Let's analyze the actual teaching effect of each link.
Review guide:
Teachers often review and guide by asking questions, so as to review old knowledge, build a bridge between old and new knowledge and stimulate students' interest in knowledge by asking questions. However, can it be achieved by requiring three or four students in each class? In fact, even a very clever teacher (the questions are carefully designed) can only help a small number of students to review old knowledge and prepare for new lessons. Students with poor grades will never be able to consolidate what they have not mastered during the questioning time. Moreover, teachers' unilateral guidance can only make students recall old knowledge driven by teachers' language, and there is no or little personal experience of "subject problems", which is not easy to stimulate students' interest in understanding. It can be seen that review guidance can only help some students recall the knowledge related to new knowledge, so that students with positive learning motivation can enter the new class with a fuller mental state.
Teach new lessons:
This is the essence of traditional lessons. Well-prepared teachers use vivid, incisive and concise language to explain the formation of concepts, the proof of theorems, the derivation of rules and their application through intuitive and illustrated explanations and examples of teaching AIDS. Under normal circumstances, it is always based on the teacher's explanation, interspersed with some enlightening questions, or let students do some exercises. When the teacher speaks, the students listen, the teacher writes, the students take notes, the teacher asks the students to answer, and the students learn mainly through the senses. Even if there are a few thinking activities (such as answering questions), they are completed under the guidance of the route designed by the teacher in advance, and there is no independent cognitive activity. Therefore, among students in middle and lower grades, there is often a phenomenon of "understanding as soon as you listen, forgetting as soon as you throw it, and making mistakes as soon as you do it".
Consolidate the new lesson:
Traditional teaching often takes completing a large number of exercises and answering typical exercises as the consolidation of new courses. It is essential for students to understand and remember new knowledge through imitation exercises, but it can't be limited to this. Effective consolidation can only be achieved by repeating the cycle and applying what they have learned in new situations.
Summary:
Summarizing work is often done by teachers. Because middle school students are not interested in empty preaching, such a summary is only formal; Sometimes teachers ask students to summarize themselves, but because there is no independent thinking activity in class, ordinary students can only recite the articles in the textbook mechanically or repeat what the teacher said. Such a summary can not cultivate the comprehensive generalization ability of most students.
Advantages and disadvantages of traditional methods
(1) contributes to the formation of knowledge system.
Practice has proved that this teaching method, if used properly, has the characteristics of clear steps, clear organization and interlocking, which is beneficial for teachers to impart systematic knowledge. At the same time, the mathematical knowledge presented by teachers to students has the logical order of disciplines, and such learning is easier to form systematic knowledge than students' self-exploration and self-discovery.
(2) It is helpful for students to form mathematical concepts quickly and accurately and understand relevant knowledge.
In traditional teaching, the teacher's careful explanation clears the obstacles for students to understand and makes learning less detours; In addition, while teachers impart knowledge, they also reflect teachers' own feelings, styles and accomplishments, and students will be unconsciously influenced during class. Moreover, when students attend classes, the auditory and visual systems play a role at the same time, which makes it easier to form knowledge representation than reading alone. So we say that under the condition of students' active learning, traditional teaching is more conducive to receptive learning than other teaching forms.
(3) In-class imitation exercises, short after-class comprehensive exercises and systematic review after the unit, such spiral cycle training is helpful to the cultivation of basic skills.
To sum up, the traditional teaching method has obvious effect on mastering double basics, which has been proved by years of practice. However, there are also some drawbacks that need to be reformed.
(1) The control of the teaching system in the traditional teaching mode mainly comes from teachers, but the students' learning subjects fail to participate in the control, which makes the internal interference from students unable to be adjusted timely and accurately, and the teaching system cannot achieve real dynamic balance.
(2) The traditional teaching mode adopts the way of imparting knowledge by teachers, and there is no or little process of "discipline producing problems". Students are generally in a state of passive acceptance, and there is no predetermined direction and requirement for learning action. Students' subjective initiative can not be fully exerted, and their ability of observation, thinking and imagination can not be developed rapidly.
