Reflections on teaching fractions and division

Understanding and mastering the relationship between fractions and division can not only deepen the understanding of the meaning of fractions, but also lay the foundation for later learning improper fractions, mixed numbers, the basic properties of fractions, ratios, and percentages. Therefore, fractions The relationship with division plays an important role in connecting the previous and the following in the entire textbook. Next is the reflection on teaching fractions and division brought to you by Xuela. I hope you like it. Reflection Example on Fractions and Division Teaching 1 Mathematics teaching should start from students’ life experience and existing knowledge background, so that students can feel that mathematics is around them and learn mathematics in life. To make students realize the importance of learning mathematics and improve their interest in learning mathematics. Fractions and division are relatively abstract contents for primary school students. The reason why mathematical knowledge at the primary school level can be understood and mastered by students is not just the result of knowledge deduction, but the result of the interaction of specific models, graphics, scenarios and other knowledge. So when I designed the lesson "Fractions and Division", I considered the following two aspects: ? 1. Start by solving problems and feel the value of fractions. ? Start with the problem of dividing the pie and let students feel that when the quotient cannot be expressed by integers, fractions can be used to express the quotient. This lesson is mainly carried out from two levels. One is to use the students' original knowledge to use the meaning of fractions to solve the problem of dividing a pie into several equal parts and express it in commercial fractions; the other is to use physical operations to understand how to divide several pie into equal parts. Several parts can also be expressed as fractions. These two levels of development are designed from the perspective of problem solving. ? 2. The expansion of the meaning of fractions is synchronized with the understanding of the relationship between division. ? When expressing the quotient of integer division as a fraction, use the divisor as the denominator and the dividend as the numerator. Conversely, a fraction can also be viewed as dividing two numbers. It can be understood as dividing ?1? evenly into 4 parts, indicating such 3 parts; it can also be understood as dividing ?3? evenly into 4 parts, indicating such 1 part. In other words, the process of understanding and establishing the relationship between fractions and division is essentially synchronized with the expansion of the meaning of fractions. ? After teaching, I reflected on my own teaching and found that in terms of the state of mathematical knowledge stored in students' minds at the primary school level, in addition to being abstract, it should be mathematical knowledge that can be converted between abstract and concrete. The whole class teaching has the following characteristics: ? 1. Provide rich materials and experience the process of "mathematicalization". ? The understanding of the relationship between fractions and division is based on the use of concrete tangible objects and pictures as the medium, using hands-on operations as the method, and generating mathematical knowledge with the support of rich representations. It is a process of constantly enriching the perceptual accumulation, and gradually abstracting and modeling process. In this process, attention was paid to the following aspects: first, providing rich mathematics learning materials; second, on the basis of making full use of these materials, students gradually improved the conclusions they discovered, from text expressions to equations expressed in words and then to To express it with letters, it has experienced a process from complexity to simplicity, from daily life language to mathematical language, and also experienced a process from concreteness to abstraction. ? 2. The problem lies in the method, and the content carries the thought. ? Mathematics learning is a process of problem solving, in which methods naturally reside; learning content carries mathematical ideas. In other words, mathematical knowledge itself is only one aspect of our learning of mathematics. What is more important is to use knowledge as a carrier to penetrate mathematical thinking methods. ? As far as fractions and division are concerned, the author thinks that if we teach just to derive a relational expression, we have only caught the tip of the iceberg. In fact, with the help of this knowledge carrier, we also need to pay attention to the thinking methods such as induction and comparison contained in it, as well as how to use existing knowledge to solve problems, so as to improve students' mathematical literacy.

