As an important part of basic knowledge, mathematical thinking method is different from basic knowledge. In addition to the basic mathematical methods, other thinking methods are in a hidden form, infiltrating into the process of learning new knowledge and using knowledge to solve problems. Today, Park Shin-bian Xiao brings you how the teaching design embodies the mathematical ideas and methods.
Infiltrate mathematical thinking methods in the process of solving problems
Problem solving is a psychological activity with thinking as its connotation and problem goal as its orientation. It is an activity to achieve learning goals through thinking in a new situation. "Thinking activity" and "exploring process" are the core of problem solving. Problem solving in mathematics is different from that in other scientific fields. Solving problems in the field of mathematics not only cares about the result of the problem, but also cares about the process of getting the result, that is, the whole thinking process of solving problems. Solving mathematical problems is a thinking process according to certain thinking countermeasures. In the process of solving mathematical problems, we should not only use logical thinking forms such as abstraction, induction, analogy and deduction, but also use non-logical thinking forms such as intuition and inspiration to explore ways to solve problems.
Problem is the core of mathematics, and the process of solving mathematical problems is essentially a process of constantly changing propositions and repeatedly using mathematical thinking methods. Mathematical thinking method is the conceptual achievement of solving mathematical problems, which exists in solving mathematical problems. The gradual transformation of mathematical problems follows the direction indicated by mathematical thinking methods. Therefore, solving problems can cultivate students' mathematical consciousness, build mathematical models and provide mathematical imagination. Through practical operation, we can induce creative motivation, embed mathematics into vivid thinking activities, and guide students to learn knowledge, master methods, form ideas and promote the development of thinking ability in the process of learning and applying mathematics. The process of solving mathematical problems is to use "unchangeable" mathematical ideas and methods to solve constantly changing mathematical propositions. Infiltrating mathematical ideas and methods in the process of solving mathematical problems can not only speed up and optimize the process of solving problems, but also achieve the effect of drawing inferences from others.
Refining and summarizing mathematical thinking methods in review and summary
Summary and review are important links in mathematics teaching. It is one of the functions of summarizing and reviewing to reveal the internal relationship between knowledge and summarize the mathematical thinking methods contained in refined knowledge. The summary and review of mathematics can not only stop at the requirements of reviewing and memorizing what we have learned, but also try to think about how new knowledge is produced, developed and proved. What is its essence? How to apply, etc. Summary and review are the process of deepening, refining and generalizing knowledge, which can only be realized through the active activities of hands and brains. Therefore, in this process, it provides an excellent opportunity to develop and improve ability, and it is also an excellent opportunity and way to infiltrate mathematical thinking methods.
After learning the content of a unit, students should have a clear and comprehensive understanding of the content of the unit as a whole. Therefore, when summarizing and reviewing, we should refine and summarize the mathematical thinking methods involved in this unit of knowledge; And look at the role of mathematical thinking method in the process of knowledge development in an all-round way, and analyze the learned knowledge from a new and more comprehensive angle; Improve and refine from the angle of mathematical thinking method. Because the same content can reflect different mathematical thinking methods, and the same mathematical thinking methods are often hidden in many different knowledge points, so when summing up and reviewing, we should also sort out the mathematical thinking methods and their systems from both vertical and horizontal aspects.
