Why should we cultivate students' thinking ability in images? According to the latest achievements of modern scientific research, the left and right hemispheres of the human brain have different functions. The left hemisphere is the language center, in charge of language and abstract thinking, while the right hemisphere is in charge of the comprehensive activities of image thinking materials such as music and painting. Only by matching, complementing and promoting each other can individuals develop harmoniously.
From the characteristics of children's thinking, primary school students' thinking has gradually changed from concrete thinking in images to abstract logical thinking, but at this time, logical thinking is preliminary and still has concrete images to a great extent. Therefore, cultivating students' thinking ability in images is not only their own needs, but also their need to learn abstract mathematics knowledge.
So how to cultivate students' thinking ability in images in primary school mathematics teaching?
First, fully perceive, enrich appearances, and accumulate materials for cultivating thinking in images.
Children can keenly perceive vivid, colorful, tonal and sound images, and are good at using image colors and sounds to trigger thinking. Image is the cell of image thinking, and image thinking depends on image thinking. To develop students' thinking in images, we must lay a good foundation and enrich the accumulation of image materials.
1. Hands-on operation to enrich the appearance.
Hands-on operation, let students participate in learning with various senses and observe things from many angles. For example, to teach the concept of remainder, let the students divide the sticks first: (1) How many sticks are left in every two of the nine sticks? (2) 13, distributed to 5 people on average. How many sticks can each student get? How much is left? After the operation, guide the students to express the operation process in words and talk about how to divide the sticks, thus forming an image. Then let the students close their eyes and think about how to divide the following questions. (1) There are 7 biscuits. Each biscuit is divided into 3 pieces, which can be distributed to several people. How many pieces are left? ② Pencils 12, distributed to five people on average. How many pencils can each person divide, and how many pencils are left? In this way, students can think in operation and operate in thinking, and understand that dividend is the total number, divisor and quotient are the number of shares to be divided and each share, and the remainder is not enough, and the remainder is less than divisor. Correct and clear representations are formed in the mind, and correct thinking has a solid foundation.
2. Intuitive demonstration enriches the appearance.
The unintentional attention of primary school students plays an important role, and the emergence of any new things will arouse students' interest in actively participating in the learning process. In the process of teaching, organize teaching with pictures, teaching AIDS or audio-visual means, visualize abstract knowledge and let students fully perceive the materials they have learned. Only with quantitative perceptual materials can they leave a clear image in their minds.
For example, in the teaching of "cuboid cognition", teachers can first show cuboid objects familiar to students in their daily lives, such as matchboxes, chalk boxes, bricks and so on. These objects are cuboids. Then ask the students to list their own rectangular objects (bookcases, wooden cases, thick books, pencil boxes, etc.). ), through the feeling of the object, have a preliminary perceptual understanding of what kind of object a cuboid is. On this basis, teachers guide students to read books while observing the model, and understand the characteristics of the cuboid from different positions and directions, such as the equal area of six faces and opposite faces, the length of twelve sides and parallel sides. We can know the length, width and height of a cuboid by observing the length of a vertex and three sides intersecting with the vertex. Through the flat, lateral and vertical forms of the model, it is shown that the length, width and height are relatively fixed, and the knowledge is "alive", which enables students to establish a clear and profound representation in the process of learning with their mouths and brains, and provides conditions for the rationalization of thinking.
The introduction of audio-visual teaching means into the classroom can turn the static into the dynamic and turn the near into the far. With its colorful and flexible teaching form, it provides students with demonstrations reflecting their thinking and thinking process, which can fully mobilize their psychological factors and achieve good results. For example, when teaching "Subtraction Application Problem of Finding Another Addendum", students can vividly understand the relationship between the total and the part through the slide presentation, that is, the total-part = another part.
In teaching, we should use a variety of teaching methods to make students fully perceive, establish clear mathematical representations in their minds, and accumulate materials for improving students' mathematical imagination.
Second, guide imagination and develop thinking in images.
Modern cognitive psychology believes that images can not only be stored, but also be processed and reorganized to form new images, that is, imaginary images, which is also an important way of thinking in images. Therefore, teachers should be good at creating problem scenarios in classroom teaching, such as graphic scenarios and language scenarios, to stimulate students' desire to participate in inquiry and give full play to their rich imagination.
