Reflections on the teaching of factors and multiples in fifth grade (1) Comparison and difference between teaching materials and knowledge points
1. Compare the difference of knowledge setting between new textbooks and traditional textbooks.
This part of the knowledge about number theory is the traditional teaching content, but the teaching materials have changed a lot while inheriting the excellent practices in the past. No matter from the macro aspect-the division of content or from the micro aspect-the design of specific content is original. The understanding of "factor and multiple" is different from the original textbook in the following two aspects:
(1) The concept of "divisibility" is no longer mentioned in the textbook of the new curriculum standard, and the learning of this unit is no longer introduced from the observation division formula, but the opposite is done, and new knowledge is introduced through the multiplication formula.
(2) Change the word "divisor" to "factor".
What is the reason for this change? Teachers must study the textbook carefully and deeply understand the editor's intention in order to control the textbook correctly and flexibly. Therefore, I learned the following information through studying teaching staff:
Students' original knowledge base is that they have been able to distinguish divisibility from remainder division and have a clear understanding of the significance of divisibility. The lack of the definition of divisibility will not affect students' understanding of other concepts. Therefore, the mathematical definition of "divisibility" has been deleted from this textbook.
2. Comparison of similar concepts.
(1) "factor" is not this "factor".
In the same multiplication formula, both refer to the integers on both sides of the multiplication symbol, but the former is relative to the product, synonymous with the multiplier, and can be decimal. The latter is relative to "multiple" and synonymous with the former "divisor". When "X is a factor of X", both can only be integers.
(2) The difference between "multiple" and "multiple".
The concept of "more" is broader than "more". We can say "1.5 is five times of 0.3", but we can't say "1.5 is a multiple of 0.3". When we find the multiple of a number, we use the same method as "How many times is a number", but the "multiple" here refers to the integer multiple.
Second, the application of practical teaching methods
1, which specifies the scope of application of numbers. The concept of "factor and multiple" is directly applicable to narrative method. The concept of this knowledge point is an artificially defined range. Therefore, there is no requirement for students' impressions and first contact to explore and explore, giving students an intuitive feeling. The application range of "factor and multiple" is in the category of non-zero natural numbers, and it has nothing to do with decimals, fractions and negative numbers (although it has not been learned, a few students understand it). At the same time, it is emphasized that-not 0-0 is multiplied by any number to get 0 and divided by any number to get 0. It is meaningless to study its factors and multiples. My experience is that students can clearly understand the concepts stipulated in mathematics by direct narration. Therefore, the concept of natural numbers is reviewed by direct introduction, and then the multiplication formula 3*4= 12 is written, which shows that in this formula, 3 and 4 are factors of 12, and 12 is a multiple of 3 and 4.
2. In continuous teaching, students can explore how to find the factor and multiple of a number. Pay attention to a format and symmetry in blackboard writing, so that students can find the finite and infinite contrast between multiple and factor number, and then find that the minimum factor of a number is 1 and the maximum factor is itself. The minimum multiple of a number is itself, but there is no maximum multiple. These are the details that should be paid attention to in class, and they are also very important for students to cultivate good study habits.
The second volume of the fifth grade (2) Reflections on the teaching of factors and multiples. Today, I learned a new lesson "Factors" with my children. For "factor", it is the first knowledge that children come into contact with, but for the word "factor", children are no strangers, because they have a preliminary understanding of the factors in the multiplication formula. So for this class, I have the following feelings:
First, the initial perception, the combination of numbers and shapes allows students to form representations.
In teaching, I first let students look at the picture formula through the scene map of the plane map in the textbook, and use my fifth-grade thinking to express it with different multiplication formulas. This link is relatively simple for students to list, and basically all students can list it well. Then, according to the formulas listed by students, the meanings of factors and multiples are deduced. In the design of this link, due to the diversity of methods, it provides space for different thinking and stimulates students' thinking in images. With the help of the relationship between "shape" and "number", it lays a good foundation for learning the concept of "factor and multiple" in the next step and effectively realizes the connection between existing knowledge and new knowledge. Better divide the difficulties and make students easily accept the formation of knowledge.
