Part I: Stimulating interest is the key.
Because I like mathematics, I am willing to study it, so I am willing to overcome any difficulties and obstacles in the learning process; The successful experience gained by overcoming difficulties has enhanced my interest and confidence in learning, so I prefer learning mathematics.
A very simple positive cycle is in front of us, so it is the key to learn math well and arouse children's interest. Ways to stimulate interest are:
1. kiss your teacher and believe in his way.
This is the eternal truth. How do teachers and parents do this?
1) Show your abilities and make your children admire you. For example, you can show your knowledge, strong calculation and problem-solving ability in front of children, and all children admire you.
School ICT also found in the survey of excellent college students' mathematics learning rules that many students like a teacher, even because the teacher can draw very standard circles and ellipses at will.
2) Show personality charm and make children admire it.
One or more outstanding charms in an educator's personality can easily infect children, such as humor, rigor and so on. Generally speaking, a teacher should reserve at least 200-300 jokes so that students can study easily and happily in class. There are also many children who like teachers because: "She is serious and responsible at home, and she has new tricks and debates every day."
3) Care for children with your heart.
If you want all the children to like you, treat them equally! In class, if a student with poor grades raises his hand and speaks, he should be encouraged and supported knowing that he will answer badly.
If you want to change a child, then "pet" him! "I like this teacher because she regards me as her sister." "Once I failed in the math exam, the teacher put a note on my exercise book and asked me if I had anything on my mind. I am very touched! "
Of course, parents should also actively guide their children to like teachers. For example, by discussing teachers' teaching methods and personality characteristics with children, we can guide children to pay attention to teachers' bright spots and find out teachers' thinking methods, habits and qualities worth learning.
2. Turn abstraction into vividness.
For example, when talking about examples, tell students some jingles, mathematical stories, the history of mathematical development, mathematics in life and so on. Let students feel that mathematics is around. For example, Hua's jingle "number and shape are interdependent, how can they be divided into two?" It is difficult to be intuitive when counting missing shapes; When the number of tables is missing, it is difficult to be nuanced. Algebra and geometry are integrated, they are always connected and separated. "Mathematics in life includes things around us, news and current affairs, such as: let students moderately participate in the stock issuance that many parents are keen on now; How many meters, how much oil, how much salt, etc. Spending in your home every month, per capita consumption; There is a flood in the Huaihe River basin this year, so the relationship between the upstream water level and the downstream river width should be considered when discharging flood.
In addition, games and activity scenes can also be used to stimulate students' interest in learning. For example, "the equation in the calendar", the blackboard newspaper on mathematical topics, etc.
3. Turn abstraction into image.
Now, most students are interested in computers. It is a good way to guide students to learn mathematics from this point. Teacher Liu of a key middle school in Zhengzhou uses a geometric sketchpad to let students intuitively understand mathematics knowledge. While learning geometry sketchpad, it also mobilized students' enthusiasm for learning mathematics.
4. Accumulation of successful experience.
Interest often has a lot to do with a sense of accomplishment. Every child has an innate desire to be a researcher and discoverer, which needs to be recognized and appreciated, and hopes to make achievements and progress. Educators should be good at discovering students' little progress and put forward different requirements for different students, so that they have the opportunity to succeed and experience the sense of accomplishment when they succeed.
The specific methods are as follows: Don't finish all the ideas at once when giving the child the purpose of the question, but guide the child to think independently by asking questions, or say half and leave half for him to think for himself. If the child is unable to think about the second half, at least let the child think independently to the next step. Of course, parents should give timely verbal encouragement, on the one hand, to enhance children's self-confidence and let them feel the sense of success in solving problems independently, on the other hand, parents will also improve their understanding of children in the process of encouraging them and cultivate their ability and habit of thinking deeply about the same problem.
Tip: success record book
You can also encourage children to prepare a notebook and write down their success records. The wrong textbook is very important, but only by using the wrong textbook can children pay more attention to their failure experiences, record the process of doing a difficult problem with the success notebook, record a little progress today compared with yesterday, enhance their sense of accomplishment and increase their interest in learning.
5. Create an environment for learning mathematics.
For example, some books related to mathematics can be put on the bookshelf at home, such as Secrets of Fast Calculation, Mathematical Physics for Middle School Students, Interesting Mathematics Series, Mathematics Books for Training Thinking Ability, Mathematics in Stories, etc. , recommended for children to read. Such an atmosphere can also be created in schools. A teacher said, "I will sit at the door of the classroom every day between classes and pick up a book to read." There are always several students who ask me what books I read, and they are interested in the books in my hand when they ask and answer. A few days later, I will find that one or two students take the lead in borrowing this book. After a while, this book will become popular in the class. "
Part II: We should lay a solid foundation in mathematics.
