Reflections on the teaching of fractional division under the new curriculum standard.
The new curriculum standard points out that students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. Only by establishing students' dominant position and optimizing the learning process can students' autonomous learning process be promoted. The simple application problem teaching of fractional division is one of the key and difficult points in the application problem teaching of the whole primary school. How to motivate students to actively participate in the whole process of learning, avoid tedious analysis and dogma memorization in traditional teaching, and guide students to correctly understand the number of application problems of fractional division. I made the following teaching attempts:
First, learn mathematics from life.
From the beginning, I changed the traditional practice of introducing new knowledge by reviewing old knowledge. I started directly from the reality of students' lives, led to topics through the number of classes, and then asked students to introduce the class situation, which aroused the enthusiasm of students to participate, so that students could feel that mathematics was around, learn mathematics in life, and let students learn valuable mathematics.
Second, pay attention to the process, so that students can get personal experience.
In order to let the students know what is the key to solving the application problem of fractional multiplication, I deliberately don't give any explanation. By omitting a known condition in the problem, I let the students find the problem, feel the connection between the numbers in the application problem, and try my best to let the students find the law in the learning process. Make students really understand and draw a conclusion that the key to solving the application problem of fractional multiplication is to find out the equal relationship between quantity and quantity from the key sentences of the problem.
Strive to embody the learning style of "autonomy, cooperation and inquiry" in teaching. In the past, the teaching efficiency of fractional division application problems was not high, mainly because of the deviation of teachers' teaching. Teachers like to focus on trivial keyword analysis, like to use rigorous language for rigorous logical reasoning, although the analysis is clear, it is easy to go to two extremes, or make unnecessary analysis of what students already understand; Or treat students as scholars, and still do in-depth and detailed analysis of things that were originally incomprehensible, thus wasting valuable classroom time. In teaching, I combine the application problems of fractional division with those of fractional multiplication, so that students can feel the similarities and differences between them through discussion, communication and comparison, and explore the internal relations and differences between them, thus enhancing students' ability to analyze and solve problems and saving a lot of tedious analysis and explanation.
Third, analyze the problem from multiple angles and improve the ability.
When calculating application problems, I encourage students to actively seek different solutions to the same problem, expand students' thinking, guide students to learn to analyze problems from multiple angles, and thus cultivate students' inquiry ability and innovative spirit in the process of solving problems. In addition, instead of summarizing the quantitative relationship from examples as in the past, let students memorize, for example, "Yes, occupation, ratio, equivalent is followed by unit1"; "Multiplication knows 1, division knows 1" and so on. Let students experience it personally, deepen their understanding of the quantitative relationship and solution of this kind of application problems, improve their ability and make full preparations for students to enter a deeper level of learning.
In the whole teaching process, I am the organizer, helper and promoter of students' learning. This can not only give full play to students' autonomous potential, cultivate students' exploration ability, but also stimulate students' interest in learning. Students learn easily and teachers teach happily.
Reflections on the teaching of fractional division under the new curriculum standard
Effective teaching design needs to revolve around three basic problems: effectively grasping students' cognitive basis, effectively positioning teaching objectives and effectively designing teaching process. The teaching of this course is mainly to learn how to divide the score evenly, so that students can understand the meaning of the score evenly and master the calculation method of the score evenly.
Accurately grasping students' cognitive basis is the basis of teaching design. With the learning foundation of fractional multiplication, students can quickly adapt to the learning style of this class. The logical starting point of this lesson is the meaning of integer division, the meaning and calculation method of decimal multiplication and the method of finding the reciprocal of a number. So I introduce the problem of fractional multiplication in reality, looking for the reciprocal of a number to help children review their previous knowledge. When students realize the reciprocal relationship of multiplication and division, they will ask a practical problem in life, which leads to the necessity of fractional division calculation and sets up a ladder for subsequent study.