(3) The traditional teaching mode chews the questions too carefully. When solving problems, it is often the teacher who talks at the end. Students' intelligence is not challenged and mental factors are not fully mobilized. In the process of learning, students get less positive emotional experience and poor will quality.
(4) The traditional teaching mode, which brings together 40 or 50 students and adopts the teaching of "equal amount, uniform speed and the same requirements", will inevitably lead to the situation that the top students "don't have enough to eat" and the poor students "don't have enough to eat", which is not conducive to achieving the goal of improving teaching quality in a large area.
⑤ In the traditional teaching mode, the information feedback channel is not smooth, and the feedback information obtained by teachers and given to students is mostly delayed feedback information, which makes it impossible for students with learning difficulties to take timely measures according to their learning situation. Some students have accumulated over time, reaching an irreparable level, and finally they are seriously tired of learning and become lost students.
The idea of reform
(1) Through the leading role of teachers, students change from passive position to active learning position, and from "asking me to learn" to "I want to learn".
Therefore, in the choice of teaching methods, teachers should pay attention to stimulate students' interest in learning and desire for knowledge, so that learning becomes students' conscious requirement; Pay attention to the creation of "problem situation" and start students' thinking; Carry out camera induction to make students' thinking develop smoothly; Guide learning methods, so that students can learn to think, understand, digest and absorb by themselves; Guide students to self-evaluate their own learning, so as to adjust their learning in time.
(2) In teaching activities, as far as students' psychological activities are concerned, their cognitive process, emotional process and will process are always accompanied.
Cognitive process plays the role of receiving, processing, processing and storing knowledge information; Emotional process plays a role in regulating cognitive process and strengthening learning behavior; The process of will regulates the cognitive process and emotional process, determines the direction of adjustment, eliminates interference, and achieves the expected learning goal. In the process of learning, only by making the cognitive process, emotional process and will process develop in harmony can we receive good learning results. Therefore, when choosing teaching methods, we must pay attention to choosing methods that are not only conducive to the development of cognition, but also conducive to the stimulation and cultivation of emotion and will. In teaching, we should create a teaching environment that can stimulate students' positive emotions, and then form a passionate pursuit of knowledge, positive thinking and active exploration of new knowledge. In the teaching process, we should constantly stimulate students' suspense, doubt, confusion, surprise and interest in learning, so that students can obtain successful satisfaction and positive emotional experience in the learning process. There must be some difficulties in teaching, so that students can cultivate their learning consciousness, persistence and self-control in the process of overcoming difficulties.
(3) Mathematical ability is formed and developed in mathematical activities.
In the process of learning, if students are allowed to acquire knowledge independently and deal with and solve related mathematical problems independently, their mathematical ability will be developed. Therefore, in mathematics teaching, teachers should create conditions for students to have the opportunity to observe, think and solve problems independently. In the process of learning, teachers don't need to eliminate all the difficulties in learning. On the contrary, they should consciously leave some difficulties for students to think about and solve, which is conducive to the development of students' ability. Many true knowledge of mathematics is the conclusion drawn by people through observing, comparing, associating, analyzing, synthesizing, abstracting and generalizing a large number of special situations, and then a set of rigorous mathematical theories is formed through rigorous argumentation. However, this rigor often masks the vivid side of mathematics. Therefore, in teaching, teachers should "activate" the knowledge in books, restore its original vividness, vividness and creativity, and help students understand the knowledge through observation, comparison, analysis, synthesis, abstraction and generalization.
(4) The basic structure of the discipline refers to the basic concepts and principles of the discipline and their interrelationships, and it is the general connection between the whole knowledge and things.
Mathematical thought is the crystallization of mathematical knowledge and a highly generalized mathematical theory. Mathematical method is the reflection and embodiment of mathematical thought in mathematical activities. They connect the knowledge existing in the brain, form different levels of knowledge structure, and relatively increase the intellectual value of knowledge. Therefore, to help students form a reasonable knowledge structure, we must attach importance to the teaching of mathematical concepts and principles; Pay attention to the revelation of the internal connection of knowledge; Pay attention to the excavation, refinement and generalization of mathematical thinking methods; Pay attention to helping students grasp the content of knowledge as a whole.
