Cultivate students' mathematical thinking and logical thinking ability
Clarify concepts and establish the integrity of students' thinking
Abstract logical thinking refers to the thinking activity of mastering concepts and using them to make judgments and logical reasoning. Language is the shell of thinking. Einstein once said: "The development of a person's intelligence and the method of forming concepts depend largely on language." Pupils' thinking activities are highly dependent on language because of the narrow language area and lack of mathematical language. Therefore, we should attach importance to concept teaching in teaching and make every concept and every truth clear.
How to cultivate the logical thinking ability of mathematical thinking
Strengthen training and cultivate the flexibility of students' thinking
In order to cultivate students' ability to solve problems accurately, quickly and flexibly, in the teaching of applied problems, we should pay attention to the training of writing problems by ourselves and solving many problems for one problem. Self-compiled application questions should not only consider the rationality of structure, the logic and rigor of quantitative relationship, but also consider the flexibility of thinking. The process of compiling questions is actually the process of cultivating students' initial logical thinking. The practice of multiple solutions to one question not only cultivates the flexibility and creativity of students' thinking, but also stimulates their initiative and enthusiasm in learning.
Teaching methods of cultivating students' thinking logic
Develop students' initial logical thinking ability, and ensure the certainty and non-contradiction of thinking. We must strictly abide by the basic laws of logic, and choose different teaching methods according to the logic of the textbook itself in teaching, so that students can know not only why, but also why. Teach students to tell the thinking process and problem-solving steps in an orderly and reasonable way, help students master the thinking method and improve their thinking ability.
2 students' logical thinking ability
1. Although cultivating thinking ability is an important task in primary school, each grade has its own different tasks, and students of different ages have different degrees of acceptance and understanding of knowledge. Therefore, we need to divide the tasks of each grade to make the tasks more clear, so that the requirements for students are also improved step by step.
2. Thinking ability is reflected in many aspects. Teachers need to carry out the cultivation of students' ability at every level and stage of teaching, and organize students to review and contact knowledge, combine old and new knowledge, and explore and learn specific problems in time.
How to cultivate the logical thinking ability of mathematical thinking
For example, teachers with certain teaching experience will focus on guiding students to review independently when reviewing and exploring the addition and subtraction of rounding within 20. Because students have mastered this knowledge point initially, it is necessary to master the knowledge to a new height, let them talk about the thinking of solving problems, and know the weakness of solving problems while finding the positive solution of the wrong problem. A topic can guide students to find multiple breakthroughs, learn analogy and comparison, and help cultivate students' thinking activity and sensitivity.
3. The cultivation of thinking ability should run through every part of teaching. The so-called partial content is to analyze specific problems and take specific countermeasures. Whether it is to explain the basic mathematical concepts to students, or to teach students the basic skills of calculating rules and solving problems, as well as the use of mathematical tools, we need to explore and answer according to actual examples. These examples are for students to accept and explain with their own thinking and find out the similarities and specialities with other knowledge.
3 How to train mathematical thinking logic
Pupils' abstract logical thinking ability is poor, so they need intuitive materials to arouse students' association, carry out positive thinking activities and establish concepts.
In primary school mathematics teaching, it is a good method to help students think with the help of line graphs. In learning, we often encounter such a situation. For a complex application problem, some students look at the front conditions and can't contact the back conditions. After reading the latter conditions, I forgot the former conditions. With the help of line drawing, students can better understand the meaning of the problem and master the whole picture of the application problem. At the same time, teachers can also find the advantages and disadvantages of students' thinking from the line drawings drawn by students, which is more convenient and targeted to help students.
In order to train students to think by line drawing step by step, I will start with simple questions and guide students to practice looking at pictures, drawing pictures and telling pictures. Train students to explain accurately and fluently how the known conditions and problems are represented on the diagram and what is the relationship between the known conditions and problems. I also train students to express problems and known conditions accurately and quickly with line diagrams after seeing them, and to clarify the relationship. When students master these methods, I often combine new courses to let students draw and think for themselves and learn new knowledge. For example, when I write an example, my classmates are scrambling to draw pictures on the blackboard to express the meaning of the problem. Although it is a new course, students can draw and think skillfully with the help of line drawing, not only learn new knowledge, but also draw inferences from others.
