In the lower grades of primary school, it is mainly to find the simple laws implied in given things (things, figures, simple series), express their situation in a mathematical way, and experience the related quantities. Describe the qualitative change of things, such as "I have grown taller"; Or describe the quantitative change of things "I am 4 cm older"; Or observe the pattern and reasonably infer the development trend, such as finding the law "1, 1, 2, 1, 1, 2 ..." ".In this way, in the early learning stage of mathematics, students explore the model and experience the functional relationship by observing the changes of things.
The Mathematics Curriculum Standard for Full-time Compulsory Education published on 200 1 takes exploring laws as an important content of the thought of infiltration function. Therefore, in the second stage of knowledge goal, students are required to understand the "laws" in specific situations, and gradually learn to express the laws with letters or formulas containing letters. In this math teaching contest, Mr. Xiao guessed the teacher's age with "numbers with letters", which was designed very appropriately. Let's talk about intuition first: if you are 10 years old and the teacher is older than the students 19 years old, then the teacher is 29 years old; Recalling the past, I was 6 years old when I was born in grade one, and how old was my teacher; Looking forward to the future, how old will students aged 18 be when they enter the university? Then describe it in language: what has changed and what has not. Through the calculation of several groups and the free exploration of the law, it is found that the age of teachers and students changes with the passage of time, but the relationship between teachers and students is older than that of students 19 years old will not change. Finally, the relational expression of language description, that is, the explored law, is abstracted into algebraic expression, that is, when the teacher is A, the teacher is a+ 19, and when the teacher is T, the student is t- 19. In this way, the organic combination of intuition (graphics and representation), language and algebra is an important way to learn mathematics. Xiao Lao grasped two basic principles well when infiltrating the functional thought: ① Only by creating the process of "change" can we feel the functional thought; ② Stimulate students' nature of "inquiry", grasp "unchangeable" in "change" and satisfy people's curious nature. In this way, we can not only know the past, but also predict and grasp the future by exploring the hidden laws or changing trends in given things.
In the primary school stage, in addition to using letters to represent numbers, there are many places that also contain rich functional ideas, which reflect the regularity, but the expressions are different:
1, counting, one by one, two by two ..., "positive" counting, "negative" counting. No matter how you count, students can experience, discover and describe the "law" in the process of counting.
2. Laws in calculation: the addition table within 20 and the multiplication table of 1999 also contain rich laws. Similarly, under the conditions of constant sum, constant difference, constant product and constant quotient, the relationship between two numbers is actually a function of another number.
3. Laws in the Hundred Numbers Diagram: In addition to the horizontal, vertical and oblique arrangement laws, we can also explore the relationship between two adjacent numbers in each row or column, or even the relationship between four adjacent numbers in two rows and two columns. These relationships can be expressed in words first, but try to express them in letters.
4. Variation law of geometric figures: some basic geometric figures can be obtained by triangle deformation, and the area is also closely related.
5. Basic quantitative relationship: perimeter, surface area and volume formula; Total price, unit price and quantity; Total amount of work, work efficiency and working hours; Distance, speed and time, direct ratio, inverse ratio, etc.
6. Statistical chart: especially the broken line statistical chart, the operation chart itself is the image of the function.
It can be said that function is everywhere. The infiltration of function thought in primary school can make students understand that everything is in the process of constant change, and it is interrelated and restricted in the process of change, so it is necessary to understand the changing trend and movement law of things. This is of great significance to cultivate students' dialectical materialism and ability to analyze and solve problems. Consciously infiltrating the thought of function in primary school mathematics teaching can also lay a good knowledge foundation and prepare students for learning mathematics in the follow-up study.