Reflection on the teaching of multiplication and division in grade four 1 multiplication and division is another new algorithm after multiplication and division exchange method and multiplication and division combination method. In arithmetic theory, it is also called the distribution property of multiplication to addition, because it is a single operation different from multiplication and transformation law and associative law. To some extent, it is more abstract, so it is more difficult for students. How to make students better grasp and remember? I think students' own knowledge is more memorable than what they instill. So I designed the shopping situation from the beginning, so that students can walk into life in a relaxed and happy environment and start learning new knowledge. In the teaching process, let students understand the multiplication and division method in the process of continuous perception and experience, so as to summarize the multiplication and division method by themselves. I designed it like this:
First, let students know the multiplication and division method and the distribution method from life examples.
Twenty-five groups participated in the tree planting activities. Eight people in each group are responsible for digging holes and planting trees, and four people are responsible for lifting water and watering trees. Reorganizing the teaching materials and changing the number of students in each group from (4+2) to (8+6) 25 can highlight the convenience brought by the application of multiplication and division and lay the foundation for the application of multiplication and division. And the words "digging a pit to plant trees" and "lifting water to water trees" were changed to "digging a pit to plant trees" and "lifting water to water trees", which reduced the difficulties that words brought to students' understanding.
By introducing problem solving, students can get two formulas. Grasp its meaning first, and then highlight its form of expression.
For example, (4+2)×25 means six 25s, and 4× 25+2× 25s means four 25s plus two 25s, meaning six 25s. So the numbers are the same, so they are equal. Then observe their formal change characteristics, the sum of two numbers multiplied by a number can be written as the addition of two products, and then grasp the characteristics of factors for analysis. On this basis, I am not in a hurry to let students speak law, but continue to provide students with challenging research opportunities.
With the help of different solutions to the same practical problem, students can realize the rationality of multiplication and division. This is something that students encounter in their lives. Students can understand the meaning expressed by the two formulas and successfully solve the problem of equality between the two formulas.
Second, break through the teaching difficulties of multiplication table
Let students experience the law and explore the forming process. The process value of exploring concise distribution law is no less than the value of mastering knowledge. Since it is a "law of laws", it is to let students observe, compare, guess and verify the laws of multiplication and distribution without trace in scientific process design. In the process of exploration and induction, mathematical ideas and methods from special to general and from general to special are permeated.
Compared with other laws in multiplication, the structure of multiplication distribution law is the most complicated, and the ability of equation deformation is the difficulty in teaching. In order to break through this teaching difficulty, starting from the practical problems in life, the introduced situation is open, 25 groups participate in tree planting activities, and each group is responsible for others. * * * How many students took part in this tree planting activity?
Students take the initiative to design solutions and arouse their enthusiasm. Let students choose their favorite scheme according to their own ideas, open it to students, give full play to students' subjectivity, and verify its internal laws through discovery, speculation, questioning, feeling, adjustment, verification and perfection, thus summing up the multiplication and division method. Let students freely use their knowledge, experience and way of thinking to try to solve problems. In the activity of exploring the similarities between this series of equations.
On the basis of students' existing knowledge and experience, let's study abstract formulas together, find their own characteristics, and sum up their laws. In the process of finding the law, some students observe horizontally, while others observe vertically. The purpose is to let students try to solve problems from their own mathematical reality, so that students with different thinking levels can get corresponding satisfaction and gain corresponding successful experience.
Of course, the meaning of the law of multiplication and distribution needs to be explained in combination with the form, which is more conducive to the establishment of the model.
It is necessary to reflect on the teaching of multiplication table, so teachers must treat it well. Continuous reflection can promote continuous progress. With the above article, I hope to make progress with my colleagues.
Reflection on the teaching of the distribution law of the second multiplication in the fourth grade; Calculation teaching is an important part of primary school mathematics teaching, and almost every textbook contains calculation teaching, among which "simple calculation" teaching is a "bright spot" of calculation teaching. Learning simple operations well can not only reduce the difficulty of calculation, but also improve the accuracy and speed of calculation. More importantly, it enables students to integrate the operational laws such as theorems, laws, rules and properties they have learned, so as to achieve the purpose of applying what they have learned, thus cultivating students' good calculation habits.