Second, explore independently and learn from neighbors.
After the students know the meaning of factors and multiples, next, show all the factors and let the students find 18 by themselves. In order to find all the factors of 18 better and more comprehensively, let two people at the same table cooperate with each other to complete it. Through teaching, it is found that students' cooperative ability is very strong, which can be accurately expressed in mathematical language, and most students can also find and find all the factors of 18 well in the process of cooperation.
Third, experience the joy of learning in practice.
In the last part, I designed exercises at different levels. First, let the students talk about some exercises about the meaning of factors and multiples to deepen their understanding of knowledge points. The main purpose is to make students understand that factors and multiples do not exist separately, but exist together. It is necessary to find out who is the factor of who and who is the multiple of who. According to the teaching, the students have mastered it quite well. Then it shows the factors that students look for different numbers. The design of this link adopts different forms, such as: finding friends, you do it, I do it, and the fastest way to help students understand knowledge. In this process, students are very interested and passionate, and the classroom atmosphere is warm, which also allows students to experience the happiness of learning in a relaxed atmosphere.
Disadvantages:
There are still many shortcomings in the teaching of this class. Although I know that the new curriculum standard puts forward that students should be the main body, and teachers only guide and cooperate, in the teaching process, many places still talk too much involuntarily, leaving too little room for students to explore independently.
For example, in the process of finding the factor of 18 in teaching, children are worried that it is the first time to contact the factor, and they don't know enough about the concept of the factor, so they make mistakes of one kind or another, so they guide too much and explain too carefully, so the space for them to explore independently is too small to reflect the students' subjectivity well.
Reflections on the teaching of factors and multiples in the fifth grade (3) The new textbook is different from the old one. For example, when understanding "factor and multiple", it is not based on the concept of divisibility, but directly derived from the multiplication formula. The purpose is to subtract the mathematical definition of "divisibility" and reduce the cognitive difficulty of students, although "divisibility" does not appear in the textbook. I fully embody the students' dominant position in teaching, provide enough time and space and appropriate guidance for students' exploration and discovery, and at the same time, in order to improve the effectiveness of classroom teaching, I will talk about my teaching experience from the following three aspects.
First, doubt transfer, ignite the spark of learning
A good beginning is half the battle. I use "spelling and posing" as a dialogue to get to the point, which can not only arouse students' interest in learning, but also correspond and depend on each other. Effectively penetrate and expand perception multiples and factors.
When teaching the multiple of a number, I design students to explore the multiple of 3 independently according to their own learning situation. I designed a learning link that tried to practice-cause conflict-discuss and explore. Students begin to practice independently with the requirement of "right and good". The methods for students to find multiples are: adding 3, multiplying 1, 2, 3 ..., using multiplication formula and so on. On the basis of students' full discussion, I organize students to evaluate "good". Some students think that it is good to grow from small to uppercase because it is orderly; Some students think that writing multiples is very fast, not affected by the previous multiples, and they can quickly find out what the first multiple is. Students find that they can't write multiples of 3, but they all look at each other and look around. Through discussion, the students think that ellipsis is more appropriate. A punctuation mark in the Chinese lesson solves a math problem, and students can find the problem and solve it by themselves, from which they can experience the pleasure of solving problems and the sense of accomplishment in mastering new knowledge.
Second, practice, internalize examples and understand multiples and factors.
I create an effective mathematics learning situation, combine numbers and shapes, and turn abstraction into intuition. First, let the students put the 12 square into different rectangles, then let the students write different multiplication formulas, and show the meaning of the factors and multiples of the multiplication formula with the help of multimedia. In this way, on the basis of students' existing knowledge, students can independently experience the combination of numbers and shapes from hands-on operation and intuitive perception, and then form the meaning of factors and multiples, so that students can initially establish the concept of "factors and multiples". In this way, we can fully study, use and excavate teaching materials, and use students' existing mathematical knowledge to draw out new knowledge, thus reducing the difficulty and achieving good results.
Third, pay attention to details and cultivate students' habits.
