Inappropriate operation is largely due to the lack of understanding of basic concepts, thorough grasp of basic formulas and laws, and unskilled application. In teaching, it is essential for students to firmly grasp the concepts, properties, formulas, rules and theorems needed for operation. We should focus on improving students' memory ability, teaching students memory methods, and firmly mastering some commonly used data, formulas and laws. We should go through the process from concrete to abstract, from perceptual to rational, naturally form concepts, deduce formulas and laws, pay attention to the knowledge gap reflected in students' operations, and don't simply attribute the reasons for solving problems to carelessness or problems in methods and skills. Only by mastering relevant knowledge can we make the operation clear and provide reliable basis for the operation, which is the premise of correct operation. Therefore, it is fundamental for students to learn the basic knowledge of calculation well.
Strengthen the teaching of the occurrence, development and formation of formulas and theorems.
Ignoring the preconditions of formulas and theorems and abusing formulas and theorems are the main reasons for students' low computing ability. There are many factors, but this has a lot to do with our usual teaching focus is not comprehensive enough, or the key methods are wrong, and students' cognitive laws are not harmonious. Therefore, efforts should be made in question design and content organization, so that students can personally experience the occurrence, development and formation of knowledge, make lifeless knowledge come alive, follow students' cognitive rules, and deepen students' knowledge and understanding, instead of rote memorization, so that it will not be taken out of context when applied. The focus of classroom teaching is not only the subject of formulas and theorems, but also the conditions of formulas and theorems, special circumstances and other places that are easy to make mistakes.
Third, practice basic skills and improve the rationality of operation.
In high school, a lot of mathematics knowledge often uses simple numerical operation, and numerical operation is precisely the weakness of high school students. In fact, as long as our teachers can give appropriate guidance, use formulas flexibly and draw inferences from others, students' computing ability can be improved. In order to make students master the correct algorithm, teachers should often infiltrate modern mathematical thinking methods and compare and practice some topics that are easily confused by the algorithm. Encourage students to innovate and carry out intensive training of "multiple solutions to one problem" and "simple algorithm". In order to improve students' computing ability, it is necessary for them to master arithmetic and algorithms. Only by understanding the characteristics, methods and influencing factors of computing can students' computing ability be better improved. Algorithm research is helpful to simplify the thinking process, get effective problem-solving strategies, strengthen practice, and use various forms to make students form skills.
1. Intensive training makes perfection.
An important way to improve the operation speed is to practice hard, often and repeatedly. Only through certain intensive training can students achieve the goal of "practice makes perfect". Therefore, it is necessary to carefully organize training, whether in class or after class, in addition to quantitative and qualitative requirements, there should also be certain requirements for the speed of problem solving. In the classroom, we should arrange some limited operation training and more hierarchical and targeted problem group training, so that different types of students can complete appropriate training tasks within a certain period of time, thus improving the efficiency of classroom teaching and the success rate of class.
2. Master skills and calculate quickly
It is not enough to master the general laws in mathematical operations, but also to form skilled skills. Without skilled skills, it is impossible to complete the operation simply and quickly. Therefore, we should consciously discover and summarize some skills and techniques through operational exercises. Such as method of substitution's transformation, the combination of numbers and shapes, 1 and the choice of coordinate system in analytic geometry. In addition, we should also do the following:
First of all, master the general principle of operation. The general principle of the general method is not only conducive to the orientation of operation, but also conducive to improving the speed of operation. Therefore, we should master the transformation of basic numbers and form some basic skills. For example, using multiplication formula to simplify digital calculation; Decomposition of prime factors to find the square root; Find the value of the radical by rationalizing the denominator. It is very necessary to cultivate students' correct and fast computing ability and let them master certain skills.
Second, be familiar with some methods and skills of mental arithmetic and quick calculation. Mind is a form of operation, a conscious calculation, without words, which is a sign of "familiarity" and can strengthen students' thinking inspiration. In teaching, we should strengthen the training of mental arithmetic and teach some fast calculation methods, which are very effective methods to improve the operation speed, whether it is to find the idea of solving problems or to carry out the operation process.
Third, remember some commonly used data and important conclusions. Such as the square number of one or two digits, the trigonometric function value of a special angle, some commonly used mathematical propositions, etc. Thereby expanding the capacity of knowledge, increasing the span of thinking and improving the agility of thinking.
