of different denominators, and calculate them correctly to form the basic ability of adding and subtracting scores.

Difficulties: Using the idea and method of transformation, explore the addition and subtraction of different denominator fractions. After the whole class, I feel that my teaching ability is far from enough. There are many shortcomings, but they can't be sorted out in words. The following two points are just two of many shortcomings. It is worthy of attention in future teaching.

First, the calculation should talk about liquidation and learn the algorithm. Through the analysis of the whole class, after learning the addition and subtraction of fractions with the same denominator, students have a particularly strong migration ability, so it is easier to learn. The teacher's first question is to let the students know why the scores of different denominators can't be added directly. The addition and subtraction of fractions with the same denominator is relatively simple: the denominator is unchanged, as long as the numerator is added and subtracted. This can be understood by the meaning or unit of the score. So, why can't the scores of different denominators be added or subtracted directly? In this class, although I carefully prepare lessons and draw pictures, I don't pay enough attention to arithmetic in the course of class, so many students don't understand why scores of different denominators can't be added or subtracted directly. In students' practice, charts can be used again to demonstrate why students can't directly add and subtract fractions with different denominators. The denominator in a fraction indicates the unit of the fraction. When the unit of the score is different, it cannot be added or subtracted. For example, what are 3 pounds of apples and 4 pounds of watermelons? After the students understand this, they can come up with others by themselves.

Second, the understanding and treatment of teaching materials: take this lesson as an example. I designed this class around the important and difficult points in teaching. In the review and introduction part, I introduce it by dividing points, finding the least common multiple of denominator and adding and subtracting fractions with the same denominator. Although this has several advantages, addition and subtraction of fractions with the same denominator can not only pave the way for reviewing the necessary knowledge of decimal units, but also learn 1/4+3/65438.

In addition, in the combination of graphics and teaching, students can also know that the scores of the same unit can be added or subtracted. But in the step of finding the calculation method from the chart, the teaching methods are not all in place, and students can't understand the approximate score well through the chart. I can ask, "What kind of graph is Figure 1/4+ Figure 3/ 10?" Such questions can make students' thinking about knowledge collide with sparks. Then, after students' answers and teachers' graphic explanations, students can have a clearer grasp and understanding of why this process should be divided.

This lesson, there are too many key points in design, and it is difficult to implement. There is no good breakthrough in difficulty. After preparing lessons and taking this class, I deeply feel that the teacher's teaching philosophy is very important, and what I usually hear and feel is infiltrated into the classroom to help primary school students learn mathematics and understand mathematical reasoning. In addition, if you want to have a good class, the prepared teaching plan is of course important, and you must also have rigorous teaching content, interlocking teaching links, fascinating teaching scenes, solid teaching skills and teaching concepts that keep pace with the times. Only in this way can we make continuous progress and innovation.

Reflection on the Teaching of Fractional Addition and Subtraction (VII)

This lesson is taught on the basis that students have mastered the addition and subtraction of fractions with the same denominator and realized the significance and basic properties of fractions, focusing on helping students understand and master the addition and subtraction of fractions with different denominators.

First, let the students review the meaning of the score. After showing a series of scores, let the students freely choose the scores to form the addition formula and classify them. Then, through the calculation of a group of fractions with the same denominator, let the students recall the old knowledge, arouse the existing experience of calculating fractions with the same denominator, and let the students realize that only fractions with the same fractional unit can be added. Then, let the students realize the natural transition and reveal the questions according to the characteristics of another group of fractional addition. In the teaching of 3/ 10+ 1/4, the connection between old and new knowledge is highlighted, so that students can experience and transform their ideas in the process of mathematics learning. First of all, let the students think, can they calculate directly like reviewing questions? Why not? It is emphasized that the denominator is different and the decimal unit is different, so it cannot be combined directly. Since they can't, how can you find the answer of 3/ 10+ 1/4? It is suggested that we can solve it with the knowledge about fractions we have learned. Teachers patrol, guide and observe students' inquiry and participate in students' inquiry. I invited three students to communicate, let them fully describe their own exploration process, face the whole class, and then exchange calculation methods, focusing on asking students to explain why they should go too far first. Make students fully realize that scores with different denominators have different fractional units, which can't be calculated directly, but can only be calculated directly after converting the scores with the same denominator into general scores. On this basis, let students have a clear idea: divide first and then calculate. For the subtraction of fractions with different denominators, let the students solve it themselves.

After solving the addition and subtraction of fractions with different denominators, guide the students to sum up "How do you think the addition and subtraction of fractions with different denominators can be calculated?" After full exploration and thinking, the students quickly summed up: divide the fraction first, and then calculate it according to the calculation method of adding and subtracting the fraction with the same denominator. The teacher wrote on the blackboard: general score → transformation, and explained that the result should be turned into the simplest score in the end.

