"Mathematics Curriculum Standard" has clearly pointed out: "Mathematical thinking method is a rational understanding of mathematical laws. Forming a certain mathematical thinking method through mathematics learning is an important purpose of mathematics curriculum and should be infiltrated into teaching. " Mastering the scientific mathematical thinking method is of great significance to improve students' thinking quality, the follow-up study of mathematics, the study of other disciplines and even the lifelong development of students. The formation of mathematical thinking method is a gradual process, which requires long-term training and early training of teachers, especially in the teaching of lower grades.
First, the infiltration of functional thinking methods in the teaching of lower grades
Engels said: "The turning point in mathematics is Descartes' variable. With variables, motion enters mathematics, with variables, dialectics enters mathematics, with variables, differentiation and integration become necessary immediately. "We know that movement and change are the essential attributes of objective things. The value of function thought lies in that it reflects the interrelation and internal laws between objective things with the viewpoint of movement and change. For example, in the third question on page 10 of the second volume of senior one, the idea of "change and invariance" can be infiltrated into students' cameras in time.
On the infiltration of mathematical thinking method in lower grade teaching with examples
Although the concept of function is not mentioned in the textbook, the first-year students can't understand it, and the teacher doesn't need to tell the students what a function is, but the teacher should infiltrate the idea of function in teaching: after the students get the results, the teacher should guide the students to observe in time: What did you find? Let the students find that the number before the minus sign is 1 1. When the number after the minus sign changes, the final result will also change. In other words, students vaguely find that the result of the operation changes with the change of subtraction.
Second, the infiltration of the combination of numbers and shapes in the teaching of lower grades
Number and shape are two aspects of the research object in mathematics teaching. Combining the relationship between numbers and spatial forms to analyze and solve problems is the idea of combining numbers with shapes. "Combination of numbers and shapes" can promote the coordinated development of students' thinking in images and abstract thinking, communicate the relationship between mathematical knowledge and highlight the most essential characteristics from the complex quantitative relationship with the help of simple diagrams represented by figures, symbols and words.
For example, teaching the lesson "Multiply two numbers by one number" (National Standard Soviet Education Edition, Volume 4, page 69),
On the infiltration of mathematical thinking method in lower grade teaching with examples
According to the topic map, students can not only be independent, but also have various algorithms.
( 1)20x3=20+20+20=60
(2) Two tens multiplied by three get six tens, which is 60.
(3) Because 2×3 = 6 and 20×3 = 60.
On the infiltration of mathematical thinking method in lower grade teaching with examples
When teaching 14x2, students can also explore the algorithm independently according to the above theme map: first calculate two tens to get 20, then calculate two fours to get 8, and finally combine them-* * to get 28. However, how to help students combine arithmetic with algorithm, internalize arithmetic into algorithm, and present the steps and processes of thinking in a vertical form? The result of vertical calculation of 14x2 is an abstract process, which requires students to establish vertical models independently, and it is difficult for junior students without intuitive graphic support. Therefore, at this time, the teacher still tries to help students go through the process from concept to abstraction with the help of advanced graphics, such as showing this lesson step by step in the order of calculation: which part of the diagram is calculated by 2×4? 1x2? (Click on the arrow diagram), make the diagrams combine, and let students find the relationship between arithmetic and algorithm through the corresponding relationship between vertical and graphic, so that students can master the algorithm on the basis of clear arithmetic.