1, strengthen the teaching of basic knowledge and skills, and improve the accuracy of operation.
The basic knowledge in mathematics is the basis of arithmetic, which is of guiding significance to operation. The confusion, vagueness and instability of basic knowledge are often the root causes of operational errors. Therefore, strengthening and implementing the "two-base" teaching is a very realistic problem to improve the operational ability, which specifically requires students to do the following:
(1), memorize some important data formulas and rules, because accuracy is the basic requirement of operation, and correctly memorizing formulas and rules is the premise of accurate operation. Some mathematical concepts, formulas, rules and properties are the basis of operation, which explains why we can do this, and some are the methods and steps of operation. The concrete program, namely algorithm, is given. Students learn related concepts, properties and formulas, remember rules and steps on the basis of understanding, and then gradually form some operation skills through a series of operation activities (that is, exercises).
(2) Understand the concepts and definitions correctly and master the formula derivation. Only by understanding the derivation of some concepts and formulas can we use formulas positively, reversely and vividly, thus improving the calculation ability. The causes of operational errors in mathematics learning are often the results of vague concepts, forgetting formulas and rules, confusion or slow application.
2. Strengthen scientific and systematic reasoning training to improve the rapidity of operation.
Poor computing ability is often caused by poor thinking ability. In teaching, students should strengthen reasoning training on the basis of mastering basic knowledge. Usually, practice requires gradual and sufficient reasons, and pay attention to the order of operation. Generally speaking, we should pay attention to the following aspects:
(1) Training must be orderly. The exercise must be carried out in a planned and step-by-step manner. In mathematics teaching, exercises can be divided into three stages: first, the stage of imitating exercises. This is an exercise under the teacher's example after learning new knowledge. The selected exercises are not difficult and change little, so students are required to operate according to the steps and rules of the examples to ensure the correctness of the operation. At this time, it is not appropriate to ask for speed. Second, the mastery stage. This is a study organized on the basis of students' initial mastery of knowledge and skills. The difficulty of exercises is appropriately improved, and the forms of exercises are diverse. Students not only need to calculate correctly, but also need to summarize the process, basis and method of operation after obtaining the correct answer, so as to raise the operation mode to the theoretical level. Third, the comprehensive application stage. At this time, you can choose a comprehensive topic with certain difficulty and train students to determine the direction of operation and the ability to use rules flexibly.
(2) Carry out variant exercises. In order to make students' ability reach the proficiency level, variant exercises must be organized. The so-called variant exercise is to change concepts and rules while other effective learning conditions remain unchanged. For mathematical operations, it is to change the non-essential characteristics of the problem and keep its structural components unchanged. Among them, the specific ways are the expression change of mathematical sentences, the exchange of conditions and conclusions, the change of problems and backgrounds, etc.
(3) Understand the practice effect in time and correct the practice mistakes in time. In ability practice, it is an effective way to improve the practice effect by letting students know the effect of the practice in time. Psychological research shows that if the following feedback information is provided to students who are undergoing ability training: ① knowing the scores of each exercise, ② encouraging and urging them constantly during the exercise, and ③ analyzing the mistakes in the exercise, the practice effect will be significantly improved. This is because, on the one hand, students understand the problems according to the feedback information, so as to adjust their learning activities and make the exercises more effective; On the other hand, it also increases the learning motivation to strive for better grades or avoid making similar mistakes again.
3, thinking flexibility training in the process of operation.
Because mathematical operation is an intellectual operation with clear direction and certain rules, after some practice, this kind of operation experience will form a certain fixed reaction mode, which will play a tendentious role in the choice of operation direction in subsequent learning. This is the phenomenon of "fixed mode" in learning. When the formed inertial thinking is consistent with the method of solving new problems, they can react quickly and get correct answers, and there are "shrinking" and "jumping" phenomena in the operation process, which is the positive role of stereotypes and a sign that students are proficient in knowledge and skills. For example, through the study of "quadratic equation of one variable", students have mastered the skills of solving quadratic equation of one variable by using formula method and factorization method. In the study of quadratic function in the future, they will react correctly quickly when they encounter operations related to quadratic equations with one variable. When habitual thinking is not completely consistent with or contrary to the solution of new problems, it cannot be solved by simple and flexible methods, and the operation process is cumbersome and lengthy, which leads to the wrong solution of problems. This is the negative effect of stereotype. In practical teaching, we should overcome and prevent the negative influence of "stereotype" and cultivate the flexibility of students' operation.
4. Pay attention to cultivating students' rational operation ability.
Reasonable calculation is to make full use of the operation law, product invariance and quotient invariance, change the data and order of operation, and make the operation as simple, fast and correct as possible. Cultivating students' simple operation ability is not only to improve their operation ability, because in the process of training, it is bound to involve the cultivation of other abilities such as observation ability and induction ability, so whether they can operate simply is actually the cultivation of comprehensive ability. At the same time, it is also necessary to cultivate students' holistic view when doing mathematical operations. Students should have a general view before calculating, and master how many steps the operation is divided into, what to calculate first, what to calculate later, what characteristics the numbers in the questions have, what information they contain, and so on.