Without a solid foundation, where did the tall buildings come from? There are many problem children who look careless and make mistakes. Careful analysis is caused by weak basic knowledge. For example, some children will say, "I just can't distinguish these two formulas." I used it wrong during the exam. " In fact, if the child not only remembers the formula, but also deduces it, then deducing it on the spot in the examination room can avoid the problem. On the other hand, children need to master and remember some basic knowledge, which can also be said to be the most basic tools, such as the square of natural numbers within 30 and the cube of 1-9.
Laying a good foundation can also be achieved by doing problems, which is different from the sea tactics. Some students may understand after doing two questions, so they don't need to do any more. Some students may need to do 20 questions. In short, in order to achieve the best understanding and memory effect, students should do more 1-2 questions after understanding the knowledge points themselves, so as to achieve 150% understanding and memory effect.
Five-step learning method to lay a good foundation;
A. Prepare well before class and take the initiative in class. Everything is established in advance, and it is abolished if it is not foreseen.
B. Listen carefully in class and take notes. You should enter the state in advance in class. The quality of preparation before class directly affects the effect of listening to lectures.
C. review in time and turn knowledge into skills. Review is an important part in the learning process. Review should be planned, not only to review the lessons of the day in time, but also to review all stages in time. I will review, think and summarize what I learned last week, last month and this semester. It is best to use the winter and summer vacations to review and consolidate all the contents before last year or this semester. At this stage of learning, it is best to consult and verify the contents that were not clear in the past. Mathematics is not a particularly outstanding student, and generally lacks confidence in learning mathematics well. If they persist in this way for two to three years, they will gradually perform well in their daily homework and classroom performance, and their confidence in learning mathematics will gradually be established, and their math scores will naturally get better.
D. Finish homework carefully, form skills and skills, and improve the ability to analyze and solve problems. Academician Yang Le, an educational authority, answered the question of how middle school students learn mathematics well in just three sentences: First, practice more on the basis of understanding; Second, accumulate more on the basis of understanding; Third, step by step. The exercise here is to do the problem and finish the homework. The exercises mentioned here, on the one hand, are to do exercises, complete homework and further reflect on the wrong questions, think through, and find similar questions to do 3 to 5 questions, so as to achieve thorough mastery, consolidation and improvement. On the other hand, combined with my own life experience, I use what I have learned to analyze and explain some problems in my life.
E. Summarize in time, and organize and systematize the learned knowledge. After learning a topic or a chapter, you should make a summary in time. The degree of implementation of each link is directly related to the progress and effect of the next link. Be sure to preview before listening, review before homework, and often make a stage summary.
When you come home from school every day, you should review your homework for the day, finish your homework for the next day, and then preview your homework for the next day. These three points are indispensable, otherwise there will be no guarantee of high-quality lectures the next day.
Mastering the above learning methods can cultivate children's basic abilities and habits in learning mathematics, such as mathematical thinking ability and verbal calculation ability. Many students can't do this now. If every student can go home at night and watch movies in his head before going to bed, what have I learned today? Review is also done in this way. How many chapters are there in a course? How many knowledge points are there in each section? What are the examples of each knowledge point? Learning is very systematic and effective.
Tip 1: Use the wrong book skillfully.
To guide children to take the teacher's exercises seriously, especially the ones they did wrong, they must think twice, find other similar bodies to do three or five more questions, fully understand and master the knowledge they have not mastered, and do a good job in thinking about the ideas and methods that teachers can solve problems, why they didn't think of it, how they can think of it in the future, and what methods are commonly used to consider such problems.
In addition, you should always borrow students' wrong books. Note when borrowing:
First, borrow the wrong books of students who are taller than themselves to enrich and broaden their knowledge.
Second, look at the wrong problem books of students who are lower than themselves, so as to often sound the alarm for themselves.
At the same time, you should make your own reading notes for your reference. Read it at least twice a week at the beginning, and then read it for a week after two weeks, so that it is gradual. This method can be applied to other disciplines.
Tip 2: Break the sand pot, review the old and learn the new.
Many children have this habit. If a knowledge point or a question stumbles them, they put it on hold. Slowly, more and more problems are put on hold and it is difficult to take them back. Therefore, it is best to solve problems that will not be solved immediately. If the conditions do not allow, be sure to write it down and solve it later. The solution can be to look up information, consult others and so on.
