However, how to help students effectively accumulate experience in basic mathematics activities in practical teaching is still worth studying. This paper briefly puts forward some ideas for your reference.
First of all, pay attention to enriching the sensory and perceptual experience in operational activities.
"Basic activity experience is the content with individual characteristics left by individuals after experiencing specific subject activities, which can be sensory perception or experience formed after reflection." In mathematics activities, students' first-hand intuitive feelings, experiences and understandings of learning materials are generally direct experiences through explicit behavior operations. The direct value of this operation is not the solution of the problem, but the perceptual knowledge of the learning materials. For example, when studying the problem of "the sum of the internal angles of a triangle", a student tore off three internal angles of an arbitrary triangle, reassembled the vertices of each angle and put them together in turn, and found that a right angle was formed, thus obtaining an intuitive visual impression: the sum of the internal angles of a triangle is 180 degrees. In this process, the student didn't spend much time, but the operation activities he tried gave him an intuitive feeling of the sum of the angles in the triangle. Although similar perception is obviously composed of individual knowledge, it still has primitive, superficial, one-sided and vague characteristics, but the acquisition of such direct experience is an indispensable and important material for establishing personal understanding.
Of course, to make this kind of experience accumulate reasonably, it sometimes needs to go through a process of judgment, screening and confirmation, because the result of students' first operation perception is not necessarily correct, and the wrong experience will have a negative impact on students' subsequent study. For example, when teaching "understanding the angle", many teachers will let students touch the "vertex of the angle" in specific objects, and then let students express their feelings. Students often answer: "sharp corners, feel stinging." This answer shows that students' cognitive starting point and initial experience are in the category of "life mathematics", which is not enough to reflect the essential characteristics of mathematics. If the teacher does not correct and guide in time, there may be a misunderstanding that the needle tip of the pointer on the clock face is also an angle and an angle is also an angle in the next exercise. Therefore, students' expected experience in mathematics activities should be distinguished from some life experiences.
For another example, when teaching "area units", teachers often try to give students a fuller representation of square centimeters, square decimeters and square meters with the help of multimedia demonstrations. This starting point is good, but in the actual teaching process, it is possible to exaggerate the role of multimedia and ignore the wrong experience brought by students' actual perception. Many teachers often point to the square magnified many times on the screen to introduce to students-the area of a square with a side length of 1 cm is1cm 2. How big is 1 cm2? Is it a square the size of a fingernail on a student's hand or a square the size of a handkerchief on the screen? If teachers don't emphasize and standardize it at this time, students' establishment of the representation of 1 cm2 will be affected, and the enlarged "1 cm2" on the screen is likely to become a false experience after students' intuitive perception and interfere with subsequent learning. Therefore, in the initial stage of experience acquisition, we should try our best to let some operational activities provide a more correct and clear experience for students' cognition, rather than ambiguous and specious perception. Teachers must pay attention to the comprehensiveness and accuracy of experience, and fully consider the above factors when providing materials, organizing operation activities, asking questions and summarizing in class.
Second, pay attention to the integration of behavior operation experience and thinking operation experience in inquiry activities.
In math class, we often throw some questions to students in specific situations, so that students can operate independently, explore independently and communicate cooperatively. Among them, there are both explicit behavior operation activities and thinking operation activities. Students can gain the experience of mathematics activities by combining direct experience with indirect experience. This kind of inquiry activity directly points to
Solve problems instead of gaining first-hand intuitive experience. Students not only experience in activities, but also experience mathematical thinking before, during and after activities.
For example, in the first class of "Statistics and Possibility" in the third grade, teachers usually let students do "touch the ball" experiments to feel the possibility. Based on the students' existing knowledge and experience, it is very possible for students to guess which color of 9 white balls and 1 yellow balls are in the known box, which is not new to students, so the teacher started the following math activities from a different angle: "(Show the box) Students, there are white balls and yellow balls *** 10 in this box, but the number of the two balls is not equal. Without unpacking, is there any way to know which color has more balls? " Faced with such problems, students at different levels will fully mobilize their existing experience to try to solve them. Some students use the method of guessing, and then they are denied by their peers because of the uncertainty of the results. Some students also think that you can touch one ball at a time to see the color, then put it back and shake it well, and touch it several times. Finally, there are many balls representing this color. At this time, hands-on operation and experiment have become the demand of students' exploration. Because students are full of yearning for the results of the experiment, their accumulated experience in mathematics activities is also full of vitality because of strong feelings. Undeniably, although some experience itself has a good guiding role and practical value in solving some problems, it needs to go through a process of conceptualization and formalization to make the experience of mathematical activities into students' individual knowledge system for a long time, which is the only way for experience and "double basics" to merge and sublimate into "thoughts".
