Mathematics is a science that studies quantitative relations and spatial forms. The idea of the combination of numbers and shapes is to grasp the essence of mathematics, combine abstract numbers and shapes, and organically combine numbers and shapes, so as to cultivate students' geometric intuitive ability. For example, how to make students understand the algorithm of dividing decimals by integers in the course of teaching decimals by integers, we adopt the strategy of combining numbers with shapes. Combine charts to make it meaningful. 1 1 small squares represent11,and colored parts represent 0.5. Distribute 1 1.5 evenly in five bags of milk, with 2 yuan in each bag and 1.5 in the rest. 1 yuan cannot be divided directly. Convert 1.5 yuan into 15, which is 15 0. 1, and distribute it to five bags of milk on average. Each bag costs 3 cents, which is three zeros.1yuan. 0.3 yuan, 2 yuan is 2.3 yuan. When the graphics can't be presented intuitively, we will convert the remaining numbers into numbers with smaller counting units for calculation. Pupils are in the transitional stage from thinking in images to thinking in abstractions. For example, by making abstract arithmetic intuitive, students can understand the calculation method of dividing decimal by integer at once and why the decimal point of quotient should be aligned with the decimal point of dividend. Geometric intuition transforms abstract mathematical language into intuitive graphics by virtue of the intuitive characteristics of graphics, which makes students slowly transition from image thinking to abstract thinking, helps students to think flexibly and opens the door to wisdom.
2. Hands-on strategy;
Understanding the meaning of operation often goes through four stages: situational awareness, action representation, language representation and symbol representation. Situations are often provided by textbooks or teachers. On the basis of perception, how can students further understand the situation and understand the quantitative relationship contained in the situation? In primary school, we usually use hands-on operation. The purpose of hands-on operation is to establish the representation of concepts. The representation and graphics formed by this activity in people's minds are very similar, and they all have specific imaging. From here on, geometric intuition gradually sprouted. For example, addition, in the hands of students, is to combine two parts, or add on the basis of one part, or move a new part from other places. "Merger", "addition" and "migration" are not abstract concepts here, but students' living operational activities. Students understand concepts from these simple operations, slowly internalize them into language, and finally summarize them to form a more standardized and strict definition.
3. The strategy of turning static into dynamic.
The strategy of turning static into dynamic has two manifestations in primary school mathematics. First, let students feel the transformation of graphics, such as the combination of basic graphics into composite graphics, composite graphics into basic graphics. There are also basic patterns that become new patterns through translation or rotation. Here mainly reflects the movement of graphics. In the primary school mathematics classroom, turning static into dynamic is more reflected in transforming static quantitative relations into visible graphics. For example, the derivation of the formula of circular area. Students will calculate the area of a parallelogram and transform the circle into an approximate parallelogram through division and assembly. Through hands-on operation, the base of the parallelogram is 1\2 of the circumference of the circle, and the height of the parallelogram is the radius of the circle. Because the area of the parallelogram is equal to the base times the height, the area of the circle is equal to π. Turning static into dynamic, students can experience the formation process of the formula of circular area, lay the foundation for students' spatial imagination, pave the way for intuitive insight, and help students intuitively understand the quantitative relationship between circular area and circular radius by using geometry. Complete teaching objectives in a short time and improve classroom effectiveness.
In classroom teaching, the combination of numbers and shapes, hands-on operation and turning static into dynamic are often used to cultivate students' geometric intuitive ability.