After accurately grasping the students' cognitive basis, how to accurately locate is the key to teaching design. In this class, it is not enough to focus only on the students' inability to calculate. In the design, we should also pay attention to the deeper elements behind the appearance, such as: Do students understand calculation? Have their thinking improved substantially? Have their learning methods improved? Do they have a positive attitude towards learning? Wait a minute. Therefore, in the formulation of the teaching objectives of this course, my focus is not only to let students calculate, but more importantly, to let students deeply understand the truth of this calculation and highlight the "process objectives" by understanding the meaning. Let the students go through the process of painting, calculating and speaking. In the process of inquiry, let children form a learning attitude of "knowing why, knowing why", gain a learning ability, and lay the foundation for students' sustainable development.
Teaching process is a direct reflection of teaching objectives in the classroom. In teaching, I pay attention to the process of students' discovering mathematical knowledge, provide students with practical opportunities, make full use of graphic language, turn abstraction into intuition, and help students understand the meaning of dividing fractions by integers, and the rationality of the method of "dividing by integers (except zero) is equal to multiplying the reciprocal of this integer". Then change the angle of exploration and present a set of formulas, so that students can verify the laws found in the operation activities again in the process of operation and comparison. Give students space to express their experiences and feelings in the learning process, such as: Who will tell us what this algorithm is like? What do you think? Students gradually accumulate original experience in the process of self-expression, and then improve their mathematical thinking through the moderate guidance of teachers.
Reflections on the teaching of fractional division under the new curriculum standard: Fan Wensan
"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. Let students know the importance of learning mathematics and improve their interest in learning mathematics. " Fraction and division are abstract contents for primary school students. The reason why mathematics knowledge can be understood and mastered by primary school students is not only the result of knowledge deduction, but also the result of the interaction of specific models, graphics, scenarios and other knowledge. Therefore, when I design the class of fraction and division, I consider the following two aspects:
1. Start with solving the problem and feel the value of the score.
Starting with the problem of dividing the cake, let the students feel that when the quotient can't be expressed in integers, it can be expressed in fractions. This lesson is mainly conducted from two levels. First, with the help of students' original knowledge, the problem that 1 cake is divided into several parts according to the meaning of score is solved, which is expressed by business score; Secondly, with the help of physical operation, it is understood that several cakes are divided into several parts on average, and quotient can also be expressed by scores. And these two levels are designed from the perspective of solving problems.
2. The expansion of the meaning of fractions is synchronized with the understanding of the division relationship.
When the quotient of integer division is expressed by fraction, the divisor is the denominator and the dividend is the numerator. Conversely, a fraction can also be regarded as the division of two numbers. It can be understood that "1" is divided into four parts on average, indicating such three parts; It can also be understood that "3" is divided into four parts on average, indicating such 1 part. That is to say, the process of understanding and establishing the relationship between fraction and division is essentially synchronous with the expansion of the meaning of fraction.
After teaching, I reflect on my own teaching, and find that the state of primary school mathematics knowledge stored in students' minds can be transformed from abstract to concrete mathematics knowledge, except abstract. The whole class teaching has the following characteristics:
1. Provide rich materials and experience the process of "mathematization".
Understanding the relationship between fraction and division is a process of gradually enriching perceptual accumulation and abstract modeling with tangible objects and pictures as the media, hands-on operation as the way and rich appearances as the support. In this process, we pay attention to the following aspects: first, provide rich mathematics learning materials; Secondly, on the basis of making full use of these materials, students gradually improve their own conclusions, from literal expression to equations expressed in words to letters, from complex to concise, from life language to mathematical language, and from concrete to abstract.
2. The problem lies in the method, and the content carries ideas.
Mathematics learning is a problem-solving process, and methods naturally reside in it; The learning content contains mathematical ideas. In other words, mathematical knowledge itself is only one aspect of our study of mathematics, and it is more important to infiltrate mathematical thinking methods with knowledge as the carrier.
As far as fractions and division are concerned, the author thinks that if we teach only to get a relationship, we just catch the tip of the iceberg. In fact, with the help of this knowledge carrier, we should also pay attention to thinking methods such as induction and comparison, and how to use existing knowledge to solve problems, so as to improve students' mathematical literacy.
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