Why do children always make mistakes when calculating problems?
Perceptual errors caused by visual transmission
Pupils, especially middle school students, are characterized by the transition from phenomenological thinking to abstract thinking, which easily confuses similar and similar data or symbols, so mistakes often occur when copying wrong data and wrong operation symbols; There are also forgetting to bring, abdicating, missing writing, missing copying, and wrong operation sequence.
In addition, the perception of primary school students is accompanied by strong emotional color, and it is easy to perceive novel and interesting "strong stimuli" while ignoring "weak stimuli", resulting in perceptual errors. For example, fill in the blanks: 5+45()5+54, and some students will fill in the equal sign, because additive commutative law's "strong stimulus" covers up the different "weak stimulus" between 54 and 45.
There are also some mistakes in the operation sequence and simple operation methods, which are also caused by the general and rough perception. Especially under the stimulation of special data, I am confused by the illusion that I can make simple calculations, such as:
20? 5? 20? 5= 100? 100= 1
4 1/5-4 1/5? 1/3=0? 1/3=0
326+2 16+484=326+484+2 16=800+2 16= 10 16
Tips: The answers to the above examples are all wrong. Parents can see if their children often make such mistakes.
Simple consciousness is not strong.
Simple algorithm is an important part of primary school mathematics. Making students master simple calculation methods is an important way to improve their calculation speed. Comparative consciousness is an important direction to solve problems.
When solving problems, there are often many ways to solve them, which requires us to be good at choosing the best and following them. Some students lack the consciousness of comparison, ignore the operation results, deduce blindly, and lack the consciousness of choosing simple operation methods reasonably.
In the high stage of primary school, the calculation methods should be flexible and diverse, and reasonable algorithms should be selected from various schemes to realize algorithm optimization.
The attention development is not perfect and the stability is not high.
Pupils, especially those in Grade One, are not good at consciously distributing attention because of their poor attention quality. They often show that their thinking and writing are not synchronized, and their attention is not focused on the "pen tip", but on the one hand, they are copying, on the other hand, their attention is shifted to the next calculation method.
Pupils' physical and psychological characteristics of "inattention, lack of integrity in observing things and short time of concentration" make them prone to calculation errors.
Because primary school students are in the stage of growth and development, they are developing from unintentional attention to intentional attention, and the quality of attention is far from perfect. Taking 23 as 32 is the directivity and concentration to be developed; Writing 9 as 6 is poor attention selectivity; Writing four digits into three digits is insufficient attention span and distribution ability.
Studies have found that the attention of children aged 7 ~ 10 lasts for 20 minutes, that of children aged 10 ~ 12 lasts for 25 minutes, and that of children aged 12 lasts for 30 minutes. Therefore, when solving the problem of simple structural steps, the correct rate is relatively high, while when solving the problem of complex structural steps, it is easy to make mistakes.
This also explains one of the reasons why the calculation accuracy of junior students is high, while that of middle and senior students is not as good as that of junior students.
Short-term memory is weak, memory errors and omissions.
A calculation problem often involves multi-step calculation, and the intermediate number needs to be memorized in a short time. However, due to impatience, hurry and fear of trouble, some of the stored information disappeared or was temporarily interrupted, resulting in "memory errors and omissions".
For example, in the successive abdication subtraction, 1 is forgotten, which leads to errors in the calculation results, such as 4020- 199, which students can easily calculate as 4020- 199=393 1, which is completely related to the storage and memory of intermediate numbers.
The influence of bad learning mentality
There are three kinds of bad mentality of primary school students in the calculation process:
One is to despise psychology, thinking that the calculation problem is a "dead problem", without thinking, ignoring the mistakes caused by the analysis of the calculation problem and the inspection after calculation.
The second is fear of difficulties. It is considered that the calculation problem is boring. Whenever you see a calculation problem with many calculation steps or large numbers, you will feel afraid of difficulties and bored, lacking perseverance, patience and confidence, which greatly reduces the accuracy of calculation.