For example, after teaching trapezoidal knowledge, students can be guided to imagine: "What shape will the trapezoid become when one base of the trapezoid is gradually shortened to 0?"? When the short bottom of the ladder extends to be equal to the other bottom, what shape does it become? " With the help of representation, seemingly unrelated triangles, parallelograms and trapezoid can be organically combined. You can also remember the area formulas of triangles and parallelograms according to the trapezoid area formula:
1
S[, trapezoid] =-(a+b) h
2
1
When a = 0, it becomes a triangle, and the area formula is: s =-ah.
2
When a = b, it becomes a parallelogram, and the area formula is: s = ah.
Third, the combination of numbers and shapes, cultivate thinking ability in images.
Mathematics is a subject that studies quantitative relations and spatial forms in the real world. Generally speaking, mathematics is a combination of numbers and shapes. Different types of mathematical graphics provide the representation materials of brain thinking in images, arouse the enthusiasm and initiative of brain thinking, improve his thinking ability in images, promote the coordinated development of individual's left and right brains, and make people smarter.
For example, illustrations designed with specific plots of applied problems in textbooks broaden the world of students' thinking in images and enhance their will to study hard. For example, examples and review questions in textbooks use colorful colors and various small animals, plants, rivers, mountains and rivers, modern airplanes, cars, ships, satellites, buildings, ancient cultural relics and books to express the quantitative relationship ... These are not only conducive to understanding the quantitative relationship, but also play an important role in the development of students' thinking ability in images and the improvement of their aesthetic ability.
Besides, the application problem teaching, because the application problem is a combination of science, art and mathematics, the prototype of the application problem is more complex and abstract, and it is difficult for students to form a clear representation after they get into their heads. If we use the method of combining numbers and shapes to draw line segments, we can help students to establish a correct representation and make clear the hidden and complicated quantitative relationship. For example, "Xiao Liang has 18 yuan in its savings box, and Xiaohua's savings is 5/6 of that of Xiao Liang, and Xiao Xin's savings is 2/3 of that of Xiaohua. How much did Xiao Xin save? " It is often difficult for students to determine the unit "1". In teaching, students can be guided to draw the following line diagram to analyze the quantitative relationship:
According to the line chart, students can quickly list the formulas: 18× 5/6× 2/3- 10 (yuan).
Therefore, the line diagram is semi-abstract and semi-concrete, which can not only abandon the specific plot of the application problem, but also vividly reveal the relationship between conditions and problems, transform numbers into shapes, clearly show the internal relationship between the known and the unknown, and activate students' problem-solving thinking. The application of line graph and the combination of numbers and shapes here better stimulate students' creative imagination, which not only develops students' thinking in images, but also realizes the complementarity of thinking in images and abstract thinking.
I found that many students can't learn to compare. Why don't they solve the problem? I can hit the nail on the head: they have no basic nature of absorption ratio.
Why am I so sure? Please listen to me one by one.
As we know, the so-called solution ratio is to solve the equation, and its solution is no different from the equation, mainly in the first step. Let's give an example:1/4:1/8 = x:110, solution ratio. The first step here is:1/8x =1/4 *110. After this step, students who can solve equations can continue to solve them. It can be seen that students who can't compete are all because they can't take the first step. The first step is listed according to "Basic Properties of Proportion". Therefore, students who will not learn from the solution ratio have no basic nature of absorption ratio.
February 24(th)
In this part of the application problems, there are problems such as finding the distance in the drawing or the actual distance. When calculating the distance in the picture or the actual distance, the solution in the book is "proportional solution" In fact, you can also use "arithmetic solution".
First, let's recall what a scale is. Scale = distance in the drawing: actual distance. We can get inspiration from this: regard the actual distance as the unit of 1. The distance in the figure is "a part of the corresponding quantity"
Therefore, the "arithmetic solution" has two relationships: "distance in the graph = actual distance * scale" and "actual distance = distance/scale in the graph".
February 26(th)
I think this thinking problem in the book is very interesting. Reminded by the previous three polygons, I learned that a polygon can be divided into several triangles with three internal angles on the polygon angle, and then "180* the number of triangles". Then you can find the sum of the inner angles of the polygon.
