Skill is a way of action or psychological activity to successfully complete a task. It is an almost automatic, complex and relatively perfect action system formed through purposeful and planned exercises. Mathematical skills are actions or intellectual activities to successfully complete a certain mathematical task. It is usually manifested in the coordination of a series of actions and the automation of activities when completing a certain mathematical task. This kind of coordinated action and automatic activity is formed through repeated practice on the basis of existing mathematical knowledge and experience. For example, the multiplication skill multiplier you learn is a two-digit number, which is formed through many practical calculations on the basis of mastering its algorithm. Mathematical skills are closely related to mathematical knowledge and ability, and there are essential differences. The difference between them lies in: skill is the generalization of action and action mode, reflecting the proficiency of action itself and action mode; Knowledge is a summary of experience, which reflects people's understanding of the regularity of mutual connection between things; Ability is a summary of some stable psychological characteristics to ensure the smooth completion of activities, which embodies the individual characteristics of learners in mathematics learning activities. The relationship between the three can be clearly reflected from the role of mathematical skills.
Skill is a way of action or psychological activity to successfully complete a task. It is an almost automatic, complex and relatively perfect action system formed through purposeful and planned exercises. Mathematical skills are actions or intellectual activities to successfully complete a certain mathematical task. It is usually manifested in the coordination of a series of actions and the automation of activities when completing a certain mathematical task. This kind of coordinated action and automatic activity is formed through repeated practice on the basis of existing mathematical knowledge and experience. For example, the multiplication skill multiplier you learn is a two-digit number, which is formed through many practical calculations on the basis of mastering its algorithm. Mathematical skills are closely related to mathematical knowledge and ability, and there are essential differences. The difference between them lies in: skill is the generalization of action and action mode, reflecting the proficiency of action itself and action mode; Knowledge is a summary of experience, which reflects people's understanding of the regularity of mutual connection between things; Ability is a summary of some stable psychological characteristics to ensure the smooth completion of activities, which embodies the individual characteristics of learners in mathematics learning activities. The relationship between the three can be clearly reflected from the role of mathematical skills.
The role of mathematics skills in mathematics learning can be summarized as the following aspects:
First, the formation of mathematical skills helps to understand and master mathematical knowledge;
Second, the formation of mathematical skills can further consolidate mathematical knowledge;
Thirdly, the formation of mathematical skills is helpful to solve mathematical problems;
Fourthly, the formation of mathematical skills can promote the development of mathematical ability;
Fifth, the formation of mathematical skills helps to stimulate students' interest in learning;
Sixth, arouse their learning enthusiasm.
Mathematical skills, according to their own nature and characteristics, can be divided into two types: operational skills (also known as sports skills) and mental skills (also known as intellectual skills).
Mathematical operation skills of length. Operation skill refers to the skill to realize the action of mathematical task activity mode mainly through the movement or operation of external body. It is an external operation activity mode composed of various local actions according to a certain program. For example, students' skills of measuring the degree of angles, measuring the length of objects and drawing geometric figures as drawing tools are such external operation skills. Operational skills have some characteristics that are obviously different from mental skills: first, they are explicit, that is, operational skills are an explicit way of activity; The second is objectivity, that is, the object of operation skill activities is physical objects or muscles; Wang is not a minimalist. As far as the structure of actions is concerned, every action of operational skills must be executed, which cannot be omitted or merged. This is an expansion project. If you draw a circle with compasses, determine the radius, determine the center of the circle, and rotate the compasses around the center with one foot, you can neither omit nor combine them, and you must perform the task in detail.
2. Mathematical psychological skills. Mathematical psychological skills refer to the way of psychological activities to successfully complete mathematical tasks. It is a cognitive activity with the help of internal speech, including psychological components such as perception, memory, thinking and imagination, and thinking is its main activity component. For example, primary school students' skills in oral calculation, pen calculation, solving equations and solving application problems are more mathematical mental arithmetic skills. Mathematical mental skills are also formed through acquired learning and training, which is different from human instinct. In addition, mathematical psychological skills are a legal way of psychological activities. "The so-called legal way of activity means that the elements of action and their order should reflect the requirements of the objective law of the activity itself, not arbitrary." These characteristics reflect the essence of mathematical psychological skills and mathematical operation skills. As a cognitive activity with thinking as the main activity component, mathematical psychological skills also have personality characteristics different from mathematical operation skills, which are mainly reflected in the following three aspects.
First, the concept of the object of litigation. The direct object of mathematical psychological skills is not the physical object itself, but the subjective image of this object in people's minds. For example, the direct object of mental activity of abdication subtraction oral calculation within 20 years is the concept of "addition and subtraction" or other calculation methods, rather than some materialized object.
Second, the implementation process of the action is hidden. The action of mathematical psychological skills is completed by internal words, and the execution of the action is carried out inside the mind. The change of the subject is very implicit, and it is difficult to observe it directly from the outside. For example, what we can directly know is the calculation result reflected by the students' external language, while the students' internal psychological activities are invisible during the calculation.
Third, the action structure is simple. The action of mathematical mental arithmetic skills does not have to be done exactly like arithmetic activities, nor does it have to be said exactly like a foreigner. Its activity process is a highly compressed and simplified automation process. Therefore, the action components in mathematical psychological skills can be merged, omitted and simplified. For example, when students master the oral arithmetic of carry addition within 20, they simply don't realize the actions of "looking at large numbers", "trying to make up numbers", "dividing decimals" and "making up ten", and the whole calculation process is compressed into a simple process that blurts out.