(1) Numbers and Algebra
The cognition of numbers includes the cognition of numbers, the reading and writing of numbers, the comparison and sorting of numbers, and the calculation of numbers mainly includes operations such as addition, subtraction, multiplication and division.
The key content of this part is that addition and subtraction need to be proficient in oral calculation, mental calculation and table calculation; Multiplication requires mastering 99 multiplication tables and vertical calculation; Division requires proficiency in oral calculation and column calculation.
In order to strengthen the operation ability, students need to learn the deformation of formulas, such as addition, subtraction, exchange, association, distribution, borrowing and carry.
When children reach the fifth grade, they will learn the oral calculation and column calculation of addition, subtraction, multiplication and division of decimals and fractions; The sixth grade will learn the concept, operation and simplification of algebraic expressions.
(2) graphics and geometry
Geometry and shape include the understanding, classification and naming, attributes and characteristics, and assembly of graphics. For example, learn the properties of triangles, rectangles and squares, and calculate the perimeter and area.
In the fourth grade, I began to learn the concept and nature of distinguishing plane graphics from three-dimensional graphics and cultivate a sense of space. Primary school mathematics also involves the knowledge of geometric transformation, and students need to learn the concepts and calculations of translation, rotation and symmetry.
(3) Statistics and probability
Data and statistics include data collection and collation, data representation and analysis, data comparison and reasoning. For example, learn the concepts, calculation and application of mean, mode, median, variance and standard deviation.
(4) Synthesis and practice
Synthesis and practice are mainly applied problems, including applying mathematical knowledge to real life to solve problems, such as calculation, measurement and timing in daily life.
Secondly, what mathematical thinking ability does primary school mathematics cultivate?
Combining the above four knowledge plates of primary school mathematics, parents should pay attention to cultivating their children's mathematical thinking ability from the following four aspects.
(1) computing power
Repeated practice: Practice makes perfect is a simple truth, but repeated practice is a time-consuming and brain-consuming thing, so it is not simply to let children do a lot of the same problems, but to make them interested and stick to it for a long time. This is to consider the diversity and interest of the problem.
Secondly, the understanding of arithmetic, which is often ignored, requires children to put more energy into understanding. For example, in the fourth grade, when learning the distribution law, there are a lot of exercises to use the distribution law to make clever calculations, such as
23 * 37 + 23 * 63 = 23 * (37 + 63) = 23 * 100 = 2300,
If we ask, what is the truth of the law of distribution? Why does multiplication have a distribution law? Why can you use the distribution law to do such a clever calculation? How many parents and children can answer accurately?
(2) Logical reasoning ability
Parents should guide their children to think actively: in the process of tutoring their children to complete their homework, guide them to think about the nature and laws of the problem. Why do you understand this? Why is this method suitable for this type of topic? Help them form a logical closed loop, so that every step to solve the problem is justified and cannot be swallowed.
Furthermore, encourage children to solve problems in various ways: if a problem is not finished, encourage children to think more about whether there are other solutions. For example, the formula method of a topic will be more direct and faster than the drawing method, but if the child can solve it again with the drawing method, he will accumulate one more method to solve the problem. The next time you encounter another problem, the formula method can't solve it, and children will naturally think of the drawing method, but children who have not accumulated this logical idea can only be empty. Practicing one more problem is also an effective way to exercise their logical reasoning ability!
(3) Spatial thinking ability
Parents should pay attention to cultivate their children's habit of observation: for example, children like football and have very interesting three-dimensional graphics. That is, each side has the same length, and each vertex looks exactly the same, with three sides and three angles; The stitching divides the football into a plurality of regular pentagons and regular hexagons; So the polyhedron of football is the same in many places. If you turn it upside down, it looks exactly the same from different angles. In mathematical terms, football has good symmetry. So football is also called semi-regular polyhedron.
Secondly, encourage children to practice: parents can encourage children to explore their relationship with space by playing with space toys, and the brain can also take the opportunity to develop space imagination. Lego models that children love to play with are excellent teaching AIDS for cultivating spatial imagination. You can also do manual activities, such as origami, window grilling, etc., so that children can build their imagination in the changes of space and plane.
(4) the ability to use life.
Encourage children to solve difficult problems in life with mathematics. Distribute tableware, cakes, supermarket checkout, calculate full discount, calculate travel time and distance, and participate in the distribution of travel budget. Understand abstract mathematical formulas in specific scenes of life, and you can solve life application problems in the exam.