What is the effectiveness of teaching? What are the three indicators to consider students' effective learning?

Xu Kai, a teacher from Shangrao No.2 Middle School, has made a lot of discussions on the theoretical level of effective teaching, but what teachers lack is not the indoctrination of ideas, but the targeted guidance on teachers' teaching behavior at the practical level. Starting from the three dimensions of teaching effectiveness: time, result and experience, this paper discusses the follow-up and improvement of effective teaching teachers' teaching behavior, and seeks the path of effective teaching, thus effectively improving classroom teaching efficiency. Learning time refers to the time spent learning a specific content, that is, learning efficiency, that is, learning speed. Obviously, the faster the learning speed, the less time it takes to learn a specific content, and the higher the efficiency. To improve learning efficiency, we first need to spend time on learning and establish a sense of limited learning time. Classroom teaching can't waste time not studying. Second, we should improve the learning quality per unit time. How to make students learn faster and more in class? The principle of fast speed put forward by zankov has given us profound enlightenment. Zankov thinks that the teaching progress is too slow, and a lot of time is spent on monotonous and repetitive lectures and exercises, which hinders the development of students. He advocates that the teaching speed can be obtained by reducing the repetition of teaching materials and teaching processes, the breadth of knowledge can be obtained by accelerating the teaching speed, and the depth of knowledge can be obtained by expanding the breadth of knowledge. He said: As long as students master what they have already learned, they will go forward and teach them more and more new knowledge. This means constantly enriching students' minds with new knowledge, rather than stagnating and monotonously repeating what students have learned. But at the same time, this principle should not be confused with hasty actions in teaching work. Fast progress does not mean to do things in a hurry in class, but to let teachers and children work calmly. In classroom teaching, the frequency of content is low and the pace is slow, which easily leads to the complication of simple problems, the ineffectiveness of teachers' teaching behavior, and the lack, slowness, learning and expense of students. When teaching vertical calculation of carry addition in grade one, a teacher organized the whole class to discuss the carry point in vertical calculation: Student 1: I think the carry point should be written between ten digits and one digit, so I can understand it as a carry point. Health 2: I think the carry point should be written in the tenth place, so it is obviously a number in the tenth place. Health 3: I think it should be written as standard 1. Health 4: I think it should be written as inclined point. In the vertical teaching of carry addition, the focus of teaching is how to calculate how to add the numbers in the ten digits after carry, rather than how to write 1. It is of no value for teachers to organize such classroom discussions, but it takes up students' mathematics study, thus wasting time on fake study. Therefore, in classroom teaching, teachers should be good at critically analyzing the effectiveness and rationality of all aspects of teaching, making rational and effective use of teaching time, and making every minute of the classroom play its value. It is the pursuit of value-added teaching to let students learn more and faster. Teaching theory puts forward that teaching can be divided into low-value teaching, equivalent teaching and value-added teaching. Value-added teaching has the characteristics of rich connotation, broadening extension, changing form, transforming public knowledge into personal knowledge, transforming dead knowledge into living knowledge, internalizing knowledge into wisdom and internalizing knowledge into character. The characteristics of mathematics determine that the essence of mathematics teaching is a kind of value-added teaching. Mathematics constructs its own kingdom with various forms of language symbols, which is abstract; Mathematics forms its own theoretical system, with impeccable logical proof and rigor. However, even in mathematical science, it is difficult to deduce many new mathematical ideas and methods only through logical deduction, which requires keen observation, association and intuitive guess and epiphany. Mathematics learning can not simply follow the deductive road from concept to concept and from theory to theory, but should restore the theoretical system derived from logic to a lively knowledge generation system. Pursuing the value-added of mathematics teaching, one is to transform the academic form of mathematics into the educational form. Mathematical expression is boring, which often gives people a cold feeling, but mathematical thinking is fiery and lively. How to ignite and arouse students' fiery thinking and appreciate the cold beauty of mathematics is the fundamental task of mathematics education. The task of mathematics teachers is to return to nature and restore the formal logic chain of mathematics to the fiery thinking of mathematicians when they invent and innovate. Only after thinking can we finally understand this cold beauty. The second is the transformation from symbolic knowledge to life state knowledge. Re-activate the structured book knowledge with symbols as the main carrier, and realize