Model essay 1: Teaching strategy of mathematical concepts in junior high school Abstract: The definition in mathematical concepts is the basis of the knowledge system of mathematical science and the core of the basic knowledge of mathematics in middle school. The definition of mathematical concept is also the cell of mathematical thinking and one of the foundations of mathematical ability. It can be seen that if you want to master a subject, you must master the core and fundamental concepts of this subject. Therefore, teachers should explore the methods and strategies of mathematics concept teaching, so that students can learn mathematics better.
Keywords: junior high school mathematics; Concept teaching; Methods and strategies
The definition of mathematical concepts is the foundation of mathematical knowledge system and the core of basic knowledge of mathematics in middle schools. Mastering a subject means mastering the core and fundamental concepts of this subject. In this sense, mathematics teaching = concept teaching+proposition teaching+problem solving teaching.
First, the meaning, composition and characteristics of mathematical concepts
1. Meaning: Mathematical concepts generally refer to the reflection of the quantitative relationship of the objective world and the essential attributes of spatial forms in the human brain. Mathematical concept is the foundation of mathematical knowledge system, the cell of mathematical thinking and the carrier of knowledge and methods. 2. The composition of the concept: the name, definition, symbols, examples and attributes of the concept. For example,? Parallel lines? Is it the name of the concept? ; Two straight lines that don't intersect in the same plane? Is the definition of the concept; ? ∥? It is a symbol; Parallel lines in different positions and directions can be regarded as positive examples and their variants? ; Two straight lines with nothing in common are called parallel lines? Can be seen as a counterexample; ? Parallel lines? Its attributes are transitivity, equal isosceles angle, equal internal dislocation angle and complementary internal angles on the same side. 3. The characteristics of the concept: generality and abstraction.
Second, the status quo of mathematical concept teaching
Status quo 1: Pay more attention to results than processes. ? A definition, several points for attention. . One step in place, example training, repeated practice, meet the exam, and succeed quickly. ? Concept teaching = problem-solving teaching? Large capacity training; Classic language? It is better to teach concepts than to talk about a few more topics. ? Concept 2: Example teaching replaces the generalization process of concepts. I think that applying concepts means understanding concepts, and I don't know how to teach concepts, but only know? Imitation+training? .
3. Teaching methods of mathematical concepts
(A) the teaching process of concept formation model
Concept formation? If the key attributes of a certain mathematical object are mainly independently summarized by students on the basis of analysis, analogy, speculation, association and induction of a large number of different examples of similar mathematical objects, then the way to obtain this concept is called concept formation. The psychological process of concept formation is: 1. Perception and discrimination of different situations; 2. The abstraction of a kind of * * * in the same situation: 3. Linking this * * * with the concept in memory: 4. Different from other known concepts; 5. Summarize essential attributes; 6. Definition.
(B) the general steps of concept formation mode teaching
1. Concept background and introduction (positive example); 2. Students analyze, compare and synthesize different typical cases (let students give more examples); 3. Summarize the essential characteristics of * * * from examples, and get the essential attributes of the concept; 4. Definition (accurately expressed in various mathematical languages); 5. Concept discrimination (citing positive and negative examples, analyzing key words and investigating special cases); 6. Application of concepts (representativeness, formation of operation steps through concept judgment); 7. Form a conceptual system (establish a conceptual system and improve the cognitive structure).
(C) the teaching process of conceptual assimilation model
1. Assimilation of the concept? New mathematical concepts are formed by adding other new features on the basis of existing concepts. At this time, students use the existing knowledge in the cognitive structure to process and transform the new concept, so as to understand the meaning of the new concept. This way of acquiring concepts is called concept assimilation. 2. Type: There are two situations: the new concept and the old concept have affiliation and there is no affiliation. (1) There is no subordinate relationship between the new concept and the old concept. State concepts directly with definitions? Example or explanation? Do you understand the meaning of the new concept? Understand the essential attributes of new concepts. (2) There is a subordinate relationship between the new concept and the old concept. The general process of concept teaching is as follows: ① presenting the first organizer; ② Definition (genus+species difference); Concept discrimination (citing positive and negative examples, analyzing key words and investigating special cases); ④ Application of concepts (representativeness, operation steps of forming concept judgment); ⑤ Form a conceptual system (establish a conceptual system and improve the cognitive structure).
Fourthly, the strategy of concept teaching.
Policy 1: Execute? Chunks? The so-called chunk in teaching refers to the information processing process of combining several smaller units into familiar larger units in memory. Case: Find the unary quadratic inequality AX2+BX+C > When solving the set of 0, it is usually divided into a △& lt; and a 0, △=0, △ <; 0 Discuss three situations, including six situations before and after. Strategy 2: overall perception, actively constructing knowledge and methods Ausubel's meaningful learning theory. Learning principle:? Progressive differentiation? And then what? Comprehensive integration? .
( 1)? From overall background to local knowledge? Structure teaching based on
Case: Concept teaching activity of function 1: a preliminary feeling of the relationship between two variables in life 1. The process of change; 2. Two variables; 3. A correspondence, that is, one quantity changes with another quantity.
(B) from thinking strategies to specific methods of structural teaching
What does Zhang Jianyue think of mathematics teaching? Understand the basic routines of mathematical objects? As one of the core goals, that is, through learning, let students master the basic thinking path and basic operation methods to study and solve such problems.