The teaching of multiplicative distribution method is based on the students' study of additive commutative law, additive associative law, multiplicative commutative law and multiplicative associative law. Multiplication and division are also the difficulties in learning these laws. Therefore, for the teaching of multiplication and division, I don't pay attention to the regular mathematical language expression, but pay attention to guiding students to actively participate in the process of understanding, experiencing and discovering mathematical laws, learn dialectical thinking, cultivate good thinking habits, and truly implement students' dominant position.
In teaching, I mainly achieved the following points:
1. Pay attention to students' existing knowledge and experience. Interest is the catalyst for forming good study habits. Taking the familiar situations around students as the starting point of teaching can stimulate students' active learning needs and create interesting learning situations closely related to their living environment and knowledge background. That is, according to the diagram, we ask a question: how much does it cost to buy five coats and five pants? By comparing the two formulas, we can awaken students' existing knowledge and experience, consciously participate in the teaching of new knowledge and stimulate students' interest in learning.
2. Guide students to explore actively. It is an important task for math teachers to cultivate students' learning habits of active inquiry. Let the students solve problems in different ways according to the provided questions, so as to get the equation of (65+45)×5=65×5+45×5, and let the students observe and initially perceive the "multiplication and division method". Let's take another example: if we want to choose two other clothes and buy the same quantity, how much do we have to pay for one * * *? Can you ask a * * to pay in two ways? Let students feel the existence of multiplication and distribution law in the process of solving problems again. Then I guide students to observe, initially find the law, then guide students to verify their findings with examples, get more equations, continue to guide students to observe until they find the law, and question whether there is a counterexample, and then unanimously determine the existence of the law and get the letter formula.
For the teaching of multiplication and division, I emphasize observing, comparing and summarizing the listed formulas through various calculation methods, boldly putting forward my own conjecture and verifying it with examples, so that students can feel complete. Let students experience the basic process of mathematical research in class: the process of perception-guess-verification-summary-application. Students not only discovered multiplication, division and distribution independently, but also mastered the method of scientific inquiry and developed their mathematical thinking ability.
3, pay attention to cooperation and communication, multi-directional interaction. Students can learn to cooperate and communicate with others in the process of learning mathematics knowledge, which is also a good study habit, and advocating the dynamic generation of classroom teaching is an important concept of the new curriculum standard. In mathematics learning, each student's thinking mode, intelligence and activity level are different. Therefore, in order to make different students develop in mathematics learning, I base myself on the multi-directional interaction among students, teachers and students, especially through mutual inspiration and supplement among students, to cultivate their sense of cooperation and realize the active construction of "multiplication and division method". In such an open environment, students learn from others, experience the process of guessing, verifying and summarizing knowledge, and experience the happiness of success. It not only cultivates students' problem consciousness, but also broadens students' thinking and strengthens the organization of thinking, and students also take the initiative to learn.
4. Exercise design pays attention to the development of students' thinking ability. In the design of exercises, I basically respect the knowledge system in textbooks. In the fourth exercise, the comparative exercise of three groups of questions is mainly to consolidate students' understanding of multiplication and division, so that students can experience the simplicity of calculation through comparison. In the process of calculation, we will choose a more reasonable method to calculate, which will help students improve the correctness of calculation and help students develop good calculation habits. When I design teaching, I first show a set of questions. After the students found the connection between them, I intentionally asked the girls to do a simple question, so that the students could initially feel that the questions done by the girls were relatively simple. Then I showed the second group, or deliberately asked the girls to do a simple question, so the girls had priority. So far, I have guided students to find that sometimes it is easier to add first and then multiply, and sometimes it is easier to multiply first and then add. You can choose it reasonably according to the actual situation, even.