While cultivating and training students' logical reasoning ability, I also pay attention to cultivating students' abstract generalization ability.
I pay great attention to "bridging" and "paving" in the process of training. For example, when talking about the formula for calculating the area of a triangle. Before class, let each student cut a rectangle, a square and a parallelogram with paper. In class, let the students divide the rectangle into two equal triangles, and then inspire the students to find the formula of triangle area according to the formula of rectangle area calculation.
After "cutting and spelling" and calculation, the students list the formulas for finding the triangle area. This kind of training is often carried out consciously, and students' abstract generalization ability is gradually improved. In addition, I also attach great importance to strengthening the training of students' language and thinking in teaching, and strive to make thinking conform to rules and language conform to norms.
4 Cultivation of mathematical logical thinking ability
Develop students' innovative thinking and cultivate their innovative ability.
Students' thinking often begins with activities. In teaching activities, teachers should create a good environment for students to practice and experience, and fully let students cut, spell, fold, draw and touch. This can concentrate students' attention, stimulate their interest in learning, make their learning lively and interesting, and help them abstract mathematical knowledge, form concepts and develop their thinking. In operation, they should boldly let go of the operation form, which is more conducive to the cultivation of students' creative ability.
For example, when teaching "Cognition 2", let the students put a stick on the desk to indicate the number of 2. When observing, the students can release it correctly, and I am sure. Later, I followed the instructions: Can you put out other forms of 2? "As soon as the students heard these words, their little hands took active action. So, I asked students to put a pendulum on the blackboard, and the result was a dozen: "=, >,< In this operation, students can understand the meaning of" 2 "and break through the key and difficult points of teaching. Students can use innovative thinking to promote innovative consciousness and give full play to the role of autonomous learning and inquiry learning. Students learn experience from operation activities and think positively, which is conducive to developing students' innovative potential, giving students a classroom atmosphere of psychological integration, thus cultivating students' innovative thinking ability.
Design similar questions and training to cultivate and develop students' analogical thinking ability.
In order to develop and improve students' new knowledge and original knowledge structure, teachers must also strengthen the cultivation and improvement of students' analogical thinking ability. For example, before teaching "addition and subtraction of fractions with different denominators", the teacher must let the students review the contents of integer addition and subtraction, decimal addition and subtraction and fractional addition and subtraction with the same denominator, and boil them down to a whole knowledge. Then the teacher leads the students to conclude that the addition and subtraction problems can only be added and subtracted directly if the counting units (or decimal units) are the same.
In the new lesson, teachers can design similar questions: ① Can scores of different denominators be added or subtracted directly? Why? (2) What should I do first to add or subtract fractions with different denominators? (3) How to change different denominator scores into the same denominator score? By thinking about this similar problem one by one, students will naturally think analogously: addition and subtraction of scores with different denominators? Can't you just add and subtract different decimal units? Become a fraction with the same denominator? General score? Add and subtract.
Error-prone point of function
Error-prone point 1: the meaning of each undetermined coefficient.
Error-prone point 2: master the solution of various analytical functions skillfully, and several undetermined coefficients need several points.
Error-prone point 3: Use the image to find the solution set of inequality and the solution of equation (group), and use the image properties to determine the increase or decrease.
Error-prone point 4: two variables use function models to solve practical problems, and pay attention to the differences between equation, function and inequality models to solve problems in different fields.
Error-prone point 5: image classification by function (parallelogram, similarity, right triangle, isosceles triangle) and the solution of classification.
Error-prone point 6: You must find the coordinates of the intersection with the coordinate axis. The solution of maximum area, minimum distance sum and maximum distance difference.
Error-prone point 7: the application of the thinking method of combining numbers and shapes should also pay attention to solving problems in combination with the nature of images. The combination of function images and graphics can learn the method of decomposing complex graphics into simple graphics, and graphics provide data for images or images provide data for graphics.
Error-prone point 8: The range of independent variables is: the square root of quadratic form is non-negative, the denominator of fraction is not 0, the exponential base of 0 is not 0, and the rest are real numbers.