First of all, the questions raised
With the progress of the times, the only child has formed a general climate, and the cultivation of various habits depends on parents and elders. In this situation, how to cultivate students' good calculation habits, improve students' calculation ability and reduce students' calculation errors is an urgent task for primary school mathematics teachers.
It is a task for students to do calculation problems now. It's not an error or omission, but a mistake in symbol or a mistake in decimal point. They are indifferent to some problems in the calculation, so they can correct them. In fact, improving students' computing ability is the requirement of society for students' life. With the development of information technology, computers and calculators have replaced complex calculations, but correct calculation methods, good calculation habits and calculation ability are still everywhere in life, such as factories, banks and shopping malls, and some of them are irreplaceable. Therefore, reducing pupils' calculation errors and improving pupils' calculation ability are the key and difficult points in teaching now and even in the future. In order to promote the improvement of students' computing ability, it is necessary to carry out research on this topic in this class, so that students can improve their understanding in research and discussion, find out the reasons for the mistakes, and improve their computing ability on a large scale.
Second, the research objectives
1. Through the analysis of a large number of wrong examples, this paper systematically classifies the causes of primary school students' calculation errors, and adopts some concrete and feasible methods to improve students' calculation accuracy and reduce and avoid some unnecessary calculation errors.
2. By studying some bad psychology of students in calculation, students can develop good calculation habits, improve their calculation ability and further cultivate their keen sense of calculating numbers.
3. Through the whole research and practice, a set of relatively perfect and effective teaching strategies to improve students' calculation accuracy has been formed.
Third, the research object
Students in Class Two, Grade Three
Four. Research contents and achievements
(1) Investigated the types of calculation errors of junior three students.
Error, in a general sense, means that the result is wrong. Such as 32- 13 = 2 1, 4× 5 = 9,42+18.
1. Misrecognition
Misrecognition is an error caused by misreading or admitting mistakes. This kind of error belongs to the perceptual error before calculation, which is common in the calculation process of primary school students. Mistakes that belong to misidentification are as follows:
Wrong writing
A typo is a clerical error that occurs when the calculation is correct and the answer result is wrong. This kind of error belongs to the error copied after calculation and is also common. Typical mistakes are correct vertical pen calculation and wrong horizontal copying. For example:
There are also some students who often make correct calculations in the draft book, but make mistakes when copying them into the exercise book.
Step 3 miscalculate
An error refers to an error in the calculation process. This kind of mistake includes unclear calculation, unfamiliar rules and inaccurate oral calculation.
Teachers should correct students' homework in time, and carefully analyze the nature of mistakes in homework, and distinguish which are wrong questions, which are wrong writing and which are wrong calculation. Only by diagnosing different types of mistakes can we find appropriate methods to suit the remedy to the case.
(2) To explore the causes of mathematical calculation errors of third-grade primary school students.
Two kinds of mistakes in students' calculation are caused by psychological factors and mistaken for mathematical knowledge and skills. According to statistics, the error caused by psychological factors accounts for about 60% of the calculation error of primary school students, while the error related to knowledge and skills only accounts for about 40%. Specifically, the calculation error has the following reasons:
1. Knowledge and skills
(1) Basic knowledge is not solid.
Some mistakes are caused by the lack of basic knowledge such as basic concepts of operation (as shown in the left picture). This error occurs because after determining the highest bit of quotient, ten digits are not quotient enough, and there is no place to write 0.
(2) The reason is unknown
Some mistakes are caused by students' failure to grasp and accurately apply the calculation rules.
When beginners divide a digit into multiple digits, students often make the following mistakes: The mistake is to continue the division without adjusting the last 0. Why do you know that 0 will continue to divide before adjustment, but 0 will not be processed? It turns out that students are calculated under the control of such psychological activities: since 0 means no, of course, there is no need to adjust it down, so only the previous 1 is left. Obviously, students only understand the special role of 0 in counting-occupying position, but they don't know that when the current digit has a remainder, the 0 of the last digit will move down and form a new number with the remainder before division; The poorly analyzed remainder 1 is in the tenth place, which means that 1 10 and 10 are both one place. Although this 1 is not enough to divide by ten, it is enough to divide by four and divide by one. Obviously, the root of the error lies in unclear concepts and unclear calculations. If the algorithm is unclear, it will become water without a source and a tree without a root. Students can deal with "standard questions", but they are helpless about variant questions. This is one of the biggest obstacles to improve computing power.
(3) basic oral calculation is not skilled.
