In daily study and work life, many people have written papers. A thesis refers to an article that conducts research in various academic fields and describes the achievements of academic research. You always have no way to write a paper? The following is the thinking method and teaching of junior high school mathematics that I compiled for you, hoping to help you.
Mathematical thinking method is the essence of mathematics, the link for students to form a good cognitive structure, the bridge for transforming knowledge into ability, and the carrier for cultivating students' good mathematical concepts and innovative thinking. In teaching, we must attach importance to the infiltration teaching of mathematical thinking methods.
Keywords junior high school mathematics thinking method teaching mode
There are two lines in mathematics teaching, one is the open-line mathematics knowledge teaching, and the other is the hidden-line mathematics thinking method teaching. Mathematical thinking method is the essence of mathematics, the link for students to form a good cognitive structure, the bridge for transforming knowledge into ability, and the carrier for cultivating students' good mathematical concepts and innovative thinking. We must attach importance to the infiltration teaching of mathematical thinking methods in teaching.
1 Mathematical thoughts and methods
At present, there is no exact definition of mathematical thought and mathematical method. We usually think that mathematical thought is "people's understanding of the essence of mathematical knowledge, and it is a mathematical viewpoint refined from some specific mathematical contents and the process of understanding mathematics." Repeated use in cognitive activities has universal guiding significance and is the guiding ideology for establishing mathematics and solving problems with mathematics. " As far as the knowledge system of middle school mathematics is concerned, middle school mathematics thought is often the most common, basic and simple content in mathematics thought, such as model thought, limit thought, statistical thought, reduction thought, classification thought and so on. The so-called mathematical method refers to the procedures and ways people engage in mathematical activities, the technical means to implement mathematical ideas, and the concrete embodiment of mathematical ideas. Therefore, mathematical thinking is implicit, while mathematical methods are explicit. Mathematical thought is more profound than mathematical method, and reflects the internal relationship between mathematical objects more abstractly. Because mathematics is abstract layer by layer, mathematical methods often have the characteristics of process and hierarchy in practical application. The lower the level, the stronger the operability. In a word, there are differences and connections between mathematical thought and mathematical method. When solving mathematical problems, the general guiding ideology is to classify problems into solvable problems. In order to realize transformation, methods such as generalization, specialization, analogy, induction and constant deformation are often used, which is often called transformation method.
2. The psychological significance of mathematics thinking method teaching.
Mathematical thinking method is the link to form students' good cognitive structure and the bridge from knowledge to ability. It is clearly pointed out in the middle school mathematics syllabus that the basic knowledge of mathematics refers to the concepts, properties, laws, formulas, axioms, theorems and mathematical thinking methods reflected in mathematics. Incorporating mathematical thinking method into basic knowledge shows that the teaching of mathematical thinking method has attracted the attention of education departments, and also reflects the understanding of mathematics educators in China on the development of mathematics curriculum. This is not only a measure to strengthen the cultivation of mathematics literacy, but also the necessity and requirement of the modernization process of mathematics basic education. This is because the modern teaching of mathematics is to base the basic education of mathematics on modern mathematical ideas and use modern mathematical methods and languages. Therefore, exploring a series of problems in the teaching of mathematical thinking methods has become an important topic in modern mathematics education research.
Judging from the law of psychological development, junior high school students' thinking is a transition from formal thinking to dialectical thinking. The teaching of mathematical thinking method not only helps students to transition from formal thinking to dialectical thinking, but also is an important way to form and develop students' dialectical thinking.
From the perspective of cognitive psychology, the process of mathematics learning is the process of the development and change of mathematical cognitive structure, which is realized through assimilation and adaptation. Assimilation means that subjects bring new mathematics learning content into their original cognitive structure, and process and transform new mathematics materials to adapt them to the original cognitive structure of teaching and learning. The so-called adaptation means that when the original mathematical cognitive structure of the subject can not effectively assimilate the new learning materials, the subject adjusts and transforms the original mathematical internal structure to adapt to the new learning materials. In assimilation, the basic knowledge of mathematics does not have the characteristics of thinking and initiative, and can not guide the process of "processing". The psychological component only provides the subject with desire and motivation, and provides the cognitive characteristics of the subject, and cannot realize the "processing" process alone. Mathematical thinking method not only provides thinking strategies (design ideas), but also provides specific means to achieve goals (problem solving methods). Actively teaching mathematical thinking methods will greatly promote the development and perfection of students' mathematical cognitive structure.
3 teaching mode of mathematical thinking method
In order to better penetrate the teaching of mathematical thinking methods in teaching, I think the following different teaching modes can be adopted according to different teaching contents:
3. 1 Discover the teaching mode. Discovery teaching mode, also known as problem-solving teaching mode, is based on the teaching theory put forward by American educator Bruner aiming at the psychological characteristics of students' curiosity, inquiry and activeness. The basic procedure of discovering teaching mode is: creating situation-analysis and research-guessing and induction-verification and reflection-application conclusion. The characteristics of this model are conducive to cultivating students' exploration spirit and creativity, cultivating students' ability to think independently, collect and process relevant information, embodying students' main position and methods of studying problems, and stimulating students' interest in learning mathematics. The teaching mode of discovery method is suitable for the stage of knowledge citation. Through the exploration and discovery of mathematical knowledge such as concepts, theorems, formulas and laws, students' ability to solve problems is cultivated. Emphasize the thinking method from special to general in teaching.
3.2 "Comparison-induction" teaching mode. We advocate students to participate in practice to acquire knowledge, but students can't experience everything directly. The relationship between mathematical knowledge is very close, so it is a good method for students to participate in the process of knowledge formation from existing knowledge and experience. Use analogy and comparison to help students find out the connection and difference between related mathematical concepts and related mathematical propositions, so as to accurately understand the mathematical concept system and clarify some confusing concepts, theorems and formulas. This model is suitable for new lessons and review lessons. In teaching, structural thinking, optimized thinking, comparative analysis, induction and analogy are emphasized. For example, after similar triangles's judgment theorem is completed, teachers can compare similar triangles's judgment with congruent triangles's. First of all, it should be pointed out that congruent triangles is similar triangles with similarity ratio of 1. Compare the two theorems one by one, so that students can further strengthen their understanding of the theorems.
3.3 "problem observation-associating old knowledge-problem solving" teaching mode. In teaching, we emphasize the idea of number-shape transformation, transformation and combination. When learning new knowledge, associating old knowledge is an effective way to cultivate transformation consciousness. It is both flexible and creative in thinking. Most of them are close association, similar association and analogy association, such as fractional nature related to fractional nature, quadratic function related to linear function, shape related to number and number related to shape.
Transformation is an important problem-solving strategy, the basis of transformation is association, and transformation is the concrete form of transformation. For example, using the sign law, the four operations of rational numbers are transformed into arithmetic operations, subtraction into addition, and division into multiplication; Through elimination and simplification, the high-order equation is transformed into the low-order equation, and the multivariate equation is transformed into the unary equation; When studying solid geometry problems, they are usually transformed into plane geometry problems to solve; Turn practical problems into mathematical problems to solve.
In teaching, teachers should try their best to reveal the relationship and evolution between knowledge, explore and show the process of knowledge occurrence, so as to open students' thinking and inspire association and transformation. Pay attention to the analysis, reveal the relationship between questions and conclusions, and suggest the factors that stimulate students' association and change their motivation. In addition, the basic thinking method in mathematics is the basis of association and transformation, so we must strengthen the training in this respect.
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