Primary school students' thinking is in the initial development period, and the fragmentation and concretization of thinking are more likely to make them have a mindset. For example: "A plot of 3 hectares requires 1/4 for growing Chinese cabbage. How many hectares are left? " The formula of 3- 1/4 often appears, which is influenced by the idea of solving problems by using integers. Another example is: "A plot of land is 6 hectares, and it takes 1/4 hectares to grow Chinese cabbage. How many hectares are left? " The formula of 6×( 1- 1/4) often appears, which is influenced by the idea of solving the fractional application problem "What is the fraction of a number". Why does thinking have such a negative effect? There are two reasons:
First of all, the mindset makes it difficult for students to get rid of the interference of proactive inhibition like the above two situations, so they can't analyze and solve problems smoothly according to the correct ideas and methods.
Secondly, the mindset makes the old ideas smooth, and the traces left by the old traces in the cerebral cortex are very profound. If there is no strong and persistent new stimulus to cut them off, new ideas will be difficult to form and develop, and problems that must be solved with new ideas will not be solved smoothly.
How to prevent and overcome the negative influence of mindset?
First, the conclusion must be accurate and the experience should be comprehensive.
Primary school mathematics textbooks follow the cognitive law of children's learning, and are arranged according to the principle of the country from easy to deep and from easy to difficult. The transfer of knowledge is carried out in stages. Most of the initial knowledge is single or incomplete, so in teaching, it is necessary to prevent premature conclusions or simple induction from interfering with future learning experience.
Pupils, like adults, are constantly summing up knowledge and experience in their learning activities, but because their thinking is still concrete and fragmented, these experiences are often incomplete, and the resulting mindset often interferes with subsequent knowledge learning. For example, when beginners learn fractional division,10 ÷ 5 = 2,5 ÷10 = 2 often appears, which is caused by students' one-sided experience when learning integer division-"When doing division, divide the larger number by the smaller number". This requires the teacher to explain when teaching, that is, "we will study the division of smaller numbers by larger numbers in the future." A simple sentence can prevent students from having fantasies and "lay the groundwork" for future learning.
Second, strengthen new stimuli and replace old ideas.
Fechner, a famous German scholar, pointed out in his research that the stimulus is directly proportional to the sensation, with the stimulus increasing or decreasing by 10 times and the sensation increasing or decreasing by 1 0 times. Some students just can't think with habitual thinking. At this time, there must be a strong new stimulus to effectively force students to realize from the old ideas and methods and transfer to the thinking of new methods.
For example, when teaching more complicated fractional application problems, teachers can design a short story, which can stimulate students' learning motivation and introduce new lessons. For example, Donald took 1000 yuan to let the mouse buy him a color TV. The original price of Panda color TV is 1 1,000 yuan, the price is increased by 1/5, and the price is reduced by 1/5. Mickey mouse paid 1000 yuan, stuffed the recovered money into his pocket and went home with a color TV. Donald asked, "How much is this color TV?" "Original price 1000 yuan, price increase 1/5, price decrease 1/5. Isn't it 1000 yuan? " Mickey mouse replied. Donald shouted when he heard it! "No, no! Don't be glib. " This highlights the key issue of "price increase 1/5: Will further price reduction be equal to the original price". High-intensity new stimuli cut off students' habitual thinking about integer knowledge "a+b-b=a", and they are eager to solve the mystery of "current price". This is conducive to revealing the contradiction between new theory and new knowledge and promoting the formation of new ideas.
Third, problem group teaching broadens our thinking.
The single-line development of textbook knowledge is also the main reason for students' mindset. To this end, when dealing with the newly received textbooks, I often use problem groups for teaching. Multiple-choice questions generally appear in the form of basic questions and variant questions, which makes students have no fixed mind because of rigid structure. This is also beneficial to the vertical connection of knowledge.
Basic problem: Fishing boats caught 2400 tons in May, and caught more in June than in May 1/4. How many tons were caught in June?
Plot variation: Last year, in the activities to support the people in the disaster area to rebuild their homes, the donation of the Sixth Squadron was more than that of the Sixth Squadron 1/5, and the donation of the Sixth Squadron was 1000 yuan. How much did the Sixth Squadron donate?
Structural variant: The fishing boat caught 2400 tons in May, which was less in June than in May 1/4. How many tons were caught in June?
Narrative variant: The fishing boat Canghai fished 2400 tons in May. If it catches 1/4 tons more in June, it will be as much as in May. How many tons were caught in June?
On the basis of not violating the principle of students' acceptability, the teaching materials can also be reorganized. It is to arrange the teaching materials with strong contrast together properly for problem group teaching. For example, arranging two types of application problems "more (or less) in one number" together for teaching can not only prevent students from using subtraction to calculate the influence of this deterministic potential when they see "more", but also enable students to form a good cognitive structure early.
Variant exercise groups can also be used in practice classes. That is, change the conditions or problems of the topic, so that the quantitative relationship changes, in order to avoid fixed and habitual problem-solving methods. This is also conducive to the horizontal connection of related knowledge.
Fourth, analyze the wrong questions and deepen the concept.
The negative influence of mindset is persistent, and it is not easy to completely overcome after Protestantism, which requires continuous strong stimulation. This requires teachers to pay attention to collecting wrong questions, sorting them out, analyzing them, and then giving them back to students.
For example, the student replied, "A livestock farm has 1000 cows, which is 20% less than sheep. How many sheep are there? " The formula 1000×( 1+20%) appears. This is influenced by the old idea that "A is greater than B, that is, B is less than A". I mistakenly think that cows are 20% less than sheep and sheep are 20% more than cows, so I regard cows as the standard quantity. For the reasons of mistakes, students should be trained to accurately judge the standard quantity when analyzing the wrong questions. Second, we should design confusing questions for students to compare. This is repeated many times in order to deepen the negative influence of ideas and thinking patterns.
There are many ways and means to prevent and overcome negative mentality. As long as we adopt positive attitude and effective measures in teaching, we can overcome students' negative thinking mode to the maximum extent, help students master correct learning methods, broaden the thinking of solving problems, form good thinking quality and promote the optimization of classroom teaching.