Through this design, the students have experienced two rounds of competitions, and have a preliminary understanding of using the multiplication table to make the calculation simple, and have a strong interest in learning, which lays a good foundation for using the multiplication table to make the calculation simple in the next class. Finally, a variant question is added: "How much is 5 jackets more expensive than 5 pants?" This is a variation of multiplication and division, and this kind of problem will be encountered in the third class, so here is a foreshadowing. From basic questions to variant questions, there is an organic connection. Make students gradually deepen their understanding, and on the basis of figuring out the arithmetic, students can flexibly use what they have learned to practice according to the characteristics of the topic. Judging from the feedback in class, students are very enthusiastic and can apply what they have learned. Students' thinking ability has been developed through their own efforts and exchanges and cooperation with their classmates.
The teaching process is a process of continuous exploration and pursuit. As a math teacher, I hope to help students develop good math study habits faster and better during the limited contact time with students, so that our students can benefit for life. This is a goal worthy of my eternal pursuit and efforts.
Reflections on the teaching of multiplication table in grades four and three. First, grasp the key points. Let students understand the meaning of multiplication and division.
Draw two formulas in the textbook and write them into equations. Analyze the relationship between the two formulas and write several similar formulas. Find the law, communicate the law by language or other means, and give the operation law expressed by letter formula. This arrangement is convenient for students to experience the process of observation, analysis, comparison and proof. In the process of cooperation and communication, students' understanding of concise distribution law will gradually rise from perceptual to rational. The textbook says: The focus and key of teaching should be to guide students to discover the rules independently and communicate the rules with their peers through language or other means.
In teaching, I follow the above steps to teach. However, after I instructed the students to write the formula into an equation and let them observe the connection and difference between the left and right formulas, the students simply didn't know where to start. In their impression, connection is to connect according to the meaning of multiplication. There is no numerical analysis at all. It can be said that I was confined to my original thinking and didn't jump out to see it. After asking students to write several sets of formulas and observe and analyze the differences between the left and right sides of several sets of equations, students still can't express this law in words. The scene was cold for a while, and then I had to let the students express it directly in letters. After changing to this form, many students can write.
I don't understand why. I gave time and the group communicated. In group communication, I found that the students in our class could not find the rules at all and could not express them in words at all. Is it because the slope is not enough? There is still a problem with teaching at ordinary times. These should be analyzed one by one.
In short, this key has not been completed today.
Second, consider students' learning situation and respect students' subjective feelings.
After instructing the students to spell two formulas into an equation, I asked the students to communicate. Results Students gave two kinds of (65+45)×5=65×5+45×5 and 65×5+45×5=(65+45)×5. I wrote both methods on the blackboard. The textbook requires the first one, that is, write (65+45)×5 on the left side of the equation to help students understand the meaning of multiplication and division. I think, from the meaning of multiplication, the understanding of meaning can be done in our class. In terms of meaning, both methods are actually possible. Therefore, when students in our class use letters, there are two ways to express them: (A+B)×C=A×C+B×C and a× c+b = (a+b )× c. I wrote it on the blackboard, but I drew a star on the standard line, telling my classmates that this line is generally used to represent multiplication and division.
Third, pay attention to the changes in the law of multiplication and distribution in practice.
The significance of multiplication and division is to simplify calculation. So in practice, I pay attention to let students explain clearly how to use it. Especially think about 74×(20+ 1) and 74×20+74 for the second question. Be sure to make it clear where the 1 in brackets comes from. However, simple ideas are not deep enough. When the students finished thinking about doing the fifth question, more than half of them did not use the simple method. Even though they have practiced the fourth question.
Today I teach the arithmetic-multiplication and division. For solving examples, students can list different formulas, 45*5+65*5 and (45+65)*5, and get the same calculation result through their own calculation, and then write these two formulas as equation 45*5+65*5=(45+65)*5. Then let the students imitate several formulas, observe the equations and summarize their findings. Students will use letters to express this rule, but it is difficult to express it in words. Think about doing the 1 problem. Only a few students filled in the third question by mistake. It actually includes the following exercises. The correct rate of rewriting A*C+B*C into (A+B)*C is higher than that of rewriting (A+B)*C into A*C+B*C, which may be because the students were influenced by it before: 45 fives plus 65 fives.