Looking back on the teaching of this course, I think there are several shortcomings:

1. Not enough has been done to cultivate students' inquiry ability, but students still do as the teacher asks.

2. The design consideration of some teaching links is not careful enough, and the connection of each link is not smooth enough. For example, after reviewing the calculation method of fractional addition with the same denominator, students can guess how fractional addition with different denominators is calculated. This design can stimulate students' interest in learning and make the original boring calculation vivid.

3. In the process of calculating the addition and subtraction of fractions with different denominators, some students have forgotten this knowledge for some time and don't know how to do it. In addition, the teacher should call the least common multiple of the two denominators the common denominator, which will be easier to calculate.

In a word, if I can pay full attention to students' original cognitive level in future education and teaching, seize this teaching opportunity, plan and select some learning materials suitable for students' cognitive level, set up suitable teaching scenes, throw out questions directly, and let students discover, summarize and experience by themselves, it will be more valuable than the teacher's step-by-step guidance, and it will be more able to discover and arouse students' interest.

Reflection on the Teaching of Fraction Addition and Subtraction (8)

First, the limitations of teaching materials

1, the textbook is too abstract and far from the reality of students' life.

2. Without creating a scene for students to explore actively, students can't explore actively.

Secondly, I have the following ideas about the current teaching plan.

1, which changed students' learning style and changed traditional receptive learning into active inquiry learning.

If we teach this course according to the traditional teaching method, it will probably be a process: first review the addition and subtraction methods of fractions with the same denominator, so that students can make it clear that when two fractions are added, the units of fractions must be the same. Then tell the students that the scores of different denominators add up, and the units of the scores are different. They should be divided first, and then calculated according to the method of adding and subtracting the scores of the same denominator. Finally, arrange a certain amount of practice.

The teaching of this course completely breaks the traditional teaching methods, allowing students to find problems in situations and operate in the form of group cooperation. In the operation, students found that the fractional units were different and could not be added, so they averaged the two fractions again through the operation to make their fractional units the same, and then added. The above process is entirely the result of students' independent inquiry. In this process, every group of students are cooperating and every student is actively exploring. The knowledge that scores of different denominators should be added first is completely discovered by students themselves. Moreover, in the whole process of cooperative inquiry, students' cooperative learning ability, active inquiry ability and problem-finding ability are cultivated. In the whole process, teachers never appear in the classroom as knowledge authorities, but as collaborators and guides for students' learning.

2. Let students experience in the inquiry, and further understand that the addition and subtraction of fractions with different denominators should be divided first.

In the new curriculum standard, not only the target verbs such as "knowing, understanding, mastering and applying" are used to describe knowledge and skills, but also the process target verbs such as "feeling and experiencing" are used to describe the level of mathematical activities. It can be seen that the new curriculum standard puts forward higher requirements for students in mathematical thinking, problem solving, emotion and attitude.

The teaching process of "addition and subtraction of fractions with different denominators" is not only an inquiry process, but also a concrete mathematical activity process in which students actively participate. As an activity process, we should pay special attention to students' experience, so that students can understand the essence of comparison in specific situations and gain some experience.

(1) The inquiry information is provided by students.

(2) Students begin to calculate and get the sum of two scores.

(3) The score units of the two scores are not the same, so they cannot be added directly, resulting in students' thinking conflicts.

(4) Students summarize the rules of addition and subtraction of different denominator scores.

(5) Verification, so that students can experience the rigor of scientific inquiry.

3. Connect with real life and use situations throughout the class.

Good topic introduction can arouse students' knowledge conflicts, break students' psychological balance, stimulate students' interest in learning, curiosity and thirst for knowledge, attract people's attention and reflect the whole class. One of the arts of introducing new courses is to take the problems in life as an example, so that students can truly realize the necessity of learning mathematics knowledge and take the initiative to learn.

At the beginning of class, students became familiar with the topic of birthdays, which immediately aroused their interest in learning. Then let the students talk about the schemes of dividing the cake. On the basis of guessing whether these schemes are feasible, the problem to be studied today is "addition and subtraction of fractions with different denominators".

Then, replace the cake with a round piece of paper, so that students can take the initiative to explore, and their enthusiasm for learning suddenly rises. In practice, the effect is good.

Finally, an extra-curricular expansion problem is put forward: today we learned the addition and subtraction of different denominator fractions. Please think again with what you have learned today. Which is feasible and which is not? It not only expands students' thinking space, but also cultivates students' ability to solve life problems by using mathematical knowledge, and also plays an echo role from beginning to end.