On the other hand, we should review the solved problems and some important knowledge points regularly. When reviewing, we must think: according to the knowledge and skills we have now, is there a better way to solve this problem? Always do it, always be new.
Part III: Thinking training should be done well.
1. Try to solve a problem and exercise children's variant thinking.
To cultivate students' variant thinking, it is necessary to let students dare to innovate and get used to it. Teachers can deliberately make mistakes in the course of lectures and let students think and correct them, so that students will not be in a state of passive acceptance in class, but will always be in a state of active thinking: Is the teacher right? Is there any other way? In addition, teachers can also adopt the following methods: only one question is taught in one class, and the methods are getting better and better; Talk about a topic today, talk about it tomorrow, often. On the one hand, let students fully feel the fun of mathematics, on the other hand, it can cultivate students' awareness and ability of variant thinking, which is of great benefit to children's future life development.
In variant thinking, symmetrical thinking is a very important one. Symmetry can often solve many problems. For example, in real life, a Japanese company producing monosodium glutamate was unable to make a profit for a while, so it held an internal seminar. At the meeting, everyone put forward many methods, such as reducing costs. But it was not adopted because the effect was not obvious. Later, when doing a consumer survey, a housewife said that MSG was bottled, with many small eyes on it, which could increase the small eyes, so that everyone would use more when cooking and the sales volume would go up. This suggestion was adopted and implemented, and the effect was really good. In fact, employees consider from the source of production, and housewives consider from the consumer side. This is the symmetry of thinking.
In the process of learning mathematics, a problem from known to result, from result to known, also reflects the symmetry of thinking. There is a classic topic:1/2+1/4+1/8+…+1/256. You can count from the beginning to the end, 1/2+ 1/4=3/4, 3/4+ 1/8 = 7/8 ... You can find the rule and know that the final answer is 255/256, or you can add a 1 at the end of the formula. This is the embodiment of the symmetry of thinking.
2. Solve one problem with multiple solutions, and exercise inductive thinking.
In fact, several mathematical methods are used in each learning period. Students can often be guided to understand a certain mathematical method by solving more than one problem. For example, this class only talks about equation thought, and the next class talks about another topic.
3. Tell students questions from a developmental perspective.
In other words, the same old question:1/2+1/4+1/8+…+1/256. Students can be encouraged to do it in general, and in the process of doing it, they can extend to the knowledge points that they have learned in high school, such as arithmetic and geometric series. Children will learn easily in the future.
4. Explain to each other and collide with the sparks of thinking
A student said, "My math scores are based on topics. Because I have patience and good temper, many classmates will ask me questions. During the explanation, I gradually found that my knowledge was consolidated and my thinking ability was improved. " In addition, it is also very important to debate with students who are close to or slightly higher than themselves about the knowledge they have mastered or have not yet mastered, which will often achieve twice the result with half the effort. Even the knowledge learned through debate is deeply understood and unforgettable for life.
Part IV: Habit and persistence are very important.
Good habits make life, so does math study. The five-step learning method mentioned above is also a good study habit. In addition, children need to develop the following study habits:
Examine the questions carefully. A famous math teacher said: The depth of a problem is limited. Think more, write less, and be quick. The less you think, the more complicated you write. It is easy to make mistakes when you start to look at the questions in a hurry. Students are advised to develop the habit of reading the questions carefully before doing them. If students are careless, they can suggest reading it carefully for three times, thinking about the known conditions and ideas, and then doing the questions. The more times you practice, the more you develop the habit of carefully examining questions.
Check it carefully. This is also the way many teachers guide their students. Finish the questions and see if the results conform to the routine (mainly life experience and common sense). If you have enough time, you can check it in different ways to see if the result is correct. If time is limited, just follow the original idea. Of course, every small calculation step of a problem can also be tested by forward calculation and backward calculation.
If there is a problem, it must be solved. When you encounter problems and puzzles, you must look up the information to find a solution to the problem, which is a habit that you need to study any course or even reach a lifetime.
Tip: Take the draft paper seriously.
A student told us about his experience: "I made few mistakes because of carelessness in the exam, because I formed the habit of taking draft paper seriously." The words I wrote during the calculation were neat and serious, and the neat words invisibly gave me a more serious and careful attitude; Besides, I scratched the manuscript paper. This one describes the calculation process of this sub-topic, and that one describes that part of the topic, so that there will be no mistakes in calculation and inspection. "