Reflection on the score by integer teaching

Part 1: Regression of Scores by Integer Teaching

This part of the textbook is based on the meaning of the integer multiplication and the calculation of the score addition. Through teaching, I feel a lot:
First, guide independent exploration, understand the meaning of the multiplication of fractions and integers.
1. When introducing a new lesson, guide the students to paint 3 meters. The purpose is to let the students realize that 3 meters can be calculated by addition, or multiplication, and then use the listed addition formula to understand the score and multiply the integer. The meaning of the knowledge structure is paved for the calculation method that guides students to explore the multiplication of scores and integers.
2. Through communication and discussion, guide students to actively contact existing knowledge and experience for analysis, induction and analogy, ×3=? Further develop students' ability to reason reasoning and experience the fun of exploring and learning.
Second, to strengthen the process experience, the experience process is more convenient than the results.
In the first question of the solution, I designed 88×8/11 = when dealing with algorithm diversification and algorithm optimization. The practice allows students to use two methods to calculate and enhance the process experience. After the students experience it, they realize that the process approximation is easier and less error-prone than the result, forming an internal requirement and optimization algorithm.
Insufficient existence: The emphasis of this lesson is not enough, especially the first question of practicing and practicing. After the students complete the independence, I am not enough in organizing the communication. I only exchange the calculation methods and results of the students, ignoring how the students are painted. I have 4 3/16. Later, I found that students have a lot of methods. In fact, through the student coloring formula, you can communicate the relationship between score multiplication and fractional addition, and further understand the meaning of multiplying the score with the integer. The sum of a few points and the sum of the calculations that can be calculated by multiplication, I did not grasp the intention of the practice design of the textbook well, and did not keenly grasp the teaching resources, and consolidate the reasoning well.

Part 2: Rethinking the Score by Integer Teaching

The score multiplication integer is the first lesson of the "score multiplication" teaching, and is the starting point for students to understand the meaning of fractional multiplication. This part of the textbook is based on the meaning of the integer multiplication and the addition of the scores that students have learned.
In teaching, I make full use of the students' existing knowledge and experience, try to combine the real problem situation, combine computational learning with problem solving, and let students explore the meaning of fractional multiplication. Create an actual situation that students like, and let students list the formula according to the quantitative relationship of actual problems. It is easy for students to combine the meaning of integer multiplication and list the multiplication formulas. This processing is not only beneficial for students to actively extend the meaning of integer multiplication to the score, that is, the meaning of multiplication of fraction and integer is the same as the meaning of integer multiplication, and is a simple operation for finding several identical sums.
When calculating the rule of multiplication of teaching scores and integers, I instruct students to read, say, practice, think about it, and start with five aspects, for example: teaching 3/10×5, first Let the students know clearly, ask for 3/10×5, that is, what is the 3/10+3/10+3/10+3/10+3/10, and calculate the 3+3+3+ by the same denominator score addition method. 3+3/10, then let the students analyze the numerator part of the 5 3 plus plus 35, and calculate the result. On this basis, guide the students to observe the calculation process, especially the connection between 3/10×5 and 35/10. To understand why "the product of the same numerator and integer is the numerator, the denominator is unchanged." Then let the students try to practice 7/10×5, and then carry out collective communication to see if they can make a difference before the multiplication. It is easier to calculate the ratio than when to compare. For the sake of simplicity, it is possible to make an appointment.
In short, in this lesson, I can try to mobilize the various senses of the students, change the teaching methods based on examples, demonstrations, and explanations, change the learning methods based on memory rules and mechanical training, and guide students to participate in the learning activities of exploration and communication. In the process of letting students become passive and active, they participate in the discussion of arithmetic and the generalization of arithmetic rules.