The third is laziness and disgust. Too lazy to write, unwilling to write one more word, disgusted with calculation, regardless of the size of the number, proficiency or not, all verbal calculation, unwilling to write calculus, too lazy to draft, and even no special draft book, check the book. Often omit necessary steps, skip steps, and fantasize about quick and direct results, thus making mistakes.
Errors caused by defects in knowledge mastery
Basic knowledge in primary school mathematics, such as concepts, properties, arithmetic, laws, laws, etc. Only under the premise of profound understanding and firm mastery can students use it correctly and flexibly and form computing skills.
Because some knowledge is not understood, concepts are unclear, arithmetic is not really understood and mastered, and calculation rules, concepts or operation sequences are not well mastered, students will make mistakes in calculation and do not realize that they are wrong.
The influence of bad study and calculation habits
Good study habits are an important condition to ensure correct calculation. Therefore, the usual practice should be strict and form a good calculation habit. Some students didn't develop good living habits since childhood, so they didn't develop good study habits when they moved to study after school.
Some students have developed some bad calculation habits due to insufficient understanding of the importance of calculation, insufficient training and improper methods.
These bad habits include: don't judge the questions, don't analyze, always do verbal calculations, don't want to write calculations, don't like to make drafts, don't standardize drafts at will, use drafts (calculation books) incorrectly, omit steps (skip steps), scribble, don't check and check in time, don't consciously simplify, and don't analyze and summarize the reasons for mistakes in reflection.
Basic oral skills are not skilled and skills are not enough.
To cultivate students' computing ability, we must first start with oral computing ability. Every grade, the focus of oral arithmetic is different.
Generally speaking, from senior one to senior three, add, subtract, multiply and divide or even add and subtract within 20; Intra-table multiplication; Two digits within 100 can be added or subtracted in decimal; A simple addition and subtraction two-step calculation problem that will not abdicate within ten thousand years; Simple one-digit times two-digit number; Simple decimal addition requires skilled verbal calculation.
After the fourth grade, the content of oral calculation will gradually increase, not only to consolidate the past content, but also to memorize some data on the basis of understanding, such as: 25? 4, 125? 8, the square of 10 to 19, etc. All formulas that can be used for oral calculation by applying algorithms and properties are oral calculations.
How to correct children's always wrong calculation problems
Change bad mentality
Students in the face of calculation often appear the following psychological state:
One is contempt psychology. It is considered that the calculation problem is a "dead problem", which needs no thinking, and ignores the mistakes caused by the analysis of the calculation problem and the inspection after calculation.
The second is fear of difficulties. It is considered that the calculation problem is boring. Whenever you see a calculation problem with many calculation steps or large numbers, you will feel afraid of difficulties and bored, lacking perseverance, patience and confidence, which greatly reduces the accuracy of calculation.
The third is laziness and disgust. Too lazy to write, unwilling to write one more word, disgusted with calculation, regardless of the size of the number, proficiency or not, all verbal calculation, unwilling to write calculus, too lazy to draft, and even no special draft book, check the book. Often omit necessary steps, skip steps, and fantasize about quick and direct results, thus making mistakes.
In order to improve the calculation accuracy, we must first change the previous bad mentality.
Determine whether there is a simple algorithm, and then determine the operation order.
First of all, make clear the meaning of the question and see if there are any special requirements such as simple method and keeping a few decimal places in the number; Secondly, observe the characteristics of the topic and see if there are several simple algorithms for operation; Then, determine the operation sequence. On this basis, the relevant rules and laws are used for calculation. Finally, carefully check whether there are any mistakes, omissions or miscalculations.
We should form the good habit of careful calculation.
Some students make mistakes because they are not careful in calculus. The data is unclear and the identification is wrong. When drafting, you can't arrange the vertical tables in a certain order, which leads to the adhesion between the top and bottom, the misalignment of the same numbers, which is not convenient for inspection and easy to read the wrong data. Therefore, we must form the good habit of writing numbers vertically.
Can't blindly pursue high speed.
Correct and fast calculation is the ideal goal, but it is necessary to know that correct calculation is the premise and the most basic requirement, and high speed without correct foundation is worthless. Therefore, it is better to calculate slowly, in order to ensure the correctness of calculation and improve the accuracy of calculation.