Mathematical thought; Primary school; Teaching; Simple analysis
Mathematical knowledge exists widely in people's production and life. Elementary school mathematics knowledge is simple, but it is inseparable from the application of mathematical thinking methods. There are many ways of thinking in primary school mathematics. Being able to solve mathematical problems in different ways is of great help to cultivate students' mathematical foundation and improve their learning ability.
First, the classroom application of mathematical thinking methods
Many teachers engaged in primary school mathematics education, although aware of the importance of the application of mathematical thinking methods in the teaching process, are often vague in concept and lack of practical application. Most people rely on textbooks, lack flexibility and fail to integrate mathematical thinking methods into knowledge, which affects the effective teaching of mathematical knowledge. Students don't have a deep understanding of the essence and content of mathematical theory and can't absorb all the knowledge, so they can't put it into practice and solve mathematical problems accurately.
Applying the correct mathematical thinking method to educate students so that they can understand and use it requires teachers' persistent educational influence. This is a slow infiltration process and an effective process to improve the quality of mathematics teaching.
Second, the analysis and research of classroom application of mathematical thinking method
(A) the application of classified thinking method in mathematics teaching
The thinking method of mathematical classification is embodied in the classification of mathematical objects and its classification standards. For example, in the fourth grade triangle classification lesson of People's Education Press, triangles are divided into right triangle, acute triangle and obtuse triangle. Triangular dividing allows students to know the parts of isosceles triangle and equilateral triangle, and the relationship between the two bottom angles of isosceles triangle and the three inner angles of equilateral triangle. Through the mathematical thinking method of classification, students can understand the characteristics of angles and sides of each type of triangle through observation, operation, comparison and generalization. Different classification standards have different classification results and produce new concepts.
(B) the application of hypothetical thinking method in mathematics teaching
Hypothesis is a way of thinking that first makes some assumptions about the known conditions or problems in the topic, then calculates according to the known conditions in the topic, makes appropriate adjustments according to the contradiction in quantity, and finally finds the correct answer. For example, in the equation teaching of fifth grade primary school by People's Education Press, teachers teach students to solve equations by keeping the equations unchanged. Teaching case: The balls in the box and the balls outside add up to nine. How many balls are there in the box? Then, suppose there are x balls in the box, and the equation X+3=9 is obtained. At the same time, the symbolic thinking method is also used here, that is, X is used as the symbolic language to deduce calculus. Then the solution of the equation is obtained by using the equality relation of the equation, and at the same time, a 3 is subtracted from both sides of the equation, and the left and right sides are still equal, resulting in X+3-3=9-3. Then finally calculate the answer X=6. Hypothetical thinking is a meaningful imaginative thinking, which can make the problem to be solved more vivid and concrete after mastering it, thus enriching the thinking of solving problems. At the same time, lowercase letters represent numbers and express a lot of information in the condensed form of symbols, such as laws and formulas.
(C) the application of statistical thinking method in mathematics teaching
The statistics table of primary school mathematics is some basic statistical methods, and finding the average application problem is the thinking method of data processing. For example, in the teaching of the sixth grade textbook "Fan Statistical Chart" published by People's Education Press, the teacher gave a set of data. For example, different sports in extracurricular activities have different numbers of participants and different proportions in the class. Table tennis 12 people accounted for 30%; Football 8 people account for 20%; 5 people jump rope12.5%; 6 shuttlecock kickers15%; The other 9 people are 22.5%; It can be seen that if a bar chart is used, the percentage cannot be expressed intuitively. The teacher draws a fan-shaped statistical chart on the blackboard, telling the students to use the whole circle of the fan-shaped statistical chart to represent the class number, that is, the unit is "1", and the fans with different sizes in the circle represent the percentage. Students are guided to think about how to calculate the percentage through intuitive icons. That is, the number of people in each sport is divided by the number of people in the class, and the sum of all percentages is 100%. Finally, the characteristics of fan-shaped statistical chart are summarized: (1) The whole circle represents the total amount, and the fan-shaped represents the number of each part. (2) From the size of the fan, we can see the percentage of each part. (3) The relationship between circle and sector indicates the relationship between total quantity and partial quantity. Teachers should apply statistical thinking methods to mathematics teaching, and teach students that many problems in life can be solved by statistical methods, and all kinds of statistical methods can be used to solve problems in life.
(D) Application of analogical thinking method in mathematics teaching
The analogical thinking method is based on the similarity of two kinds of mathematical objects, and it migrates from the possible known properties of one kind of mathematical objects to another. For example, in the textbook "additive commutative law" published by People's Education Publishing House, Uncle Li is going to travel by bike for a week. He rode 40 kilometers this morning and 56 kilometers this afternoon. How many kilometers is a * *? Ask the students to use the addition and exchange formulas to get the formula A+B = B+A, and summarize the law: two addends exchange positions, and the sum remains unchanged. This is the teaching application of mathematical analogy thought. In addition, analogy is applied in the teaching of multiplication exchange law, rectangular area formula, parallelogram area formula and triangle area formula. Analogy not only makes it easier for students to understand the knowledge in math textbooks, but also makes boring math formulas easier and more convenient to remember.
Primary school mathematics thought is widely used in mathematics education and teaching, and occupies a very important position. In addition to today's practical research, there are many ways of thinking, such as comparative thinking, transformational thinking, collective thinking and other teaching forms.
In order to keep up with the pace of the continuous reform and development of primary education and teaching, and let students acquire more mathematical thinking methods and master mathematical knowledge, educators should study and summarize in the continuous teaching practice. It lays a foundation for students' continuous learning and development, thus effectively improving the teaching quality of primary school mathematics education.