Part 3: Rethinking the Score by Integer Teaching

First, respect the "mathematical reality" of students.
Before the teaching score is multiplied by an integer, in fact, many students in the class know the calculation method of the score multiplied by the integer. If you follow the general teaching procedures, students will feel that "I have known this knowledge, I have nothing to learn.", thus losing interest in inquiry. So when teaching, I proposed: "Why is the result 9/10? Why multiply the numerator with the integer?" The next teaching guides the students to explore with "why."
Second, to achieve personalization of teaching and learning.
Each student has their own life experience and knowledge base. In the face of the problems that need to be solved, they all build their knowledge from their own unique mathematical reality, which determines that different children will have different solutions to the same problem. Perspective. In this lesson, I let go of the free and multi-angle thinking of students in their own way of thinking. Students build their own knowledge and fully embody the concept of "different people learning different mathematics". Some students think about the meaning of the score multiplied by the integer, and compare the score multiply with the calculation method of the score addition; some students get the result by painting on the practice paper given by the teacher; some students have explained why The reason for multiplying numerators by integers; other students convert scores into decimals, which also yields correct results. From this, I deeply understand that no one, including teachers, can ask students to think and solve problems according to the intentions of our adult or textbook writers. Those single and rigid requirements will only hinder students' thinking. development of.
Third, the textbooks are reorganized.
This section is a boring calculation class, so I use the turtle and rabbit to play intellectual games to stimulate students' desire to solve problems, so that children can unwittingly complete the book in a competitive and challenging environment. Basic exercises. Of course, I also reorganized and adapted the contact topics of the textbooks. If I practice the first question, I will change 4 to 3, so that this problem will avoid the points, first solve the calculation method without the division, and then teach the division. Make the whole lesson naturally divided into two parts.
Fourth, some problems exist.
This lesson is generally successful, and the content in the class has been completed smoothly, but there are some problems when letting students understand that the first appointment is relatively simple. After completing the second question of the example, there are still many students who still think that they are well calculated first, so I have shown four questions. The last one has a large data, which can guide the students to get the correct conclusion. But now I feel that if I finish the 8/11×99 directly after the example is finished, it will be more direct, and the students will immediately realize the benefits of the first appointment, then do other topics that need to be scored. It is convenient.

Part 4: Rethinking the Score by Integer Teaching

Rethinking this lesson, whether it is the orientation of the teaching objectives or the organization of the teaching process, reflects a new teaching philosophy. I think there are mainly the following aspects:
First, pay attention to the learning status of students
The new curriculum standards point out: "It is necessary to pay attention to the level of students' mathematics learning, and pay more attention to the emotions and attitudes they exhibit in teaching activities." To this end, teachers in order to allow students to participate actively and actively in teaching. In the process of inquiry, it is very important to try to get the inner needs of inquiry from the very beginning. Therefore, this requires the teacher to take into account the characteristics of the knowledge itself, as well as the students' cognition and the existing level of the students, to find a suitable entry point, so that students can feel the challenge and explorability of the immediate problem, resulting in "I also To study the interest in this issue. At the beginning of this lesson, I asked the students to experience the process of origami operations—cooperation and communication—finding calculation methods to enable students to discover and master the calculation method of fractional unit multiplication fraction units. Since the materials discussed in this process are all from students, they discuss their own learning materials, their enthusiasm is particularly high, and their interest is particularly strong. They all want to find out the "my discovery" through their own efforts, and find the rules for themselves. The impression was particularly deep, and at the same time there was a desire to continue exploring and verifying the calculation of the two general scores.
Second, pay attention to the conclusion, pay more attention to the process
Traditional teaching is a method in which teachers use composite slides to let students understand the mathematics of “score multipliers”, and then use their calculation rules to carry out a lot of exercises to achieve “practice makes perfect”. "New Curriculum Standards" points out: "Mathematics teaching is the teaching of mathematics activities, which is the process of interaction and common development between teachers and students, between students." This new concept shows that mathematics teaching activities will be a student experience. The process of mathematics is the activity of students to construct their own mathematical knowledge. Therefore, the teaching time tries to let the students personally experience the learning process, that is, let the students experience the formation process of the “score multiplier” calculation process in a series of activities such as hands-on operation—exploration algorithm-example verification-communication evaluation-rule arrangement. . Here, the students are allowed to do it themselves, to enlighten, to experience, to experience, to create, and also to consider the independent choice of students' problem-solving strategies, and to take into account the cultivation of cooperation consciousness. I am convinced that this is more skilled than simply mastering the calculation method. It makes more sense.
Third, the penetration of scientific learning methods
The new curriculum standards point out: “Help them to truly understand and master basic mathematics knowledge skills, mathematical ideas and methods in the process of independent exploration and cooperation and exchange, and gain extensive experience in mathematics activities.” Therefore, teachers are guiding students through continuous thinking to obtain laws. In the process, the focus is not on the law of knowledge itself, but more importantly, the experience of “discovery”. Feel the way of thinking in mathematics in this experience and experience the learning methods of science. From the overall design of the teaching, this lesson is triggered by “special” to stimulate the students' guesses. Then, the examples are verified, and then summarized and summarized, trying to let the students experience the incomplete induction of ideas from special to general. First, let the students summarize the “score multiplier” through the activity as long as “the numerator is unchanged, the denominator is multiplied” or “the molecular multiplication, the denominator is multiplied”, and then the student uses the origami, the decimal, the score. The meaning and other methods to verify this calculation method, found the "score multiplication score, numerator invariant, denominator multiplication" particularity, and the universality of "score multiplication score, molecular multiplication, and denominator multiplication". This infiltrated the scientific learning method and the scientific spirit of seeking truth from facts.
Fourth, the confusion
How to pay attention to the whole? In the first phase of the course, when “several points are multiplied by a few points”, since students are discovering the law on the basis of their own operations, all students are interested and actively participate in the process of inquiry. In the second stage to verify the exchange "a few points by a few points", in addition to using the origami method to verify the exchange, the rest of the links are almost "occupied" by several "superior students", although the teacher has repeatedly guided "Who can understand what he meant? Can you explain it again?", "Try it with his method." But some students still can't participate in it and become "accompanied scholars." Therefore, how to face the differences of students and promote the development of students on the basis of the original, is a topic worth exploring in classroom teaching.

