I. Assembly and growth
Teacher Song mentioned two kinds of logic in sharing-"linear logic" and "spiral recursive logic". How to understand these two groups of words? By listening to the course and watching the teachers' discussions, I presented two images in my mind, one is a robot and the other is a natural person. Linear logic refers to the combination of robots, and spiral recursive logic refers to the growth of natural people. The former is to assemble some basic parts of the robot and then assemble it into a complete robot. The latter is a person's embryonic form, and then with the passage of time and rich knowledge, the functions of each part are gradually improved and strengthened, and each part grows synchronously.
How children construct the concept of generating decimals? I think it should be based on spiral recursive logic. This is the general direction, and the specific details are added to linear logic.
Decimals are no strangers to children, and they can be seen everywhere in life. For example, the price tag in the supermarket, the temperature reported in the epidemic prevention work, the running time in the Olympic Games, the record of the length of shot put and long jump, and so on. All these can form a vague decimal impression in the child's mind. This is also the initial formation of the rudiment of decimal in children's minds, and it is children's initial perception of the whole decimal.
Through a series of decimal courses, this perception is gradually refined and strengthened. In this process of refining and strengthening, linear logical thinking is needed. Can make the content of each part more clear and accurate.
Through a series of studies, children's perception of decimals is more detailed and full. By connecting these decimal knowledge with life, we can use this knowledge to solve the problems in life and explain the phenomena in life through this knowledge. Children have a more complete structure of the concept of decimals.
Children's construction of the concept of decimals grows with natural persons, but in a small scope, we should also pay attention to the special strengthening of a certain part. So spiral recursive logic and linear logic need to be coordinated.
Second, the foundation and extension
The presentation of any knowledge and the construction of any knowledge are based. In addition to the basic presentation mentioned above, the construction of decimal concept is supported by relevant basic knowledge in teaching materials.
For example, the price tag that appears in the first grade is a hidden presentation. Simply put, it is to show the decimal face and meet the children. People's Education Edition provides a knowledge base for the construction of decimal concepts.
The preliminary understanding of decimals in the second volume of the third grade gives children an overall initial impression of decimals. At this stage, children's understanding of decimals is still in a vague stage. Although it involves many knowledge points, it is still in the stage of closely connecting with real life and specific quantity. By the fourth grade, the nature and significance of the second volume of decimals have entered an accurate stage. Various knowledge points are abstracted and can be presented independently, with no specific quantity. And the decimal is included in the whole number axis, and a more systematic construction is carried out. This is also more in line with the transition stage of fourth-grade children from image thinking to abstract thinking. Then the teaching of decimal addition and subtraction. This is also the process of extending the operation law of integers to decimals. It is an extension of the concept of student number and the operation of numbers.
Third, core and pluralism.
In the construction of decimal concept, the meaning and nature of decimal is an important part of decimal concept construction. This paragraph contains many knowledge points. These knowledge points are like scattered pearls, and they need a thread to string them together. What line should I use?
I read an article shared by Wu Zhengxian, "Grasping the Teaching Materials as a Whole and Highlighting the Conceptual Essence of Numbers —— Reflections on the Unit Teaching of" the Meaning and Nature of Decimals ",and she specifically mentioned that all knowledge points should be guided by the core concept of counting units. Let all the knowledge points be connected in a string, which has an integrity.
She used a legend to illustrate the command of this relationship. It can be said that every knowledge point can be linked to the counting unit. For example, the essence of decimals is that counting units and the number of counting units change at the same time. The comparison of decimal size is the comparison of numbers in the same counting unit. With this connection, knowledge points are not scattered, but targeted and focused. In the construction of children's decimal concept, it can also play a role in threading the needle.
When we put decimals on the number axis, the core concept of this counting unit makes all numbers related and realizes the unification of the number system. For example, thousands, hundreds, several ones, several 0. 1, several 0.0 1, several 0.00 1 ... These counting units, the ratio of two adjacent counting units is 10, and they all belong to the decimal system.
Taking the counting unit as the core, the concept of building decimals for children actually grows naturally in the needs of daily life on the basis of integers. This natural growth coincides with the spiral recursive logic we discussed earlier.
Grasping the core concepts, then linking and expanding, our digital system will have diversified expressions. It can be an integer, a fraction or a decimal. Different expressions, their counting units are regular and feasible, and they all point to decimals. The so-called "never leave" captures the core concept, and all extensions and all multiple representations are better connected.
Now our "double reduction" activities are in full swing. Students' homework time and study time are greatly reduced. But our goal is to reduce the quantity without reducing the quality. How to reduce the quantity without reducing the quality? This requires our teaching to spend more time on big concepts and core concepts. Because lower-level concepts, more basic concepts and more essential knowledge, such as big concepts and core concepts, are more conducive to students' application and expansion if they learn well. It is more conducive to students' follow-up study.
How children construct the concept of generating decimals? Simply put, it is to refine, focus, link and expand the core concepts. And follow the general law of students' learning knowledge, from romance to precision to synthesis, so that the concept of decimal grows naturally in students' consciousness, reaches clarity and achieves comprehensive application.