Think about the third subitem 74*(2 1+ 1) and 74*2 1+74 in the second question. I'll let the students who think they are equal explain their reasons. Students can rewrite the formula as 74*2 1+74* 1 for reuse. After the students understood, I added 77*99+77=□(□○□) to let the students fill in the blanks, and the completion was much better. In the expanding exercise, I added A * B+B =□ (□□□) and A * B+B =□ (□□□ □) to let the students further understand the meaning of multiplication and division. However, students are often used to the formula 48*3+48*2 to calculate after thinking about doing the fifth question, but they can't use the (3+2)*48 to calculate flexibly. Although simple calculation by multiplication and division is the content of the next class, I also reflect on my own teaching shortcomings. In the teaching of examples, I only pay attention to getting the equation, but ignore asking students to compare the formulas on both sides of the equation. So this shortcoming can be made up in the calculation and comparison of the fourth question.
I believe that after this profound reflection on the teaching of multiplication table, teachers will do better in the future teaching, and I also hope that other teachers can learn from the main points and students can master the key points of learning.
Reflection on the Teaching of Multiplication Table in Grade Four The teaching of multiplication table is based on students' study of additive commutative law, associative law, multiplicative commutative law and associative law. This is a law that is difficult for students to understand and describe. Therefore, in teaching, I let students understand the multiplication and division method through continuous comprehension, experience and practice, so as to achieve the effect of mastering it skillfully.
First, from the students' existing life experience, through observation, analogy, induction, verification and application, deepen and enrich the understanding of multiplication and division. Infiltrate the method of understanding things from special to general, and then from general to special, cultivate students' ability to explore, discover and solve problems independently and actively, and improve students' awareness of mathematics application.
Secondly, in the teaching process design of this course, I try my best to embody some ideas of the new curriculum standard, pay attention to proceeding from reality, closely link mathematical knowledge with real life, and let students learn knowledge through experience. Example: Design a scene where a school buys books. Ask the students to help with their ideas. Xiu: "45 yuan has a story book and 35 yuan has a science and technology book. Buy three books each. How much does a * * * cost? " Ask students to try different methods to get: (45+35)×3=80×3=240 (yuan), 45× 3+35× 3 =135+105 = 240 (yuan). At this point, let the students observe that the results obtained by the calculation method are the same, and the two formulas can be connected by "=". Let students feel the model of multiplication and distribution law. Thus, the concept of multiplication and distribution law is introduced: "When two numbers are multiplied by the same number, you can multiply the two addends by this number respectively, and then add the two products, and the result remains the same." Expressed in letter form: (a+b) × c = a× c+b× c.
The atmosphere in this class is active and the students are very motivated. Through practice, it can be found that the child did not master it as expected. I will continue to strengthen my practice next class.
Reflections on the teaching of multiplication and distribution law in fourth grade 5 1. The teaching of multiplication table should not only pay attention to its shape and structural characteristics, but also pay attention to its connotation.
By solving the problem of "how many kilometers is the total length of Ji-Qing Expressway" in teaching, and combining with the specific living conditions, the result of (110+90) x2 =10x2+90x2 "is obtained, and only the shape characteristics of the equation are paid attention to in teaching, that is, the sum of two numbers is multiplied by one. Lack of understanding from the perspective of multiplication meaning. At this time, the teacher can ask, "Why are the two formulas equal? "Here, we should not only understand that the two formulas are equal from the perspective of problem solving, but also understand from the perspective of multiplication meaning, that is, the left side represents 200 2s, and the right side also represents 200 2s. So (110+90) x2 =110x2+90x2.
2, pay attention to distinguish the characteristics of multiplicative associative law and multiplicative distributive law, and do more comparative exercises.