Part 5: Rethinking the Score by Integer Teaching

The knowledge base of fractional multiplication is based on the calculation method of the denominator fractional addition method and the meaning of the score and the meaning of integer multiplication. At the beginning of the class, I reviewed the content and then entered the teaching of scores and integers.
The algorithm for fractional multiplication is simple. When multiplying, the denominator is unchanged, and only the integer and fractional molecules are multiplied as numerators. When teaching this content, I paid attention to the importance of the new textbook in mathematics, and noticed the connection between the graph and the formula, and fully let the students perceive the process of painting and painting before calculating. Therefore, it is easier to get the results of the calculations in the future. Furthermore, the "meaning of the fraction by integer" is also organically infiltrated, paving the way for later knowledge.
In a class, because students are more likely to accept content, there is spare time in the class. Students' understanding of arithmetic is relatively clear, but the problem still exists is the part of the approximation. Some students like to calculate the results and then divide them. They are not willing to adopt the calculation process. This part should also be thoroughly explained. Students may be ignorant of this kind of approximation in the calculation process, and the understanding of such an appointment is not clear enough. Learning scores are multiplied by integers, and students will definitely encounter the problem of first-minute splitting or first-multiplied after the calculation. If you just want to get a correct result, then neither the former nor the latter will matter. If you don't make a mistake, you will get the correct result. Obviously, we also need students to develop good calculation habits, higher calculation speed and calculation accuracy! Then we must let the students understand which ideas are more reasonable and help them to follow up. As the first lesson of fractional multiplication—the fractional multiplication of integers, it forms a good calculation habit of calculating the first and the first, and plays an important role in improving the accuracy and speed of calculation of students. When the teaching score multiplication is divided in the process, the subject I give to the students is: ×5, and two methods are listed for the students to compare. But I don't think this question can be reflected in the superiority of the first part of the calculation process. The title should be changed a bit more complicated, become "13 × 5/26", and who is going to compete with the students. If a student directly multiplies the numerator by an integer, the speed will of course be very slow. When the fastest classmates show their own practices, other students suddenly realize that they can understand the first part of the calculation process and can simplify it. . In this way, when students do fractional multiplication, they are not only satisfied with the “molecular and integer multiplication product, the denominator remains unchanged”, but the main point of “candidate points that can be divided”.