? Sample Reflection on Teaching Fractions and Division 2? The relationship between fractions and division is taught after students learn the meaning of fractions. The purpose is to enable students to initially know the division of two integers, whether the dividend is less than, equal to, or greater than the divisor. Their quotients can all be expressed as fractions. ? The teaching of this part of the content can not only deepen students' understanding of the meaning of fractions, but also serve as the basis for later learning of improper fractions, mixed numbers, the basic properties of fractions, ratios, and percentages. Therefore, the relationship between fractions and division plays an important role in the entire textbook. It plays an important role in connecting the previous and the next. If the relationship between fractions and division is taught purely from a formal perspective, students can learn very solidly. However, the calculation of 3?4=3/4 is often ignored. In order to let students know what is happening and why. , I organize teaching like this: ? 1. Understand new knowledge through practical operations? In teaching, I designed such a teaching situation, and divided a piece of cake equally among four children. How much did each person get? Let the students Take a round piece of paper to represent a piece of pie and divide it into points yourself to arouse your understanding of the meaning of fractions. Then it was shown that the 3 pieces of cake should be divided equally among the 4 children. How much would each child get? A group of four people would find a way to divide the 3 round pieces of paper equally among the 4 children. And let the group send representatives to the stage to demonstrate the scoring process. Through hands-on operations, students came up with two different ways of dividing, and derived two meanings, that is, each person gets three-quarters of a piece of cake, which can also be said to be a quarter of three pieces of cake. Through this In the process, students fully understood the arithmetic of 3?4=3/4. ? 2. Make students understand why fractions are used to express the results of division equations? After students understand the relationship between fractions and division, I consciously designed several exercises like this. 1?3= 8?9= 2?6= Let students write the calculation results in their exercise books and see who can finish the calculation first. As a result, some students raised their hands in one or two seconds, while some students took a long time to write down the calculation results. After the report, guide students to think: What is the difference between 1?3=0.333? and 1?3=1/3 8?9= 0.88? and 8?9= 8/9? The students’ most direct answer is: use recurring decimals to express Quotient calculation is too troublesome, and it is not quick and easy to use fractions to express it. At this time, tell the students that in the future, when calculating the quotient of dividing two integers, use fractions to express their quotient when the division cannot be completed or there are decimals in the quotient. This is simple, fast, and less error-prone. ? 3. Take the opportunity to extend the meaning and pave the way for subsequent learning. ? Introduce the difference between fraction and quantity to students for the first time. For example: ①? Divide a piece of cake into 4 equal portions. What fraction of the pie does each portion get? How many pieces of cake does each portion get? ② "Divide a 2-meter-long rope into 7 equal parts, and the length of each part is What fraction of the rope is this? How many meters long is each section? "③" Divide 4 kilograms of salt into 5 equal portions. What fraction of the weight of each portion is the total amount of salt/How many kilograms does each portion weigh? First let the students understand this The first of the three questions asks for "fraction rate". Fraction rate has no unit. The total number is regarded as the unit "1". Divide the unit 1 evenly into several parts and find out what fraction of one part is the total number. First, it is obtained by dividing the unit ?1? by the average score. For example, the scores for the first three questions are 1?4=1/4 1?7=1/7 1?5=1/5. The second question is to find the quantity of each portion. Each quantity has a unit. It is obtained by dividing the total quantity by the average number of portions. The second question of the first three questions must have the name of the unit. The algorithms are 1?4=1/4 (sheets) 2?7=2/7 (meters) 4?5=4/5 (kilograms)? Here, after the students understand the fraction and the quantity of each portion, they will prepare for the following The learning of fractions and percentage word problems provides a good foundation. 4. Allow students to construct new knowledge independently. When students find that the dividend in division is equivalent to the numerator in the fraction, and the divisor is equivalent to the denominator in the fraction, guide the students to put the numbers. Replace them with their names: dividend?divisor=divisor/divisor.

