The basic pattern of many mathematical problems is: what are your known conditions, what formulas and theorems you have studied (in fact, they are also known conditions), and what kind of results you want to achieve. Then, what children have to do is to find a solution to the problem through their own thinking and judgment between the known conditions and results.
Let's talk about how children close to school, especially children aged 5 or 6, do it.
Personally, I think we can cultivate children's mathematical thinking ability from the following aspects: quantity, calculation, classification, time, space, correspondence, sorting, abstraction and solving. All these need to be achieved through observation, concentration, memory, imagination and problem-solving ability.
Let me say it alone.
(1), quantity
Includes two parts: number and quantity, and the most basic part of number is counting. Counting means that children can figure out how many there are, such as counting directly, counting backwards, counting across, jumping and so on. As parents, we are more concerned about this.
What I personally add is: first, the decomposition and combination of numbers. The decomposition and combination of objects and numbers within 10 need the cooperation and practice of parents. Second, cardinal number and ordinal number should be gradually infiltrated and perceived in play and life, and some children who enter school early will be confused with these two. Like the fifth and the first five.
Quantity, I think, includes comparison and measurement. The comparison is purely specific size, length, thickness and so on. Measurement includes the perception of scales, weights and other units. Take the time to take children to measure natural objects and transition to standard tools. Natural objects are simple, such as measuring the length of the runway with a stick, or measuring the width of the pencil box with a rubber, to let him know that the measurement is measured in units, and this unit is unified, so that he can understand and feel the unit in the simplest measurement. Slowly transition to the standard number of units, such as often playing with building blocks, putting small cubes and squares, and slowly sensing one cubic meter and one square meter. In this way, it will be easier for children to learn unit names in primary school, especially in the fourth grade. Parents who enter school in September should follow the principle of "half a step faster" and use games (such as buying and selling things, stocks and other activities) to infiltrate RMB conversion and time exchange in their lives. This is the difficulty of grade one.
(2) Calculation
I believe that most parents must teach their children to add and subtract in kind. What's more, physical perception must be carried out in large quantities. In the process of calculation, more children can spontaneously understand the truth and discover the laws and characteristics in a large number of appearances. This is especially obvious when the abdication subtraction is less than 20. For example, Xiao Ming has 10 candy, Mao Mao has 8, and Xiao Ming has several more than Mao Mao. How many pieces is Mao Mao less than Xiaoming? Doudou has 20 pieces of sugar. He gave the children eight pieces of candy. How much is left? Although subtraction is used, it is actually different. The former is the comparative type, which is the focus of grade two, and the latter is the residual type. For parents, it is important to help children understand the difference between the two, not to calculate the final result.
Supplement: The general program flow of calculation is:
In the early days, children used their fingers to calculate the addition and subtraction within 10. Decomposition and combination of numbers. Transition to decomposition is subtraction, and combination is relationship training of addition. Perceptual calculation of physical operation (you can use the ten-point method, pay attention to multi-directional thinking 2+ 1=? 7= several plus several or several minus several or several plus several plus several, and so on). Mental arithmetic exercise (doing actions in the brain to operate) Fast calculation training (based on the principle of simplicity, fun and variety). These are better reflected in Montessori teaching. If you don't have or are interested, you can buy some things in the math area from Taobao or make your own learning tools with waste things (especially children are advised to follow suit and exercise various abilities, such as sticking cubes, hands-on ability and space concept). )
(3) Classification
In order to develop children's thinking, we must attach importance to diversified classification. For example: a triangle, a circle, a triangle, you will classify triangles into one category; Not only the shape, but also the color, texture, price and so on. Can better exercise the clarity of children's thinking. It is also necessary to prepare a multi-solution for children at the level of consciousness.
(4) Time
In addition to knowing the clock, let the children know where the pointer goes 10 minutes. Let him feel the time and feel for himself how long 10 minutes is. This is the focus and difficulty of the first grade, and our parents must play with them more. Children can learn by analogy. Besides, it doesn't matter even if the child can't. After the third grade, all children can tell the time. On the one hand, it is repeated in life and homework. On the other hand, children's brains can learn, improve and digest themselves. "Children should be raised slowly and carefully."
(5) Space
In addition to letting children feel up, down, left, right, back and forth, they should also cultivate their spatial construction ability. From three-dimensional to plane, we must combine the two feelings, so that children can find the first immersive feeling. For example, a small cube is surrounded by six faces. What are the characteristics of each surface? How many sharp points are there? What else can you find?
The games we often play with our children, such as building blocks and puzzles, are all about space construction. Building blocks are random, creative and three-dimensional space construction; It is a purposeful plane space construction to figure out what kind of pictures to put together in advance before the puzzle. It is suggested to do more hands-on operation and play more, so as to pave the way for geometry in junior and middle schools in the future. Children with poor spatial imagination will be in trouble in junior high school. Just like me, in the face of graphics, the auxiliary lines can't be seen at all. Of course, in addition to building blocks and puzzles, children's spatial imagination can be enhanced through paper-cutting, origami, hand shadow, drawing graphics and simple graphic reasoning.
Usually, in the game, children should try their best to know the difference between object-centered cognitive spatial relationship and others-centered cognitive spatial relationship. The two are different. You have to experience it in operation, you have to.
(6) Communication