Oral calculation is the basis of written calculation. Calculate a written calculation, four operation problems, at least two or three, and more than twenty basic oral calculations. If one of these basic oral calculations is wrong, then the whole written calculation problem is wrong. According to statistics, in the error of pen calculation, add 96.5%, subtract 82%, multiply 92.7% and divide 73.2%. It can be seen that the unskilled basic oral calculation is an important reason for students' calculation errors.
2. Psychological factors
Any calculation is carried out under the adjustment of psychological activities. Most of the mistakes made by students in solving calculation problems are not mistakes in the calculation process, but psychological problems of students. The specific performance is as follows:
(1) thinking interference
Students' mentality has its positive side. But its negative impact should not be underestimated. Negative thinking mode is habitual, biased and taken for granted, which will seriously interfere with and inhibit the smooth progress of learning. For example, after putting "300-50" in questions such as "240 ÷ 60,450 ÷ 90,360 ÷ 40", many students often miscalculate "300÷50=6".
(2) Pay attention to instability
Students are not attentive in class and homework. In the process of calculation, they often enter 0 plus 0 when copying questions, 1 when copying wrong numbers or symbols, 3 and 4, which leads to misunderstanding and writing mistakes.
(3) Emotion is fragile
Students' mood is easy to fluctuate and their will quality is poor, so they often can't always do their homework seriously. When calculating, students hope to work out the results quickly and keep a stable attitude towards familiar and easy questions. However, when they encounter features with large data, complex appearance or unfamiliar features, they will have rejection psychology and cannot patiently examine the questions. Blind calculation under the mentality of being afraid of difficulties and complexity will inevitably lead to higher error rate.
3. Calculation habits
There are many calculation errors, and the problem is not arithmetic. It is not the ability, but the study habit. Students often have the following bad study habits in computing:
(1) Distracted
This is a bad habit formed in long-term life and study. This kind of students are always not good at focusing on the calculation object, and they are not attentive and careless when calculating. If you are not careful in calculating the copied questions, you often copy the wrong numbers and symbols, or you are careless in doing your homework and miss some calculation links, which will often lead to calculation errors.
(2) the operating procedures are chaotic
Some calculations are simple, but they often make mistakes. For example, when we analyze the calculation process of students who make mistakes in multi-digit addition and subtraction in continuous advance and retreat, we often find an obvious * * *: when advancing and retreating, sometimes the ""is marked vertically, and sometimes it is not marked; Sometimes the carried-forward 1 is added first (or the returned 1 is subtracted first), and sometimes it is added (or subtracted) later. There is no consistent operating procedure at all, so it is very confusing and confusing.
(3) scribble
Some students do not pay attention to the writing format when drafting, and their handwriting is scrawled, and some figures are blurred. When copying into the exercise book, there is a phenomenon of copying the wrong figures. If some students write "7"1"6" and "0" wrong. Also, due to the disorder of the arrangement when drafting, there are often one east and one west topic, and the number does not correspond to the topic.
(4) Lack of the habit of checking.
Even if there are some mistakes in calculation, if you have the habit of checking and checking, it is not difficult to find the problems and correct them yourself. Students who often make mistakes in calculation have no such habit.
(3) The countermeasures to reduce students' calculation error rate are studied.
It is not terrible for students to make mistakes in solving problems. It is important to provide students with thinking methods to find out the causes of errors, correct them in time, master the correctness and avoid repeating the same mistakes. The causes of primary school students' calculation errors are generally knowledge, skills and psychology, and prevention and correction of errors should also start from these aspects.
1. Strengthen the teaching of basic knowledge
(1) Strengthen mathematical understanding
In order to prevent students from making arithmetic mistakes, we must carefully study the teaching materials and strengthen the teaching of arithmetic and calculation, so that students can firmly grasp the laws of arithmetic and calculation. This is the premise and foundation of correct calculation.
In calculation teaching, students should be guided from concrete to abstract step by step, so that students can participate in the concrete deduction process of rules, understand arithmetic and explore algorithms, and cultivate their ability to explore arithmetic and algorithms independently. Strengthen the teaching of basic principles, apply the law of grasping the foundation to promote migration, and improve the calculation accuracy.
(2) Strengthen oral practice.
Oral arithmetic is particularly effective in developing students' wit, agility and short-term memory. In order to effectively practice students' basic calculation skills, we should start with oral calculation and ask students to do basic oral calculation correctly and skillfully. At present, students' oral arithmetic has not been strengthened in the lower grades, but in the higher grades, their oral arithmetic ability is very weak. Therefore, teachers should attach importance to oral arithmetic training, insist on practicing every day, and compare speed.
A: Stick to the special training before class for 5 minutes.