The most common mistake students make when looking for a factor of a number is to miss it, that is, to find it incompletely. How to find out all the factors in a certain order is also the difficulty of this course. Therefore, when students communicate and report, I combine the thinking process described by students with the lens guidance to form an organized blackboard writing, such as: 36÷ 1=36, 36÷2= 18, 36÷3= 12, 36 ÷.
Undoubtedly, such blackboard writing helps students to think in an orderly way and form a clear problem-solving idea. Teachers can match the blackboard writing factors end to end as in textbooks, and it is not easy to miss them. Students will also feel that as the process goes on, the smaller the interval, the less the number to be considered. When they find two adjacent natural numbers, they will naturally stop looking. The teaching of writing format details not only avoids the teacher's lengthy explanation, but also effectively breaks through the teaching difficulties. I believe that it is beneficial to students and the classroom to moisten things like this.
Because this class is a concept class, a lot of things are said by the teacher, but it does not mean that students passively accept it. Before teaching, I knew that the time of this class would be very tight, so when preparing lessons, I carefully studied the teaching materials and carefully analyzed the lesson plans to see where the time could be less, so I summarized the characteristics of multiples, shortened the demonstration time of this link and presented it directly with three small questions. I think the actual effect is ideal. In the classroom, we should also use multimedia to present the factors that students are looking for in time and guide students to sum up their findings: the smallest factor is 1, and the biggest factor is themselves. It is necessary to keep up with personalized language evaluation in time, activate students' emotions and keep their thinking active.
Reflections on the teaching of factors and multiples in the fifth grade (4) First of all, we must distinguish between "multiples and factors" and "multiples and divisors".
The two statements of "multiple and factor" and "multiple and divisor" are only different from those in the old and new textbooks, but in fact they all refer to the same number. (that is, the factor is also a divisor)
Second, why didn't the tenth textbook mention divisibility when it talked about "multiples and factors"?
Maybe my thoughts are still influenced by old textbooks. In my opinion, when it comes to "multiples and factors", we should talk about divisibility, because divisibility is the condition for learning "factors and multiples", and students can learn divisibility without this condition. As long as the teacher is not careful in teaching methods, students will soon enter the decimal. But in the actual teaching process, I also realized the benefits of not mentioning divisibility in textbooks. However, a new question rises in my heart. When and under what mathematical environment did the concept of "divisibility" be put forward in the S edition textbook? Will it appear in the sixth grade curriculum reform? I will keep hope.
Thirdly, teachers should pay attention to "flexibility" when teaching multiples of 2, 5 and 3.
1, when teaching multiples of 2 and 5, we use the same method to find their multiples, which is easy for students to master, and they can quickly name multiples of 2 and 5 and accurately find their multiples. At this time, the teacher should turn the students' thinking to how to find multiples of 2 and 5 at the same time. Then guide students to summarize the characteristics of being multiples of 2 and 5 at the same time, and further increase their knowledge.
2. When teaching the characteristics of multiples of 3, teachers should first ask students to find the characteristics of multiples of 3 with multiples of 2 and 5, so that students can't find the characteristics of multiples of 3 when trying this method. At this time, teachers should guide students to sum up the characteristics of multiples of 3 in another way. Using this feature, teachers can consciously write some numbers (there are multiples of 3 and multiples of 3, and
When the students are familiar with the characteristics of multiples of 3, the teacher's topic changes. Can you summarize the characteristics of multiples of 9? Under the teacher's inspiration, students' interest in knowledge increased greatly, and then the teacher inspired students to find the characteristics of multiples of 9 by finding multiples of 3, and students can easily summarize the characteristics of multiples of 9. By looking for the characteristics of multiples of 9, students not only consolidate the characteristics of multiples of 3, but also expand their knowledge, thus achieving the purpose of consolidating and transferring knowledge.
3. When students master the characteristics of multiples of 2, 5 and 3, teachers should guide students to further summarize and synthesize these three characteristics, so as to get the characteristics of multiples of 2, 3 and 5 at the same time.
Through such teaching, students can truly feel the word "flexibility" and develop their knowledge vertically and horizontally.