(5) Make students change from "learning" to "learning".
In the process of teaching, teachers should pay attention to helping students master learning methods and guide students to grasp all aspects of the classroom, such as preparing well for class, making material and psychological preparations, paying attention to lectures in class, actively exploring and thinking, especially using eyes and ears, combining hands and brains, etc. It is also necessary to help students learn to find problems, think about problems, learn to associate, learn self-study methods, and learn self-evaluation and self-correction.
Since 1980s, many educators and mathematicians in our country have carried out teaching reform under the guidance of modern teaching theory, and preliminarily summarized some new teaching modes on the basis of practice. For example, Qingpu County's "pilot teaching mode", Lu Zhongheng's "self-guided teaching mode", Li Shifa's "six-lesson unit teaching mode", Guangzhou No.1 Middle School's "start-research teaching mode" and Li Gengnan's "self-guided discussion teaching mode" and so on.
Operating principles and requirements of mathematics teaching design
According to teacher Pan Yongqing's summary of Weifang City, Shandong Province, there are mainly the following points:
1. Scientific teaching objectives
This goal should meet the following scientific requirements:
(1) Goals should be concrete rather than abstract.
(2) The goal should be measurable and easy to operate. For example, understanding the definition of quadratic root can
(3) the goal should be hierarchical and step by step. There should be different levels from memory, understanding, application to synthesis, from low to high. This reflects the ability of knowledge transformation and the requirement of gradual internalization.
(4) the goal should be phased. Learning objectives should be put forward in stages from the aspects of students' age, psychological characteristics and cognitive level. For example, the concept of absolute value, rational number requires beginners to find the absolute value of a specific number;
(5) the goal should be comprehensive, with both direct and indirect goals. The objectives include mathematical facts, mathematical concepts, propositions, methods, knowledge structure, mathematical skills and experience in mathematical activities. The indirect goal is to learn the ideas, experiences and behaviors indirectly obtained by mathematics, such as mathematical attitude, mathematical thought and consciousness, mathematical ability, self-study and creativity, ideological quality and personality quality.
2. The orderliness of knowledge structure
The knowledge system of logical order is convenient for memory, association and application. Instructional design should strive to construct knowledge structure to promote the emergence of new cognitive structure. Do two things:
First, clarify the knowledge points and their essential relationships, and form an organic framework of knowledge structure. For example, the establishment of same base powers's multiplication law is essentially the meaning of power and the application of multiplication law; Learning the square root operation essentially changes the existing research direction of finding the square power into finding the base of the known power.
The second is to find out the way of presenting knowledge, that is, to clarify how the teaching materials present knowledge and its connection. The presentation of teaching materials is "simple", some abstract and some deviate from students' existing knowledge and experience.
3. Adaptability of cognitive structure
"Cognition" is a cognitive activity for learners to understand their own objective world and subjective world. Mathematics learning is a process in which new knowledge interacts with students' existing cognitive structure to form a new cognitive structure.
(1) Predict students' cognitive basis. (1) Design diagnostic test questions, and design test questions from the connection between old and new knowledge to test whether students have the necessary knowledge and experience. ② Pay attention to different types of students in daily teaching, and consider further optimizing gifted students while meeting the needs of most students, so as to make up for and develop the underachievers accordingly.
(2) Follow the cognitive law. First of all, we should follow the cognitive process from perceptual to rational, from concrete (inducing concrete) to abstract, and then from abstract to concrete (rational concrete). Perceptual materials are not only the basis of forming appearances, but also the starting point to guide students to abstract generalization and rational analysis. Teaching design must provide students with rich perceptual materials, such as vivid examples, pictures, graphics, slides, videos and teaching AIDS. On the basis of perceptual materials, we should consider how to guide students to make comparison, analysis, synthesis, induction, deduction and abstract generalization. Further guide them to understand the complex diversity and various connections of mathematical objects, thus enriching the connotation of mathematical concepts and raising the initial abstraction to rational concreteness. Secondly, follow the cognitive law from understanding to application, and introduce orderly training into the classroom. The traditional teaching method of bulk speaking in class and concentrated practice after class is not desirable, and the time and space after class are uncontrollable, so the defects in practice can not be made up in time. To introduce orderly training into the classroom, we need to design training questions from low to high, from simple to complex, from monotony to change, from simulation to innovation, which are suitable for students of different levels and can guide students' thinking to develop and deepen continuously.
