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Liu Song primary school mathematics
Last week, I had the honor to participate in the teaching seminar of "Leading Thinking Development with Core Problems", a topic of primary school mathematics teachers under the background of core literacy of famous thinking teaching and research institutions. At the scene, I saw famous teachers such as Hua Yinglong, Luo, Gu Intelligent and Tang, as well as their wonderful classes and lecture reports with unique teaching ideas. There are 16 high-quality classes for teachers, which are thought-provoking and thought-provoking.

At the end of every half day, I will communicate with my colleagues. "Say" is not only to find * * *, but also to extract information from the experience and perspective of former people. "Writing" is not only to express your thoughts, but also to exercise your writing ability.

Teacher Wu Zhengxian gave us a wonderful general evaluation lesson (addition, subtraction, multiplication and division). The original planned teaching content is "Understanding Equation", but we have learned it after hearing the children's feedback. Teacher Wu temporarily adjusted the general evaluation of computing teaching, integrating addition, subtraction, multiplication and division, so that students can understand the relationship between part and whole from specific stories, not only let students understand the significance of addition, subtraction, multiplication and division, but also independently construct the relationship between algorithms.

Teacher Gu Intelligent studied percentages. Based on the pre-test, Mr. Gu learned that most children have seen percentages in their lives, so he broke the teaching process of textbook arrangement, first let the children give examples of percentages they have seen, and then let them make sentences with percentages. In the process of making sentences, the children gradually deepened their understanding of the meaning of percentage. After class, Mr. Gu also gave a special lecture on "Innovative Teaching Based on Learning Situation", which once again conveyed to the teachers the importance of cultivating children's innovative thinking by cultivating their questioning ability. Good teaching must be "teaching because of learning" and "different because of learning"

Teacher Liu Song is studying the meaning of fractions. Before class, Mr. Liu asked the children 1+ 1= 1 under what circumstances. Thinking mode makes children only know how to explain 1+ 1=2. It makes sense to suddenly explain 1+ 1= 1, not to mention children. I don't think most teachers can think of it. After a short silence in the classroom, suddenly a child said, "A drop of water plus a drop of water or a drop of water". Teacher Liu asked the students to say this sentence three times, because the important things were said three times. After that, the other children and the teachers present suddenly realized and clapped involuntarily. Teacher Liu's teaching design is relatively novel, which is different from the perspective of textbook compilation. Using a branch to measure the length of the blackboard, children can understand the process of measurement from the generation of the score and realize the significance of the score from the measurement results. Starting from the whole "1" (that is, the unit "1"), the distinction between "rate" and "quantity" makes children gradually understand the relativity and absoluteness of scores. Finally, expand the other meaning of fractions and let children understand the meaning of fractions from the perspective of division. For example, when calculating division, 7÷7, 6÷7, 8 ÷ 7...A ÷ B can all be expressed by a single fraction, which makes the meaning of the fraction move from single to perfect. "Thinking from another angle will lead to different experiences and gains" was repeatedly emphasized by Mr. Hua in class. The curriculum standard puts forward that "mathematics teaching activities, especially classroom teaching, should not only stimulate students' interest in learning, but also stimulate students' mathematical thinking and encourage students' creative thinking. "Thinking and creation begin with guiding students to think from different angles. In fact, many problems in life will have different results and feelings if we look at and deal with them from another angle.

? Listening to Mr. Hua Yinglong's "Mathematical Stories in Military Parade" on the spot is different from watching CDs. Listen to the math stories in the military parade and solve the mystery of' 6m' for the sacred moment. If I explain Dongfang -4 1, I think the data is temperature, and the teaching process is temperature, so I will have a deeper understanding of' knowing well' and' China speed'. In my opinion, this class can no longer be evaluated simply by achieving "four basics" and "three abilities". Teacher Hua said that this class was given on 20 15, 20 18 and 20 19. How to break through? Mathematics not only impart knowledge and skills, but also impart emotional attitudes. Praising the military parade, eulogizing the motherland, loving life and discovering the beauty of mathematics around him is what he wants to convey to every student and teacher present. Mathematics class is no longer just numbers and shapes, but also feelings and aesthetics.

Many people don't want to choose the calculation course of the public course, because they feel boring, the theoretical explanation is not thorough, and students don't know what to learn. But after listening to Mr. Luo's written talk, I have a new understanding of computing teaching. A 48÷3= 16, children gradually understand that the word calculation and vertical form of division are related in questioning, independent thinking, group communication, questioning and reflection, and hands-on operation, and they are all expressions of the process of dividing things. An excellent computing class can inspire teachers to design the thinking of computing teaching, and also make teachers think about the essence of mathematics. For the teaching of calculation, some teachers may feel that there is no need to talk about arithmetic, no need to talk about it, or no time to talk about it, as long as children can calculate and do problems. Mathematics is reasonable. Besides teaching students how to do it, it is more important to let them know why. Teacher Zhang Qihua said, "Mathematics is not a simple calculation of addition, subtraction, multiplication and division, nor a simple superposition of knowledge and skills. The most precious wealth that mathematics can leave us is to use the light of rational thinking to cut off the cognitive prejudice that false intuition may bring, so as to guide students to reach the essence and core of the real world through complex representations and mathematical thinking methods. "

Harvest 1: Curriculum design can start with "opening meridians and restoring knowledge chain"

What I hear most in Songshan Lake is "course design". At first, I could only think that curriculum design is activity design, because "activity is curriculum", but after a period of thinking and learning, I realized how superficial my understanding was.

