1, the connotation of the idea of combining numbers with shapes
"Number" and "shape" are the two most important parts in the process of mathematics teaching, and they are also the objects that are often studied in mathematics teaching. In the process of mathematics teaching, "number" and "shape" are combined, and the abstract and difficult "number" is understood by intuitive and vivid, and the characteristics of "shape" are explained by detailed "number". Combine them organically and cooperate with each other. It unifies abstract and difficult concepts with intuitive and easy-to-understand graphics, thus easily solving mathematical problems.
2. The application of the combination of numbers and shapes in the teaching of mathematical concepts in primary schools.
2. 1 Establish a model and introduce concepts.
Considering the limited understanding ability of primary school students, students' understanding and mastery of concepts must be taken into account when introducing mathematical concepts. When introducing the concept, we should first establish an intuitive model, so that students can understand its appearance and understand the connotation of the concept more deeply. The establishment of model representation is students' impression based on the analysis of perceptual materials. When introducing concepts into primary school mathematics teaching, graphic demonstration is the most common and useful modeling method. Pupils are still in the stage of thinking in images and need rich and vivid perceptual materials to understand abstract mathematical concepts. In the process of teaching mathematical concepts, we should fully show the similarities between abstract concepts and vivid graphics, and demonstrate the essence of difficult concepts with the most expressive graphics. Through the combination of numbers and shapes, students will easily master the mathematical concepts they have learned and remember them deeply.
It is difficult for students to understand the concept of multiples in the teaching process of multiples. How to teach students the concept of multiple in the simplest and clearest way, so that they can fully grasp it? Graphic demonstration is definitely the simplest and most effective method. In teaching, two triangles can be regarded as one, and four squares can be placed below, which are divided into two parts. Teach students to observe that there are 1 twos in a triangle and two twos in a square. In two parts, it can be expressed in mathematical language: the number of squares is twice that of triangles. In this simple graphic demonstration, students will naturally transition from the simplest "number" and "number of copies" to "multiple", which will not be abrupt and difficult to understand, thus easily grasping the essence of the concept of "multiple".
When using intuitive graphics to build models to help students understand, we should pay attention to discretion. Don't put too much energy into graphic demonstration to enhance the stimulating effect of graphics on students, which will lead students to focus on graphics and lose interest in understanding concepts. Graphic demonstration is only a means for students to intuitively feel the essence of concepts and better understand the essence of mathematical concepts, which needs to be concise and clear.
2.2 Step by step analysis and formation
There is a process for students to understand mathematical concepts. It is not enough to use only one figure in teaching. It is necessary to ask questions step by step on the basis of graphics, induce students to think at a deeper level, and let students experience the process from intuitive perception to profound understanding of concepts. Students should not only understand concepts, but also be able to use them. Therefore, when introducing concepts, we should further promote the graphic representation of students' understanding, analyze the formation process of concepts, enhance the visualization of problems, and expand the depth of problems, thus inspiring students to think at a deeper level. In teaching, students need to recall the process of concept introduction, observe and analyze how abstract concepts become images, thus forming a grasp of new concepts.
When the concept is abstract and difficult to understand, teachers can guide students to observe and analyze with vivid objects in the teaching process. For example, in the teaching of the concept of "volume", teachers can first guide students to observe the eraser and chalk box and ask which object is bigger, so that students can initially perceive the concept of "volume". Then you can put water and small stones in the beaker. Let the students observe the change of water level in the beaker and ask: Why does the water level rise? How much did it go up? Students can understand that the space occupied by objects is "volume" from the rising water level. How much the water level rises is the volume of pebbles in the water. Through in-depth discussion, students can easily realize that "volume" is the size of the space occupied by objects. Students not only understand the concept of "volume" because of interesting experiments, but also have a deep impression on it, and they can also apply this concept more skillfully in the future.
When building conceptual models and setting situations, teachers should pay special attention to the progressive levels and the organic combination of concepts and graphics. In the teaching process, we should also use questions to induce and inspire students, so that students can find problems through observation and then analyze and solve them. Teachers need to guide students to observe and analyze the essential attributes of concepts when they form a superficial understanding of concepts, so that students can learn the whole process step by step, understand the formation of the whole process and complete the understanding of concepts.
2.3 Start painting and understand the essence.
It is difficult for primary school students to transfer practical problems to mathematical problems with life experience, thus forming an understanding of mathematical concepts. Therefore, in the usual teaching process, teachers should guide students to draw with tools according to the actual teaching situation and help them understand the essence of concepts. Through painting observation, students can establish their own concept representation, expand the concept of space and improve their spatial thinking ability. So as to cultivate students' abstract thinking, analysis and generalization ability.
In triangle teaching, it is difficult for students to understand the concept of "height" of triangle. Without graphics, it is difficult for teachers to explain the meaning of "high" and students will not understand its essence. Therefore, in this case, the teacher can guide the students to draw by themselves, and go through a process of finding the "height" of the triangle, which will impress the students with the "height". Teachers can guide students how to cross a certain point and make a vertical section of a straight line; Then guide the students to cross a vertex of the triangle and make a vertical line segment of the bottom, which is the "height" of the triangle. Students can also fully understand the concept of triangle "height" through drawing exercises. Through a large number of drawing exercises, students can find the characteristics of each figure, fully mobilize their enthusiasm, cultivate their ability of observation and drawing, and understand the essential attribute of "Gao" more vividly.
In the process of students' hands-on drawing, students should be guided to sum up their experiences and feelings in this process, so as to fully and comprehensively understand mathematical concepts. Instruct students to draw, so that students can find the fun of learning and mastering knowledge in the process of drawing, so that students can find ways to learn mathematics in the process.
3. Think about the combination of numbers and shapes.
When using graphics to help understand mathematical concepts, teachers can use intuitive and vivid graphics to make abstract mathematical concepts easy to understand and intuitive, which is convenient for students to understand and analyze. In the teaching process, teachers need to use clear theories to help students understand and master. When analyzing problems, we should turn graphic problems into quantitative problems or conceptual problems into graphic problems according to specific conditions, so as to make complex problems simple and clear, help students understand accurately, find out the essence of concepts, and cultivate and expand students' logical thinking ability.
When you encounter complex geometric figures, you can try to express them with simple quantitative relations. Complex graphic relations are expressed by simple algebraic operations. Encourage students to observe graphics, analyze the meaning of numbers in graphics, and solve complex graphics problems with the help of the operation of quantitative relations. In this way, students can fully understand the ideological connotation of the combination of numbers and shapes, be familiar with the thinking method of the combination of numbers and shapes, and better use the method of the combination of numbers and shapes in the process of learning mathematics, so that students are sensitive to the combination of numbers and shapes.
"Combination of numbers and shapes" is an important mathematics learning method. It is a two-way process, and it is necessary to deal with the combination and cooperation of the two according to the actual situation. In the process of teaching mathematical concepts in primary schools, teachers should pay attention to the reasonable guidance of students' application of "combination of numbers and shapes", so that students can form a good habit of using "combination of numbers and shapes" in the learning process. Attention should be paid to cultivating students' mathematical thinking ability, so that students can achieve the unity of numbers and shapes when learning mathematics, which is of great significance to students' future mathematics learning.