4. Initiative of ability training
There are many abilities in mathematics teaching, such as abstract generalization, thinking transformation, logical thinking, spatial imagination, mathematical operation, self-study and creation. In the final analysis, it is to cultivate the ability to analyze and solve problems.
The teaching design should be as follows: ① I believe that most students have the physiological and psychological foundation to develop their abilities, and design different ability requirements and training strategies for different types of students. (2) The background materials to show the process of knowledge generation should be as rich as possible, and problem scenarios should be created to stimulate the enthusiasm for knowledge and thinking. (3) Design a detailed knowledge generation process, appropriately reproduce the thinking process of discovering knowledge at first, and make necessary processing according to teaching needs. ④ Designing students' thinking contradictions in the process of cognition, revealing and guiding students to solve contradictions and forge ahead. ⑤ Design methodology. It is design that guides students how to read, think, observe, remember, organize and explore.
5. Students' independent participation
(1) Design the problem scientifically. Mathematical activities begin with problems, and there is no mathematical activity without problems. The design of questions should not only consider students' cognitive basis, but also give students room to think. We should consider the following aspects: ① Ask questions from the connection between old and new knowledge; ② Asking questions leads students to observe, compare, analyze, synthesize, induce, deduce, abstract and generalize; ③ Ask questions through examples (including counterexamples); ④ Ask questions from guiding mathematical thinking methods and thinking directions.
(2) Design appropriate variant training. This paper reveals the essence of concepts from multiple angles, sides and levels, and examines the depth of students' understanding and the discrimination of confusing and error-prone content with specious questions.
(3) Design more detailed classroom student activities. Such as observing, thinking, listening, discussing, calculating, reading and answering questions. From the content to the process and matters needing attention should be considered in detail. Taking the observation of the positional relationship between two circles as an example, the following items should be designed: ① Comparative thinking in observation should not only compare the five positional relationships between two circles themselves, but also compare the positional relationship between two circles and other figures. (2) Review and association in observation, such as the description of the positional relationship between straight line and circle, point and circle, and two straight lines. (3) Scientific generalization in observation, such as first guiding and summarizing the positional relationship between two circles, then guiding and drawing lessons from the experience of describing the positional relationship between straight lines and circles with distance, and summarizing the relationship between center distance and radius.
6. Family "resonance"
The so-called emotional resonance refers to the emotional resonance between teachers and students.
In order to create conditions for promoting emotional "resonance", teaching design should do the following: ① stimulate learning enthusiasm by expounding the meaning of what you have learned; (2) By guiding students to induce conjectures, the intrinsic motivation for the conclusion of argument is generated; ③ Stimulate students' emotional impulse to study deeply by revealing the essential relationship and movement changes of mathematical objects; ④ By guiding students to participate in the process of thinking formation and production, we can taste the fruits of intellectual labor and strengthen the psychological needs of continuing learning; ⑤ By setting appropriate steps, guide students to learn successfully, so as to experience the joy of success and enhance the persistence of interest; ⑥ Encourage students to pursue the happiness of overcoming difficulties and experience the satisfaction of solving difficulties through appropriate praise and encouragement.
7. Timeliness of feedback correction
Timely feedback and error correction is one of the main measures to solve the contradiction between unified teaching and individual differences of students. Teaching design should consider the organizational form, method, content, time arrangement, effect and matters needing attention of classroom and unit feedback correction. For example, classroom observation, throwing stones for directions, discussion, assignment and evaluation, target display and inspection, unit formative test and evaluation, etc.