According to the content of the new curriculum, we can arrange some oral arithmetic problems purposefully and systematically, and conduct oral arithmetic training within 5 minutes before the lecture, which can play a role in reviewing the old and learning new things. For example, when learning "multiplier is the multiplication of two digits", you can arrange the oral calculation content of multiplication and addition; If "divisor is the division of single digits", you can arrange the oral calculation content of multiplication and division. This practice is time-consuming and laborious at first, but as long as you practice openly and stick to it every day, you can see great results.
B: Various forms of oral arithmetic training.
Visual arithmetic training presents oral arithmetic problems to students in the form of slides, small blackboards and oral arithmetic cards. Time is limited, let the students write down the oral calculations in turn, and then exchange marks to see who can calculate quickly and accurately. This kind of quick calculation competition has obvious effect.
Listen to the formula, train the teacher to read the questions orally, and let the students write the numbers in the oral calculation book. After reading the questions, the teacher can find out how many students reported the numbers. You can also ask several students to report the number continuously, and the teacher can correct it at any time. This kind of training method is difficult, which requires students to listen carefully, think actively, calculate quickly, and use their ears, brains, mouth and hands together.
The relay training teachers show the exit cards one by one, either calling the roll or letting the students answer first. They can also count each question vertically and horizontally in the order of seats, and say the numbers one by one as quickly as driving a train. This kind of oral arithmetic training can cultivate students' flexibility and agility.
Command-oriented training teachers hold verbal arithmetic cards, constantly flip and change directions, and use cards instead of sticks to conduct command-oriented verbal arithmetic training like traffic police; Focusing on the students who do oral arithmetic, the students behind the card push and then count, and the students in front of the card slot count and move to the left.
The improvement of basic oral calculation ability will greatly reduce the mistakes in written calculation. On this basis, strict writing training will enable students to reach a higher level of calculation.
2. Cultivate students' good psychological quality.
Many students' mistakes are caused by psychological factors. Therefore, to correct mistakes, we must strive to correct bad psychological quality.
(1) Positive guidance to relieve psychological pressure.
Teachers should also reduce students' psychological pressure, be strict with students, regard some mistakes made by students in the learning process as normal things, make great efforts to help students find out the reasons and correct their mistakes, and don't be too responsible and critical. Let students feel safe psychologically. For example, guide students to copy homework questions, pay attention when doing homework, and concentrate on completing homework; We must have the spirit of overcoming difficulties and not retreat from difficulties; Overcome the defects such as carelessness, carelessness and careless inspection; We should also guide students to build up confidence and believe that they can do their homework well and get good grades.
(2) Cultivate observation ability and thinking ability.
Computing power is restricted by general ability. It is necessary to fundamentally improve the ability of calculation, especially to cultivate the ability of observation and thinking. Good observation ability is often reflected in the ability to quickly detect details that are easily overlooked. Students are required to carefully examine the questions, master the overall structure, use skilled oral calculation skills, skillfully predict the characteristics of the questions in advance, and judge whether they can be counted. This can be trained by comparing and observing similar problem groups. In each problem group, the differences in question types are subtle, so it is necessary to find out their differences as soon as possible, which is helpful to cultivate the ability to observe details.
3. Cultivate students' good homework habits
Good habits last a lifetime. In computer teaching, we should pay attention to the cultivation of students' good homework habits from the beginning of the lower grades, and make students gradually develop good homework habits through strict requirements.
(1) Learn to write a draft.
The calculation of a large number of elementary arithmetic and application problems generally needs to be listed vertically in the draft book, so the usage specification of the draft book will directly affect the accuracy of the calculation. In view of the untidy handwriting of many students' draft paper, teachers should put forward the requirements of vertical columns in the draft paper, not only to write neatly, but also to make calculations as orderly as exercise books. Check the draft regularly and evaluate the results. Often praise students who have written well drafts and exhibit excellent ones. In the exam, not only the test paper is evaluated, but also the draft is graded to promote the formation of students' good calculation habits.
(2) Calculation habit of operating according to procedures
A: Programmatic operation of basic calculation Only when the basic calculation reaches the level of automation can we concentrate on comprehensively grasping the general laws of various relationships and choose reasonable and flexible algorithms for comprehensive operation. Automation depends on the establishment of a firm dynamic stereotype in the cerebral cortex, which in turn depends on the repeated training of each computing link in a certain order. Therefore, some basic calculations should not only be practiced repeatedly, but also develop the habit of operating according to procedures in order to achieve the degree of automation.