Third, pay attention to the accumulation and promotion of strategic and methodological experience in thinking activities.
The experience gained in thinking operation activities is the experience of thinking operation, such as inductive experience, analogy experience, proof experience and so on. As far as a person's rationality is concerned, the thinking process can also accumulate an experience, which belongs to thinking experience. A student who has relatively rich experience in mathematical activities and is good at reflection will inevitably enhance his mathematical intuition with the accumulation of experience.
For example, when learning "the basic nature of ratio", the textbook requires students to record the mass and volume of several bottles of liquid according to Xiaodong, and fill in the ratio of mass and volume, thus inspiring students to observe the equation, make reasonable reasoning with the existing understanding of the basic nature of fraction, and explore the basic nature of ratio. Although the ratio of liquid mass to volume is expressed by students
I don't know much about the actual meaning of "density", but because of my previous experience in exploring the law of quotient invariance and the basic properties of fractions, most students have a mathematical intuition that "ratio" has similar properties. The conclusion that "the former term and the latter term of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged" is based on the experience of analogy. In the verification activities immediately launched, students can also find methodological support from previous relevant experience. So teachers can boldly let go of this content. The more students have similar experiences, the easier it is for new knowledge to be actively incorporated into the existing knowledge system. What teachers need to do is to sort out these experiences, help students discover their essential similarities and differences, and then connect the knowledge "points" discovered by students into a series of knowledge "chains" to form a solid knowledge "network".
In the above-mentioned teaching cases, students' experience generation is carried out at the level of thinking, not attached to specific situations, but only reasoning in their minds, and the whole process tends to be more orderly. Judging from the types of experience gained, the experience gained in such activities is more focused on strategies and methods and more rational than the first two. From this point, we can see that the acquisition of thinking experience is an important channel to derive thinking mode and thinking method, and these components have a very important basic role in students' innovative activities.
Fourth, pay attention to the development of composite and application experience in comprehensive activities.
In reality, many mathematical activities will require students to participate in a variety of experiences, not only operating experience, exploration experience, but also thinking experience, and more need to have the awareness of application.
For example, the two line segments in the figure below represent two new buildings. Now, the gas will be sent from A to two buildings, and the length of the gas pipeline should be as short as possible. Can you point out the location of the pipeline?
To solve this practical problem, students need to use the knowledge that the vertical line is the shortest of all the line segments from a point outside the straight line to interpret the mathematical problems in life. If the student has the awareness of application and can draw the solution smoothly, it means that his relevant knowledge and experience have been formed, otherwise it means that it has not been well formed. For most people,
For students, always think carefully first, then design drawings, and finally practice operations. Therefore, the consciousness of application is completely based on students' thinking experience and operation experience. As Professor Zhu Dequan pointed out, "the generation of application consciousness is a sign of the formation of knowledge and experience." Taking the experience of basic mathematics activities as the core.
The application consciousness needs teachers to pay more attention to and cultivate in the teaching process.
It is worth mentioning that the more complicated mathematical activities are, the more positive emotional will is needed. This experience component is also an indispensable part of students' basic activity experience and plays an irreplaceable role in shaping good personality. When students reflect on their whole problem-solving process after the activity, they can not only feel the experience of thinking, exploring and concrete operation, but also the emotional experience of success or failure can gradually condense into a part of their own emotional characteristics and develop. Therefore, in order to accumulate students' experience in basic mathematics activities, perceptual knowledge, emotional experience and application consciousness are indispensable. Only the balanced development of activity experience can realize the all-round development of students.