The design of mathematics curriculum in compulsory education stage should not only consider the characteristics of students' mathematics learning at this stage, but also conform to students' cognitive laws and psychological characteristics. The designed course should not only stimulate students' interest in learning and arouse their mathematical thinking, but also fully consider the characteristics of mathematics itself and reflect the essence of mathematics. While presenting mathematical results as knowledge and skills, we should attach importance to students' existing experience and let students experience the process of abstracting mathematical problems from the actual background, establishing mathematical models, seeking results and solving problems. Drawing lessons from famous teachers' classes, whether it is Wu Zhengxian's General Theory, Liu Song's Significance of Fractions, Hua Yinglong's Stories in Military Parade or Zhang Hongwei's Perimeter of Rectangle and Square, can reveal new ideas and new directions of curriculum design. Curriculum design can start with breaking the arrangement of traditional teaching materials, connect fragmentary knowledge points in series based on curriculum standards and teaching materials, establish a "load-bearing wall", and open a "partition wall" at the same time, so that the teaching content can return to the essence of mathematics, and classroom teaching is interlocking, which not only makes children "look forward to the future", but also guides them to draw inferences from others.

? Harvest 2: There are teaching goals in mind and students in eyes in the classroom.

The teacher's class is exquisite and thought-provoking. Every word, every expression and every movement makes people feel natural, harmonious and unique. Every famous teacher has a different style in class. Some people give lectures in simple terms, with clear organization and rigorous structure. Some people's lectures are full of passion and touching. Besides knowledge and skills, it is also influenced by emotions, personality charm and values. Some people teach kindly and naturally without affectation, and teachers and students are equal and harmonious; Some people give lively and interesting lectures. Teachers of all styles have a common feature, that is, they only have teaching objectives in their minds and students in their eyes, and there is no fixed and rigid teaching process and "interlanguage". All the excitement comes from the students' speeches and performances. What the teacher said is either to affirm and encourage the students, or to make the finishing point and open the door to wisdom for the students. Sometimes I wonder why the class of famous teachers always makes the students on stage and the teachers under the stage give applause, laughter and exclamations involuntarily. As we all know, the sound of "applause" shows that students' thinking is profound. "Laughter" not only means that this is a harmonious and humorous class, but also gives people a feeling of aftertaste and nostalgia. How did you do it? The idea of shallow thinking is that the courses of famous teachers are all oriented by high-order thinking. Based on the pre-test and post-test to understand the students' cognitive level and existing experience, the teaching process is designed to meet the students' learning situation, which not only follows the iron law of teaching, makes the teaching content more targeted, but also truly achieves the goal in class and only the students in mind. The development of teaching process is to make students more rational, to make students closer to the essence of mathematics and to appreciate the cultural value of mathematics.

Harvest 3: Learn from famous teachers, be masters, and make clear the direction of professional development.

When I saw the famous teacher's classroom and returned to my own classroom, I realized that there were many shortcomings. I once heard a teacher discuss that "some teachers disappeared in the rivers and lakes after boarding the platform through a competition class." This sentence is also a wake-up call for me Which direction should my career develop in the future? After attending the on-site exhibition of provincial-level excellent courses in April this year, I often had nightmares for a while, perhaps because the pressure was suddenly released and I was at a loss, perhaps because my dream had come true and I didn't know what to pursue next. I know in my heart that my career has reached a bottleneck. My predecessors said that I don't want to be a competitive robot and don't just think about competition. Teachers' professional development is not only competition, but also learning and research. Only by calming down and continuing to learn professional knowledge can we find the true meaning of education and teaching from curriculum design and research. Teacher, fame and fortune are secondary, and student-oriented is the most important thing.

? Harvest 4: How to Implement Core Literacy

The theme of this seminar is: "Leading thinking development with core questions" in primary school mathematics under the background of core literacy. Looking back on the three-day wonderful classes and lecture reports, what is the core literacy of mathematics? Some people say that it is the "ten core words" proposed by the curriculum standard (number sense, symbol consciousness, spatial concept, geometric intuition, data analysis concept, computing ability, reasoning ability, model thinking, innovation consciousness and application consciousness). Some people say that core literacy is beyond disciplines, and mathematics teaching is only a carrier, so we should pay attention to cultivating students' cooperation, communication, critical thinking and personality, such as the 5C model (cultural understanding and inheritance) proposed by China Education Innovation Research Institute. I quite agree that in the field of subject teaching, the cultivation of subject literacy should be taken as the teaching goal, so that students can learn the thinking mode of "mathematics" on a solid foundation. Based on the above understanding, we should pay attention to the following five aspects in implementing core literacy in curriculum design.

1. The goal of classroom teaching should focus on the "key figures" and "necessary abilities" that are most suitable for primary school mathematics training.

2. The carrier of classroom teaching should pay attention to expanding the carrier outside the teaching materials and build a richer "creative curriculum" for primary school mathematics.

3. Classroom teaching behavior should pay attention to the reconstruction of the relationship between teachers and students, reshape the classroom structure and process, and add value to "teaching" and "learning".

4. Classroom teaching should pay attention to students' learning experience and make students learn easily, interestingly, valuable and meaningful.

5. Classroom teaching design can pay attention to the integration of primary school mathematics with other subjects, and improve students' comprehensive and creative problem-solving ability in "subject integration".

Learn before you know the shortage, do before you know the distance, and do before you think.