the communication between book knowledge and human life world, with students' experience world and growth needs, and with people who discover and develop knowledge and history. Generally speaking, knowledge is restored to a fresh state, and it is closely related to people's life again, so that it presents a state of life. Knowledge with inner life state can best activate and arouse students' inner learning needs, interests and confidence, and enhance their desire and ability to explore actively. Learning achievement refers to the changes, progress and achievements made by students after learning. This is the core index of effectiveness. Every class should make students have real cognitive gains, which are as follows: from ignorance to understanding, from knowing less to knowing more, never having a meeting, and never changing and improving. Learning achievements are not only manifested in double basics, but also in intelligence, especially the mastery of learning methods and the development of thinking mode. Mathematics teaching theory holds that there are three levels of mathematics training: the first level is knowledge accumulation and problem-solving skills. It is visible, tangible and easy to operate, but its functionality is weak and its application is narrow. The second layer is thinking method and problem solving method. Compared with the previous layer, the program is weak and difficult to copy, but it has strong functionality and wide application. The third layer is mathematical thoughts and concepts. It is the source power that mathematics education gives students sustainable development. Therefore, if students want to learn more deeply and thoroughly, they should be guided to transform public knowledge into personal knowledge and internalize knowledge into wisdom from three aspects: knowledge, methods and concepts. In order to make students learn more deeply and thoroughly in mathematics class, the key point is to develop students' mathematical thinking and emphasize mathematical thinking methods. First, focus on expanding the rich educational value of mathematics. Mathematics class not only involves specific propositions, theorems, concepts and operations, but also recognizes the possible levels of mathematics teaching in forming students' accurate logical thinking ability, mathematical vision and mathematical aesthetic ability. Teachers should not only understand and grasp the teaching materials from the knowledge level, but also fully interpret the rich educational value contained in the teaching content from the height of educating people. Teaching serves the active development of students in many aspects, which is the most basic foothold. Only in this way can the development of students' spiritual world be nourished in many ways from the teaching of different subjects. The development value of primary school mathematics for students is not only to provide mathematical knowledge itself, but also to provide students with unique operation symbols and logic systems, so that students can have a mathematical discourse system; Provide students with different paths and unique perspectives to understand the quantity, number-shape relationship and transformation of things, so that students can have a mathematical vision; To provide students with methods and thinking strategies to discover the quantity, number-shape relationship and transformation of things, so that students have a mathematical mind; Provide students with a unique way of thinking that can only be experienced and established in mathematics. Second, start to improve students' thinking level. First, the solutions or results of the problem are diverse; Speed refers to the speed at which students solve problems, which is not only related to proficiency, but also related to clear thinking. The second is to reflect in a qualitative way. Quality refers to students' thinking when solving problems, that is, they do not repeat or omit, and regularly look for solutions or all the results. Teachers should guide students to think, make their thinking orderly, and at the same time find solutions or results to problems. The third is to reflect it in a structured way. Structuring is to classify mathematical research objects according to their characteristics, summarize the unique points of each category, reveal the characteristics of each category, and improve students' understanding of mathematics from point to structure. Fourth, it is reflected in a mathematical way. Mathematicization is to abstract some characteristics of mathematical research objects, express them with mathematical language, graphics or patterns, and establish mathematical models. Third, efforts should be made to overcome students' tendency to learn superficially. If the teaching behavior does not conform to the learning law, it may further strengthen the phenomenon of students' lack of investment. The phenomenon that students don't participate in classroom activities is that students resist teaching activities that they don't agree with. In the process of students not participating in classroom teaching, there is a negative communication and interaction between teachers and students, and teachers' shallow teaching will inevitably lead to students' shallow learning. A large number of superficial learning processes in the classroom have wasted a lot of human resources and deprived children of a happy childhood, which is also one of the main reasons for students' overload. In the countdown class, the teacher created such a teaching situation: the teacher came into the classroom with a