B: the procedural examination of mixed operation. Paying attention to the procedural examination process can not only avoid the problem of "paying attention to one thing and losing the other", but also help to form the idea of consciously pursuing the optimization of the calculation process. The procedure for examining the questions is: take a look. What is the order of operation of the problem? What are the characteristics of numbers and operation symbols? Second, find. Find a simple method according to the characteristics of the topic. Three judgments. Simplify what can be simplified, and calculate what cannot be simplified according to the routine.
(3) Get into the habit of checking.
Ask the students to check, as part of the calculation, to see if the numbers and operation symbols in the calculation formula are copied wrong. Check in place. Look at every step of the calculation. Is there something wrong? You can check it again, or you can verify it by reverse operation. The latter can avoid repeated thinking and cover up mistakes. Mixed operation should be "step by step", and mistakes should be found in time to prevent the "chain reaction" of mistakes. We should develop serious, careful and meticulous study habits, and oppose scribbling, pursuing speed and neglecting accuracy.
Students always like to look up and see how others do it when they finish their problems in class. This is ostensibly participation, but in fact his emotions and cognition are not involved. The teacher wants the students to raise their left hand to show that they have finished, and the right hand holds a pen to recalculate. We should also teach students how to check their homework step by step. The following calculation and checking steps can be provided: Did you copy the wrong question? Is the column correct? Check it again. Are there any mistakes in the calculation? Are the numbers written correctly?
In order to make students remember the operating procedures, you can also make up a jingle to make students catchy:
Fourth, the calculation should be careful, and the number symbols should not be copied wrong.
Check the questions before calculation, and the sequence rules are correct.
Use the law correctly, step by step and do not relax.
Where does the correct result come from? Good habits are a guarantee.
Let the students use this jingle to create a relaxed, pleasant and upward learning atmosphere.
(4) Cultivate students' habit of "solving problems before thinking"
I want to know if I did it right and see if the result of the operation conforms to the meaning of the problem and real life. This will not only ensure that there will be no mistakes in solving problems, but also help to cultivate students' responsible spirit and thinking ability.
Think about the characteristics and application scope of examination questions, and promote the development of application ability; Think about the law of solving such problems, so as to improve the ability of solving problems and guide students to sum up their thinking process and apply it frequently; Think about whether there is another solution, which can broaden our thinking and improve the efficiency of solving problems.
The psychological characteristics of students are emotional instability, cold and hot. The formation of a good habit, in addition to repeated practice, should also be accompanied by strict management methods: in addition to the strict management of teachers in the school, students and parents should be mobilized outside the school. Urge students to finish their calculation homework carefully.
4. Explore the tricks of error correction
When dealing with students' calculation mistakes, you can't simply make an "X". To let students know where the mistakes are and where the key mistakes are, teachers should draw signs to remind students to observe and check the calculation process and find out the reasons for the mistakes. Typical mistakes with universal significance should be evaluated and guided by teachers in the whole class, and help students find out the reasons for the mistakes and remind them to pay attention when doing similar problems. Circulate some students' exercise books, draft books and test papers with high calculation accuracy to students, and let them introduce their own learning experience, which will shake some students with low calculation accuracy and make them change the wrong view that "carelessness" is the main cause of mistakes, resulting in the desire to improve calculation accuracy. In view of the causes of students' mistakes, we should prescribe the right medicine and take good measures to correct them.
An analysis of the research results of verbs (abbreviation of verb)
Through the analysis and research on the causes of the mistakes made by the students in the third grade of this class, a large number of examples of mistakes are analyzed, and some concrete and feasible methods are adopted to improve the calculation accuracy of students and reduce and avoid some unnecessary calculation errors. By studying some bad psychology of students in calculation, we can cultivate students' good calculation habits, improve their calculation ability and mathematics ability. Through the whole research and practice, teachers have summed up effective teaching strategies to improve students' calculation accuracy.
Confusion and deficiency in the study of intransitive verbs
1. One year's research time feels too hasty. On the one hand, as a third-grade math teacher, I chose third-grade students to do experiments. Although some achievements have been made, the effect is not obvious. Because many students' study habits are not formed overnight. On the other hand, mathematics learning is a coherent process, and the formation of mathematics skills cannot be achieved overnight. By the third grade, most of the work can only be "correcting mistakes" afterwards, and "preparing for a rainy day" beforehand is the key to improving students' computing ability. If I choose again, I will choose the follow-up study from Grade One to Grade Three.
2. In the process of this experiment, because there are too many students in the class, I always feel that the time is not used enough, and there is no time to make individual corrections and case analysis for the students, so there is still polarization in the calculation. The worst students have a very high error rate, and there are almost all kinds of mistakes. Therefore, how to use reasonable time to correct students' cases is a problem worthy of in-depth study.