3. Temper your mind and operate quickly
Infiltrating thinking training in operation training is an effective measure to improve operation speed. Because good thinking quality is a powerful guarantee to improve computing power. In teaching, we should strengthen the training of mathematical methods and thinking methods, such as mastering some commonly used mathematical methods: collocation method, method of substitution method, undetermined coefficient method, mathematical induction method, parameter method, elimination method and so on. Familiar with some commonly used mathematical logic methods: analysis, synthesis, reverse method, induction, deduction and so on. Master common mathematical thinking methods: observation and analysis, generalization and abstraction, analysis and synthesis, special and general, analogy, induction and deduction, etc. Master the commonly used mathematical ideas: the idea of function and equation, the idea of combining numbers with shapes, the idea of classified discussion, the idea of transformation, etc. It is necessary to strengthen the training of students' reverse thinking, divergent thinking, holistic thinking, structural thinking and intuitive thinking, and provide guarantee for finding simple and fast operation methods from the aspects of thinking methods, problem-solving ideas and problem-solving strategies.
Paying attention to observation, reasonable association and making good use of comparative consciousness are helpful to improve computing ability.
Teachers in vocational schools agree that students in vocational schools are not solid in junior high school learning and have a weak grasp of basic knowledge and methods, so we should keep some in mind.
Fixed knowledge and methods, and ask them to use these knowledge or methods to solve problems. It is true that the fixed way of thinking has a positive side in operation, but it also has a negative impact. When students master a certain knowledge (method), they are often used to solving problems by conventional methods. This will inevitably lead to thinking inertia and lack of awareness of multi-directional and multi-angle thinking, which is not conducive to the improvement of students' operation speed. What's more, students in vocational schools are active in thinking and just want to find a simpler and faster calculation method, so they can have more time to do other things. Therefore, the fixed thinking method will affect students' operation speed, make the operation process complicated, and thus cause students' aversion to mathematics learning. In teaching, I often guide students to think from multiple directions and angles, and strive to cultivate students' observation ability, association ability and comparative consciousness, so as to seek the best solution to the problem.
5. Regularly summarize the laws and improve the calculation ability.
Computing ability can neither exist in isolation from specific mathematical knowledge nor develop independently from other abilities. It permeates memory ability, observation ability, understanding ability, association ability and expression ability, and supports each other with mathematical ability such as logical thinking ability. Therefore, the problem of improving computing power is a comprehensive problem. In the process of teaching, only by summing up the laws frequently, constantly guiding and gradually accumulating, can the computing ability be truly improved.
Cultivate students' good study habits
Good study habits are an important factor in determining computing ability. Because of its rigorous characteristics, mathematics discipline does not allow students to be careless. Students' mistakes in calculation are partly caused by bad study habits. In teaching, teachers should let students develop good habits such as careful examination of questions, careful observation and standardized writing before doing it. In the process of learning mathematics, students can be asked not to rely on calculators when they encounter simple calculation problems, so that students can form judgments on operation results in mental calculation, oral calculation and written calculation. Good computing habits are the guarantee of improving computing ability. When calculating, students are required to look, think, calculate and check. Take a look: before doing the problem, read the problem completely, read every number and every operation symbol clearly, and have a preliminary perception. Two thoughts: on the basis of seeing the topic clearly, find out the relationship between the characteristics of the formula and each operation, choose a reasonable method according to the specific situation, and determine the operation steps. Three calculations: after determining the operation steps and methods, carefully calculate. Four checks: Look back in time to check whether the algorithm is reasonable, whether the operation symbols are copied wrong, whether the negative sign is omitted, and whether the calculation result is wrong.
Be patient when calculating, and never stop until you finish a problem and get it right. Students are required to write carefully, because only by writing carefully can students concentrate and improve the accuracy of calculation. With the passage of time, students can develop good computing habits.
In short, China's mathematics education has a tradition of attaching importance to basic knowledge and skills training and ability training, and high school mathematics curriculum in the new century should carry forward this tradition. Teaching practice shows that improving students' computing ability is a complex system engineering and a long-term task. As long as we cherish every training opportunity, carry out long-term infiltration in a planned, targeted and conscious way, and let students gradually understand the essence of computing ability, it will inevitably urge students to form the habit of performing operations correctly, reasonably and quickly, and finally achieve the goal of improving students' computing ability.