(C) from the upper concept to the lower concept of structural teaching
When a new concept is subordinate to the existing knowledge in students' mathematical cognitive structure, it constitutes a subordinate relationship. The original concept is called the upper concept, and the new concept is called the lower concept. Strategy 3: Systematically sort out and reveal the connections and laws of knowledge. Learn knowledge from a systematic perspective, put knowledge in the system, focus on the connections and laws between knowledge, and thus go deep into the essence, because connections and laws are the essence, and focus on the infiltration of mathematical ideas. Teachers can summarize the conceptual system from three aspects: 1. Establish concept network, concept map or mind map; 2. Express the relationship between concepts; 3. Reveal the mathematical thinking method contained in this concept system. Strategy 4: Use? Long-distance two-stage type? Teaching strategy? Two stages of long-distance love? Teaching strategy is to divide the teaching process of each structural unit into? Teaching structure? And then what? Use structure? Two stages. ? Teaching structure? Stage. Mainly using the method of discovery, students can discover and construct knowledge from practical problems in the process of solving problems, fully understand and experience the structural existence of internal relations between knowledge, and gradually form the structure of learning methods. ? Use structure? Stage. Mainly to let students use the learning method and step structure, actively learn and expand, and master relevant knowledge similar to the structure.
In short, the teaching of mathematical concept definition in middle schools should proceed from reality, be carefully designed and treated seriously; Take different methods to guide students to observe, analyze, compare and abstract, reveal the essential attributes of things, introduce new concepts in time, and lay a solid foundation for learning new knowledge.
References:
Yan Xu. On the teaching methods and strategies of mathematical function in junior middle school [J]. Mathematics learning and research, 20 1 1(22).
[2] Zhu Zhu. On the teaching methods of mathematical concepts in junior high schools [J]. Middle schools, 20 12(8).
[3] Li ping Strategies of junior high school mathematics concept teaching under the background of new curriculum [J]. Mathematics world: for teachers, 20 10( 10).
[4] Zhou Hua. On the teaching methods of junior high school mathematics concepts [J]. China Science and Education Innovation Guide, 2009(24).
Fan Wener: Hierarchical Teaching Junior High School Mathematics Teaching Abstract: Through the above analysis of the application and experience of hierarchical teaching methods in junior high school mathematics, we can draw the conclusion that hierarchical teaching is an intuitive embodiment of teaching students in accordance with their aptitude. This teaching method emphasizes the differences between students and objective existence, and divides students into different levels, which can improve the overall level of students.
Keywords: stratified teaching; Junior middle school mathematics
First, the junior high school mathematics application layered teaching experience
In the primary school stage, the knowledge learned by primary school students is usually relatively simple, so the intelligence differences of different students are not reflected. After junior high school, students' courses have obviously increased, and it is difficult for many students to adapt to this change in a short time. Some students who have done well in basic studies have gradually declined in academic performance. The main reason for this situation is that students obviously show different personality differences after the increase of learning tasks, especially after entering the second and third grades of junior high school. Therefore, in order to improve this phenomenon, teachers should adopt the method of hierarchical teaching in advance to solve this problem from the root, so that students can take the initiative to learn and have interest in learning, and this enthusiasm will not be erased by this heavy learning. Teachers should complete teaching tasks and improve the academic performance of all students. Teachers should implement hierarchical teaching according to the actual situation of their classes. The individualized needs of students are the main starting point and end result of hierarchical teaching. Teachers should set reasonable teaching objectives and use reasonable teaching methods to divide teaching content.
The design of course content should conform to the characteristics of students' psychological development, and teachers should teach students in accordance with their aptitude and be more targeted. This hierarchical teaching method can effectively stimulate students' interest and enthusiasm in learning, fundamentally improve the efficiency of mathematics classroom and improve the teaching quality. Mathematics is a very logical and scientific subject, and this high abstraction focuses on the cultivation of students' ability. The structure of mathematics knowledge is rigorous, so students have certain differences in mathematics classroom teaching. Teachers should combine these differences, use these differences, teach students in accordance with their aptitude, and refer to students' personality characteristics and psychological tendencies to ensure that students can have matching goals at every level. Teachers set different requirements for different students and choose different teaching methods, which can stimulate students' enthusiasm for learning, make students change from passively accepting knowledge to actively learning mathematics, and make each student improve on the basis of the original mathematics learning. Hierarchical teaching takes into account the differences among students and meets the needs of all students' all-round development. Hierarchical teaching can fully mobilize the initiative and enthusiasm of students and cultivate their good habits. Hierarchical teaching is student-centered, which greatly improves the teaching quality of the school, improves students' initiative and enthusiasm in learning mathematics, strengthens students' quality in all aspects, and effectively improves the polarization of students' mathematics scores. Hierarchical teaching can form a good classroom atmosphere. Hierarchical teaching can not only stimulate students' interest in learning mathematics, but also stimulate students' interest in different subjects, so hierarchical teaching is a very effective method and can improve the quality of mathematics teaching in an all-round way.
Two. conclusion
Through the above analysis of the application and experience of hierarchical teaching method in junior high school mathematics, we can draw the conclusion that hierarchical teaching is an intuitive embodiment of teaching students in accordance with their aptitude. This teaching method emphasizes the differences between students and objective existence, and divides students into different levels, which can improve the overall level of students. Hierarchical teaching can effectively increase students' interest in learning mathematics, improve students' enthusiasm and initiative in learning mathematics, and cultivate students' mathematical thinking ability and innovation ability. The application of hierarchical mathematical methods can improve the quality of junior high school mathematics teaching.
refer to
1. the influence and prospect of virtual teaching and research on the professional development of mathematics teachers in primary and secondary schools: China education informatization 2008-02-23