How to improve the computing ability of senior high school students
In high school mathematics learning, with the deepening of learning content and the continuous improvement of operation level, there are more and more problems exposed by high school students in operation. Students do not pay enough attention to the improvement of computing ability, which not only affects the development of thinking ability, but also inevitably affects the improvement of teaching quality. In teaching, through case analysis, it is found that there are at least three factors that cause arithmetic errors: First, writing errors. For example, symbols and coefficients of number and formula operation, scrawled handwriting, misreading when looking at "trance"; Second, formulas, theorems, definitions and rules are not accurately remembered, and they are not deeply understood and used flexibly. For example, the properties of functions, logarithmic operation rules, trigonometric sum and difference times and a half formulas, the product and geometric meaning of vectors, the properties of conic curves, binomial theorems, several types of probability judgments, and the operation rules of derivatives. Third, the problem-solving thinking training is not in place and the process control is not strict. I. Rational Development of School-based Mathematics Textbooks In order to enable all students to learn mathematics well and improve their mathematical operation ability, some knowledge has been deleted from the current junior high school mathematics textbooks, thus greatly reducing the difficulty of some contents. Junior high school mathematics content has low requirements for operation, and the training is not in place, which leads to poor students' operation ability and seriously affects senior high school mathematics performance. For example, in the operation of numbers and formulas, many students' problems are always reflected in the deformation and simplification of formulas. School-based textbooks should supplement the teaching content of polynomial operation. Such as cubic sum, cubic difference, cubic sum of two numbers, cubic difference of two numbers and square formula of sum of three numbers in multiplication formula. For example, analytic geometry in senior high school requires a high relationship between straight lines and conic curves, which is the focus of the college entrance examination. The related contents of quadratic equation of one variable should be added: discriminant and Vieta theorem of quadratic equation of one variable, quadratic equation of one variable and quadratic equation of two variables. In order to solve these problems, we must develop school-based teaching materials suitable for the actual situation, solve the connection problem of mathematics knowledge in junior high school and senior high school, and lay a solid foundation for mathematics teaching in senior high school. Second, pay attention to the learning process, improve the operation ability 1, accurately understand and firmly grasp the concepts, properties, formulas, rules and some commonly used data needed for various operations; A deep understanding of concepts, properties, formulas and rules directly affects the choice of methods and the speed of operation. Fuzzy concepts, formulas and rules will definitely affect the accuracy of operation. In order to improve the operation speed, it is still necessary to remember some commonly used data. Such as the square number of natural numbers within 20, simple pythagorean number, special trigonometric function value, etc. 2, master the general operation method, general rules, flexible use of concepts, properties, formulas and rules for operation. Our teachers can collect some flexible exercises according to the content of the textbook, cultivate students' flexibility in operation, guide students to collect, summarize and accumulate experience, form skilled skills and improve the simplicity and rapidity of operation. 3. Strengthen the operation practice. To effectively improve students' computing ability, it is necessary to strengthen practice, which should be purposeful, systematic and typical. By changing one question, changing one more question, solving one more question and using one more method, the proficiency, accuracy, flexibility and organization of operation are cultivated. Cultivate students' thinking depth and improve their computing ability in the form of exercise group training. 4. Improve the reasoning ability in operation. The essence of mathematical operation is a process of deducing results from known data and formulas according to the definition and nature of operation, and it is also a process of reasoning. Whether the operation is correct or not depends on whether the reasoning is correct. If the reasoning is incorrect, the operation will go wrong. Pay special attention to the equivalent transformation in operational reasoning. 5. Get into the habit of checking calculation and master the method of checking calculation. During or at the end of the problem-solving operation, it is necessary to check the operation process and results in order to correct the mistakes in the operation process or results in time and master the checking calculation method. The methods of inspection usually include: reduction method, substitution method, evaluation method, inverse operation and so on. Cultivating the habit of inspection and improving the ability of thinking monitoring in the process of operation is one of the specific requirements for forming and developing the ability of operation, which can not be ignored in learning. Third, learn to reflect and improve the accuracy of operation. Students who are good at reflection can constantly correct their mistakes, scientifically design operation procedures, improve the accuracy of operation, and gradually develop good operation habits. 1, reasons for reflection errors There are many reasons for students' calculation errors, especially in the connection between symbols, representations or concepts and propositions between students' old and new knowledge, there are coding errors or negative transfer. It is common for students to make mistakes in calculation. Teachers should make full use of this kind of teaching resources, guide students to objectively study the causes of mistakes, study their relationship with correct solutions, correctly use the reasonable components of students' wrong solutions, and truly play the positive role of wrong solutions in teaching. 2. Reflecting on the operation process in mathematics teaching, teachers should not only pay attention to whether students can calculate correctly according to laws and formulas, but also help students understand the operation theory and find a reasonable and fast operation method according to the conditions of the topic. The nature of the operation and the calculation goal are different. By comparing the different operation methods reflected in the calculation process, students can be guided to understand the influence of different strategies adopted by each operation method on the result acquisition. 3. Reflecting on the result of operation Reflecting on the result of calculation is not only to test whether the result is correct, but more importantly, to examine whether the result is reasonable. We should also cultivate our own computing ability in teaching and put forward a set of solutions: independent, accurate, fast, reasonable and standardized. For example, when solving the problems of straight lines and conic curves, many students are very afraid of endless operations. With the idea of algorithm, they have a framework to solve the problem. Students are full of confidence in the future and know every sub-link. I believe that as long as they persist, they will win. With the implementation and promotion of the new curriculum, computing ability has become a very important aspect that affects the development of students' ability. Middle school mathematics teaching should listen carefully to students' thinking process, find out the causes of operation errors, strengthen students' understanding of the meaning of operation, master the method of selecting appropriate algorithms and operation tools according to the needs of problems, cultivate the consciousness and ability to verify the accuracy of results and estimate the rationality of results, and effectively develop students' operation ability.