2. Mathematics teaching embodies mathematics thoughts and methods.
(1) Infiltrate "method" and understand "thought". Because junior middle school students have poor mathematical knowledge and weak abstract thinking ability, taking mathematical thinking method as an independent course still lacks the proper foundation. Therefore, we can only use mathematical knowledge as a carrier to infiltrate the teaching of mathematical thinking methods into the teaching of mathematical knowledge. Teachers should grasp the opportunity of infiltration, attach importance to the process of putting forward mathematical concepts, formulas, theorems and laws, the process of forming and developing knowledge, and the process of summing up problems and laws, so that students can develop their thinking in these processes, thus developing their scientific spirit and innovative consciousness, and forming the process of acquiring and developing new knowledge and solving problems with new knowledge. Ignoring or compressing these processes and blindly instilling knowledge will inevitably lose the opportunity to infiltrate mathematical thinking methods again and again. For example, the chapter "Rational Numbers" in the first volume of junior high school algebra textbook is missing a section-"Comparison of Rational Numbers" compared with the original textbook, and its requirements run through the whole chapter. After the teaching of number axis, it leads to "two numbers represented on the number axis, the number on the right is always greater than the number on the left" and "all positive numbers are greater than 0, all negative numbers are less than 0, and positive numbers are greater than all negative numbers". The whole process of solving the ratio of two negative numbers after absolute value teaching. Teachers should grasp the principle of gradual infiltration in teaching, even if the focus of this chapter is prominent and the difficulties are scattered; It also infiltrated the idea of combining form and number into students, which was easy for students to accept.
In the process of infiltrating mathematical thinking methods, teachers should carefully design and organically combine them, consciously and imperceptibly inspire students to understand all kinds of mathematical thinking methods contained in mathematics, and avoid the wrong practices such as mechanically copying, generalizing and being divorced from reality. For example, when teaching the solution set of quadratic inequality, we should combine the image of quadratic function to understand and remember, sum up that the solution set is between and outside two roots, and use the method of combining shape and number to successfully complete the transition between old and new knowledge.
(2) Training "methods" and understanding "thoughts". The content of mathematical thought is quite rich, and the methods are difficult and easy. Therefore, infiltration and teaching must be carried out at different levels. This requires teachers to be fully familiar with the textbooks of junior middle school, study the textbooks, try to dig out all kinds of factors that permeate the mathematical thinking method in the textbooks, carefully analyze this knowledge from the perspective of thinking method, and implement the teaching of mathematical thinking method from easy to difficult according to the different age characteristics, knowledge mastery, cognitive ability, understanding ability and acceptance ability of junior middle school. For example, when teaching multiplication with the same base number, students should be guided to study the operation methods and results of the same base number with a specific base number and exponent, so as to summarize the general methods. After obtaining the general law of using A as the base and M and N as the index, students are required to apply the general law to guide specific operations. In the whole teaching, teachers have infiltrated the mathematical methods of induction and deduction at different levels, which plays an important role in cultivating students' good thinking habits.
3, active mathematics classroom atmosphere
1. The language should be kind and full of emotion, so that students can have fun in learning.
In order to keep students' positive learning attitude and enthusiasm, teachers should use friendly and touching classroom teaching language in the teaching process to ensure the teaching effect. Teachers should be kind to some poor students in the teaching process, maintain their self-esteem, and don't criticize, satirize and dig at students too much, otherwise students will lose confidence in learning mathematics in the long run. To let students take the initiative to participate in learning, it is necessary to give students appropriate encouragement. In the teaching process, when teachers ask students to answer questions, they can use more positive and encouraging language to evaluate students, so that students can have confidence in learning, gain a sense of accomplishment in learning, and then arouse students' interest in learning. Because mathematics is abstract, difficult to understand and logical, teachers should use language to create an interesting learning atmosphere, stimulate students' interest in learning and let students take the initiative to learn mathematics.
2. Happy practice-let the math class come alive and explore.
Practice is the source of creation. Without practical activities, mathematics will become passive water and a tree without roots. Modern educational thought holds that mathematics teaching should be the teaching of mathematics activities, and students' thinking activities can only be activated through mathematics activities, and the spark of innovation can come out in generate. Therefore, in practical teaching, it is necessary to combine classroom knowledge learning with social experience to make students' learning channels diversified and learning methods vivid. Hands-on practice is the "key" to open students' closed minds, awaken their sleeping potential, activate students' sealed memories and release imprisoned emotions, so that students' knowledge and experience can be deepened, enriched and vivid in hands-on practice.