The characteristic of multiplicative associative law is the continuous multiplication of several numbers, and the characteristic of multiplicative distributive law is the sum of two numbers multiplied by the sum of one number or two products. Students are particularly prone to make mistakes in exercises such as (40+4)×25 and (40×4)×25. In order to make students master it better, they can do more comparative exercises. For example, compare 15×(8×4) and15× (8+4); 25× 125×25×8 and 25×125+25× 8; In practice, you can ask: What are the characteristics and differences of each group? What are the characteristics of operational research? Can the calculation be simplified by using the algorithm? Why are you doing this?
3. Let students practice multiple solutions to a problem, experience the process of diversification of problem-solving strategies, optimize the algorithm, and deepen students' understanding of the law of multiplicative association and the law of multiplicative distribution.
Such as: calculation125× 88; 10 1×89 How many methods can be used? 125×88① vertical calculation; ② 125×8× 1 1; ③ 125×(80+8), etc. 10 1×89① vertical calculation; ②( 100+ 1)×89; ③ 10 1×(80+9), etc. Guide students to compare and analyze different problem-solving methods. When is the multiplicative associative law easy to use and when is the multiplicative distributive law easy to use? The multiplicative associative law and the multiplicative distributive law are obviously used to simplify the calculation. The multiplicative associative law is suitable for the formula of continuous multiplication, while the multiplicative distributive law is generally aimed at the formula with two operations. It is the goal of students' autonomous behavior to strive to achieve "calculation with simple algorithm", and they can flexibly choose the appropriate algorithm according to the characteristics of the topic.
Step 4 practice more
Practice the typical topic several times. Pay attention to the arrangement of practice quantity and time when practicing. You can practice every day at first, 1-2 days, and once a week later/kloc-0. The typical question type can be (40+4) × 25; (40×4)×25; 63×25+63×75; 65× 103-65×3; 56×99+56; 125×88; 48× 102; 48×99, etc. For special topics, you can practice intermittently and put forward the requirements that eugenics needs to master. Such as 68×25+68+68×74, 32× 125×25, etc.
The reflection on the textbook of multiplication table teaching in the fourth grade provides such a main picture: in spring, students carry out tree planting activities, and there are 25 groups, 4 people in each group are responsible for digging holes to plant trees, and 2 people are responsible for carrying water to water trees. The question to be solved is: 1. How many people are taking part in tree planting activities? Students list the formulas in two different ways, and then through calculation, they find that the two formulas can be connected by = (that is, 25 (4+2) = 254+252), so as to summarize the multiplication and division method by comparing the similarities and differences between the two formulas on both sides of the equal sign. When I teach in a class according to this teaching design, I find that the effect is not ideal, which is manifested in two points:
① Some students just mechanically recited the formula of the multiplication table, for example, when they saw 3544, they couldn't think of 3540+354;
② Because we don't really understand the connotation of multiplication and division, we can't understand its inverse application and the application of multiplication and division when the difference between two numbers is multiplied by a number. For example, they think 6464+3664 (64+36) 64; 265( 105-5)=265 105-2655。
In view of this situation, I redesigned the teaching plan. A question has been added: How many more students are responsible for digging holes and planting trees than those responsible for carrying water and watering? In this way, the students listed two other formulas and connected them with an equal sign after calculation: 25 (4-2) = 254-252. Next, I guide students to observe and compare the two groups of formulas, and fully discover the similarities and differences. In this way, students can find the connection between things, grasp the essence, find similarities, promote communication, and successfully realize self-construction and knowledge creation. Students' discoveries are naturally richer and more profound: whether it is the sum of two numbers or the difference between two numbers multiplied by a number, you can multiply this number first, then add or subtract. In addition, I also instruct students to observe the equation from right to left, trying to understand the multiplication distribution law in the sense of multiplication, that is, four 25 plus two 25 equals (4+2) 25, and four 25 minus two 25 equals (4-2) 25, which helps students to break through the teaching difficulty of reverse application of the multiplication distribution law.
Through the different teaching designs of the two classes, I think that studying the textbooks carefully, thinking more and excavating valuable resources in the textbooks will make the connotation of the textbooks broader and deeper, and also provide a broader space for cultivating and developing the flexibility of students' thinking.