February 28(th)
I don't think any of the above questions should tell us that "xx" is certain. Because the above problems can be "proportional" as long as there is a "certain". The title tells us "xx must", doesn't it tell us that the two quantities in the title are "proportional"?
February 29(th)
In life, there are many examples of inverse proportion. For example, the total number of apples is fixed and the number of baskets is inversely proportional to the weight of each basket. Because: number of baskets * weight of each basket = weight of apples (certain).
March 2(nd)
I found that someone failed the math exam every time. I have a way to get them through-listen carefully in class. In fact, as long as you listen carefully in class, even if you have a bad memory, you can still live. Because what you teach in class is what you want to test, as long as you understand and listen carefully in class, you don't need to memorize those contents.
I am a good example: listen carefully in class and understand everything the teacher says. I read the contents of the book once or twice at most, and I get an "A" every time.
It's so easy, why don't students do it?
March 3
When I finished "1-4" by "normalization method", I tried to solve it by other methods. I thought about the first question first, and thought: The third lesson is called "Application of Proportion", and proportion must be used. So, I wrote the proportional relationship of this problem: the total hectares are in direct proportion to the cultivated time. Relationship: total hectare/cultivated land time = cultivated land speed.
With this in mind, I came up with another way to understand this problem: solving it with equations. You can set the number of hectares of cultivated land as x, and write the number of this question in proportion: cultivated land area/cultivated land time = cultivated land area/cultivated land time. According to this ratio, the equation can be listed: 1.25/2=x/8. In fact, the two equivalents of this equation are velocity.
After I solved it with this idea, it was correct with the examples in the book. I found that my thinking was the same as that in the book.
March 4
I remember that there is a true or false question on the eighth page of class exercises: the area of a square is proportional to its side length. You said this question is wrong, because you didn't say "the side length is certain".
In my opinion, even if he said "the side length is certain", it is still wrong. Because if one side has a certain length and the other side has a certain length, the square area = side length * side length. Then the product obtained by multiplying two definite numbers is also a definite number. The area of a square is constant, and so are its two sides. Isn't the area of a square proportional to the side length?
March 6
Through the last assignment and this assignment, I think everyone can definitely sum up the difference between the "normalization method" and the solution method. Here, I want to be the first person to eat crabs.
First of all, when solving a problem, the "normalization method" is to finish one step and then think about what you can ask for next. The "solution ratio" method only needs you to understand the proportional relationship of this problem, and then you can list the equations to solve the problem. Obviously, this is naturally the simplicity of the "solution ratio" method.
But for some students, the error rate of "solution ratio" method is very high. Because the first step of the "solution ratio" method, once the "proportional relationship" is wrong, the whole problem will disappear. However, they did not absorb the contents of "positive proportion" and "inverse proportion", so it is easy to produce and even won't make mistakes.
They are familiar with the normalization method, even if they only do one step, they can get some points in the exam.
But on the whole, the "solution ratio" method is simpler and more convenient.
March 8
Through today's study, we know an application problem that can be solved in many ways and learn how to solve it.
This kind of application problem is very interesting. It can observe the problem from different angles, for example, it can be solved according to the direct proportional relationship, it can be solved according to the inverse proportional relationship, and it can also omit some conditional solutions.
There are many kinds of problems. If it doesn't require us to solve them with proportional knowledge, it has at least four solutions.
March 4
In fact, it is easy to type' *' in many books. This is the law that we have discovered for a long time. Today I will use examples to verify this sentence.
The example I gave is the eighth question on page 29 of this book. Enough nonsense, now just "input" and "8*". This problem, although not related, can be used to understand the "certain" quantity of this problem, in which a certain quantity is the overlapping part. It can be seen that the proportional formula listed later in solving the problem is equal to the overlapping part. The method of finding the overlapping part is obvious-"a *1/4 = b *1/6". I think it's enough to tell my classmates this proportional formula, not to mention the formula, right?
If someone can't do this problem, it's really meaningless. Even if you say "I don't know how to analyze the topic like me", it's useless. Because, the teacher has given us the proportional formula of this problem: a* 1/4=b* 1/6. You don't need to think at all.
So this problem should be something that everyone can do. Of course, unless you are a person who "cooked in front of you, but you still don't know how to eat."