3. Create scenes to mobilize the classroom atmosphere
Psychologically, primary school students are curious, skeptical, love beauty and lively. As a teacher, we should think more from these aspects and give full play to the role of non-intellectual factors in learning. In the classroom, the teaching method of combining learning with playing is created, so that students can play in middle school and in school. There are many ways to create scenes in the classroom. According to the actual situation of the students in this class, we should choose appropriate methods, provide specific contents, lively forms, novel and moving things, and show them in an appropriate way so that students can truly appreciate the fun. For example, when I was teaching the composition Remember a Game, I created such a classroom scene. I played a game of sticking my nose with my students. Naturally, the game was very interesting, and all the students laughed. In the game, I ask students to carefully observe the game process and the characters' language, movements and demeanor, and talk about their own experiences or feelings. In a class, students' enthusiasm is always high. In this way, the two long-standing problems of "what to write" and "how to write" are solved, students' interest in learning is improved, and the classroom atmosphere will be more active.
4. Stimulate the interest in learning mathematics
Let students enjoy the happiness of success and let them feel the happiness of success.
Psychologists' research shows that interest can make students succeed. Teachers should make students feel happy and happy after continuous success, generate a sense of achievement in learning, generate a sense of happiness in learning, move towards more success, get success again and again, and stimulate students' lasting interest in learning. Teachers should start from the actual situation of students, create opportunities for students to compete freely, encourage students at different levels to achieve different degrees of success, let students jump up and pick peaches, and gain students' confidence in learning. Teachers can create opportunities for students to solve different problems and let students complete different learning problems.
Teachers should educate students to face all students and teach them in accordance with their aptitude, so that each student can feel successful and enjoy learning. In the teaching process, teachers should educate students to pay attention to the depth, accuracy and speed of learning. Teachers should pay attention to intensive lectures and make students concise. Teachers should explain the difficulties of each class in class, and teachers should also teach at different levels according to the characteristics of students' subjects. Teachers should let students study and practice boldly, which is in line with the characteristics of students' in-depth research on the subject. They should ask students to complete mathematics learning tasks under the guidance of teachers, stimulate students' learning potential, encourage more practical links, pay attention to the requirements of homework, let students complete more tasks on the basis of basic problems, design a good teaching process, and guide students to think about high-quality topics.
Teachers should use the beauty of mathematics to improve students' learning potential.
Mathematical beauty is different from natural beauty and artistic beauty. The beauty of mathematics in teachers' teaching is mainly inner beauty, logical beauty and rational beauty, while mathematics actually contains hidden beauty, profound beauty and ideological content beauty. Teachers should guide students to understand and discover the beauty of mathematics, and through the application of abstract mathematical symbols, mathematical formulas and mathematical theorems, guide students to explore mathematics learning ideas, carry out intellectual activities and enrich students' emotions. Mathematics teachers should guide students to deeply analyze mathematics emotion, stimulate students' interest in learning mathematics, educate students to effectively master mathematics learning content, improve students' mathematics learning ability, develop students' mathematics creativity and realize the value of mathematics teaching.
Teachers should guide students to learn to discover and understand the game function of mathematics, exercise their minds through mathematics learning, and let students explore the mysteries of the mathematical world and feel the beauty of mathematical activities. Teachers should make use of the beauty of mathematics textbooks, let students explore the beauty of mathematics, stimulate students' motivation and interest in learning mathematics, guide students to think positively, fully feel the beauty of mathematics and pursue it. When a math teacher asks questions, the teacher should let students fully feel the beauty of mathematics and attract students' interest in learning. When students analyze problems, teachers should let students feel the quality of mathematical thinking and guide them to master the mystery of mathematical learning. When summing up mathematics, teachers should let students learn the beauty of harmony, unity and simplicity in mathematics, so as to reduce their burden of mathematics learning and let students fully feel the wonderful structure of mathematics knowledge.