doll in his hand, and the children's eyes were quickly attracted by the doll. The teacher turned the doll 180 degrees and asked: What's wrong with the doll now? The students replied in unison: the doll is upside down. The teacher went on to say: in mathematics, there is also such a countdown, and the countdown is the countdown. The score of 1/8 is in turn 8/ 1. What is the inverse score of 8/9? A student thinks that the score of 8/9 is 9/8 upside down. Another student disagreed with him and said, Teacher, he is wrong. The score of 8/9 should be 8/6 upside down, because if you turn this number upside down and rotate 180 degrees, it seems that 9 is 6 upside down. At that time, the whole class burst into laughter and the teacher was at a loss. The teaching of basic concepts is very important, and students' understanding of concepts will be different with different learning processes. In this case, the children's understanding deviation is because the problem situation created by the teacher only understands the meaning of reciprocal unilaterally, but does not guide the students to construct the meaning of reciprocal from the mathematical point of view and reveal the essential attributes of the concept. Therefore, in order for students to learn deeply and thoroughly, it is necessary to turn superficial learning into a thinking mathematics learning process and take problem solving as the center of mathematics teaching. Learning experience refers to students' learning experience, that is, psychological experience accompanying or arising from learning activities. This is an important dimension neglected by traditional teaching considering effectiveness. Confucius said: Knowing is better than being kind, and being kind is better than being happy. Learning experience is the soul of teaching effectiveness, and students' growing love for learning is the internal guarantee of teaching effectiveness. Britain's new "primary school syllabus" clearly shows that all students should study happily and successfully. Excellent teaching can bring children the possibility of life they deserve, and happiness is every child's birthright. So the combination of the two is the most powerful. Children learn better when they are excited and involved, but what can arouse their excitement and participation? That's excellent teaching! Teaching and learning in primary schools. Enjoying the fun and happiness of learning is the premise of children's happiness and happiness in life, and the guarantee of forming study habits and establishing lifelong learning consciousness. In education, if we sacrifice some time to learn scientific and cultural knowledge to cultivate and protect students' interests, hobbies and love for learning, exploration and creation, then in the near future, students will definitely get back these improved knowledge for the second time; However, if students are allowed to learn and master some systematic scientific and cultural knowledge at the expense of their interests, hobbies and love for learning, exploration and creation, or even their health, body, mind and morality, these lost interests, hobbies and love will not only make the scientific and cultural knowledge they have learned and mastered lose their life and luster, but also make them completely lose their motivation and desire to learn, explore and create in the near future. Therefore, students' personal experience and emotional attitude are not marginal things, but as important as knowledge literacy, which is an indispensable basic quality for a fully developed person. In order to make students learn more interesting and enjoyable, teachers should think about how to make students experience that mathematics learning is not daunting and boring, but a kind of happy and wonderful fun through the change of students' teaching behavior. As Einstein said, education should treat what is provided as a precious gift for students to enjoy, rather than let him undertake an arduous task. Huang Aihua, a special-grade teacher, once had a lesson on comparing numbers within 10,000 yuan. This lesson focuses on the competition between the Yangtze River team and the Yellow River team, and takes interesting game competitions as the carrier for teaching. The class is divided into two teams, and the students are carefully organized to compete in three rounds to see which team has a big four-digit number. The students went through the process of numbering from the unit, from the low number to the high number, and from the high number. The mathematics in each draw was decided by lottery. The three rounds of competition are interlocking, step by step and in one go. In the interesting math contest, they deeply understood the relationship between the size of numbers and the number of digits. At the same time, the three mathematical activities contain rich mathematical knowledge, mathematical ideas and mathematical methods, which make the output of classroom teaching naturally appreciated. The whole class had fun, learned happily and realized easily, which made students' thinking jump in the joy of success. The above three indicators are interrelated and mutually restricted, and have inherent unity. To consider the effectiveness of students' learning, we must comprehensively consider these three elements. Effective teaching is an idea, a value pursuit and a teaching practice mode. Effective teaching should pay attention to three elements: time, result and experience, so that students can learn something worthwhile, think and enjoy learning, and effectively improve classroom teaching efficiency.