At this time, let students use the letters a and b to express the relationship between division and fractions in their exercise books. Most students wrote: a?b=a/b. The teacher took out the writing on the blackboard of a slightly inferior student and deliberately praised this student. While praising him, he suddenly turned around and gave the student a big cross on the back of his homework. Just when the students were all surprised and asked why they were wrong, a few quick-thinking people shouted first and said: "b cannot be equal to 0!" I immediately seized this opportunity and asked: "Why can't b be equal to 0?" . I continue to use the example in class to distribute a piece of cake equally to 4 people, and each person gets 1/4 of the cake. Let the students talk about what "4" in this fraction means. If "4" is replaced, What about "0"? The students suddenly realized: the denominator represents the number of equal parts that the unit "1" can be divided into, and it is meaningless to divide the unit "1" equally into "0" parts. When using letters to express the relationship between fractions and division----?a?b=a/b(b?0)?Students often forget that b here cannot be 0. Through such analysis, students can more deeply understand the reason why the divisor cannot be 0 in division, so the denominator in fractions cannot be 0. This does not directly tell students that the divisor cannot be 0 in division. The divisor is equivalent to the denominator in the fraction, so the denominator cannot be 0 either. But by analyzing the actual meaning of a fraction, students can fully understand the reason why the denominator in a fraction represents the number of parts of an average score, so the denominator cannot be ?0?. ? Shortcomings of this lesson: Although students have a thorough understanding of the connection between fractions and division, there are still differences between them that have not been guided to summarize. Division means dividing two numbers. It is an operation and an equation. A fraction can express the relationship between the numerator and the denominator, and it can also express a numerical value. ? Sample Reflection on Teaching Fractions and Division 3? Understanding and mastering the relationship between fractions and division can not only deepen the understanding of the meaning of fractions, but also lay the foundation for later learning of improper fractions, mixed numbers, the basic properties of fractions, ratios, and percentages, so , the relationship between fractions and division plays an important role in connecting the previous and the following in the entire textbook. The new curriculum standards point out: Students' teaching and learning content should be realistic, meaningful and challenging. These contents should be conducive to students' active observation, guessing, verification, speculation and communication and other teaching activities. This shows that Creating effective learning situations can guide students to carry out independent, exploratory, and cooperative learning activities and promote students' active participation. ? Therefore, when introducing the new lesson, I deliberately designed two division calculation problems: 8?9= 4?7= ? When the students saw these two division calculations, they breathed a sigh of relief and said: ?Such a simple two calculations? A question!? So I started a competition between men and women in the class, with boys taking the first question and girls taking the second question. After giving the order, the boy buried his head in calculation. Hu Wenxin, who was quick-thinking, already knew the answer and didn't even start writing. I signaled her not to tell the answer. I went around in a circle, and most of the students already had the answers under the prompts of the students who had already done it. Only a few boys were still calculating. ? After the report, I caused the students to think: What is the difference between 8?9= 0.88? and 8?9= 8/9? The students’ most direct answer is: using recurring decimals is not as fast and simple as using fractions. This introduction enables students to understand that the division of two numbers can be expressed as a fraction, laying the foundation for further learning about the relationship between fractions and division. ? After that, students can quickly use fractions to express the quotient by showing the formula for dividing two numbers. ? Use 1?3=1/3 in the example to guide students to discover that the dividend in division is equivalent to the numerator in the fraction, and the divisor is equivalent to the denominator in the fraction. Let students replace the numbers with their names: dividend?divisor=numerator /denominator. At this time, I asked students to use the letters a and b to express the relationship between division and fractions. Xue Longfeng went to the blackboard and wrote seriously: a?b=a/b. When I saw this student writing very seriously, I immediately praised her and asked the students to applaud her. Just when everyone was happy for Xue Longfeng, I made a small mark behind the calculation she wrote.

The student immediately expressed confusion. The teacher had praised her just now, but now he was judging her. A few quick-thinking people shouted first, saying: "b can't be equal to 0!" I immediately seized this opportunity and asked: "Why can't b be equal to 0?" The class suddenly became quiet, and no one could tell the reason. This difficulty is about to be broken through, and I feel a little excited. I continued to use the example of dividing a piece of cake equally among 3 people, and each person got 1/3 of the cake, as an example: Who can tell me what the 3 in this score means? Some students gave examples Hand answer: ?Think of the cake as a unit? 1?, ?3 means the number of equal parts to divide the cake. ?What if ?3? is replaced by ?0?? The students finally understand: the denominator represents the number of equal parts that the unit ?1? is divided into, and it is meaningless to divide the unit ?1? equally into ?0? parts. Just this?a?b=a/b(b?0)?Students often forget that b here must be emphasized and cannot be 0. Through such analysis, students can more deeply understand that the divisor cannot be 0 in division, and the denominator cannot be 0 in fractions. ? I think I handled this link better. Instead of directly telling students that the divisor cannot be 0 in division, the divisor is equivalent to the denominator in the fraction, so the denominator cannot be 0 either. But by analyzing the actual meaning of a fraction, we fully understand that the denominator in the fraction represents the average number of parts, and naturally cannot be divided into ?0? equal parts. ? There are successes and shortcomings. After class reflection, students have a relatively thorough understanding of the connection between fractions and division, but the differences between them are not guided in class to discover and summarize. Division means dividing two numbers, which is an equation, while a fraction is a number. This shows that my interpretation of the teaching materials before class was not deep enough and I had not yet grasped the integrity and coherence of the knowledge. In future teaching, strive to achieve a deep understanding of the teaching materials, and at the same time, consult more materials in order to expand and extend the knowledge of the teaching materials.

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