The educational features of Montessori mathematics, how to make children like mathematics

Based on Montessori educational ideas.

Part 1: Mobilizing interest is the key

Because I like mathematics, I am willing to learn it, so I am willing to overcome any difficulties and obstacles encountered in the learning process; overcome The successful experience gained from difficulties has enhanced my interest and confidence in learning, so I like learning mathematics more.

A very simple positive cycle is before us, so learning mathematics well and mobilizing children's interest are the key. Methods to arouse interest are:

1. Be close to the teacher and believe in the teaching.

This is an eternal truth. Whether it is a teacher or a parent, how can we achieve this?

1) Show your ability and let your children admire you. For example, you can show off your extensive knowledge, strong calculation and problem-solving skills in front of the children, and the children are all impressed.

In its investigation of the mathematics learning patterns of outstanding college students, School Information Communications also found that many students like a certain teacher, even because the teacher can easily draw very standard circles and ovals.

2) Show your personality charm and let your children admire you.

The outstanding one or more charms in an educator’s personality can easily infect children, such as humor, rigor, etc. Generally speaking, a teacher should reserve at least 200-300 jokes to make students learn easily and happily in class. There are also many reasons why children like their teachers: "She is very serious and responsible, and she has new tricks every day, such as debates, etc., she is good at doing anything!"

3) Care for children attentively.

If you want all children to like you, treat them equally! In class, if a student with poor grades raises his hand to speak, you should encourage and support him even though you know that his answer will be a mess.

If you want to change a child, then "favor" him! "I like this teacher because she treats me like her own sister." "Once I failed a math test, the teacher put a note in my homework and asked me if I had anything on my mind. ? I’m so touched!”

Of course, parents should also actively guide their children to like their teachers. For example, by discussing the teacher's teaching methods, personality characteristics, etc. with the children, we can guide the children to pay attention to the teacher's shining points and discover the teacher's thinking methods, habits and qualities that are worth learning.

2. Turn abstraction into vividness.

For example, when explaining example questions, we can tell students some jingles, mathematical stories, the history of mathematics development, mathematics in life, etc. based on the questions. Let students feel that mathematics is around them. For example, Hua Luogeng's jingle on the combination of numbers and shapes: "Numbers and shapes are essentially dependent on each other, so how can they be separated into two sides? When numbers are missing shapes, it is difficult to intuitively understand; when shapes are missing numbers, it is difficult to understand the subtleties. Algebra and geometry are one entity, and they are always connected and never separated." Life Mathematics in the middle school includes things around them, news and current affairs, etc., such as: allowing students to moderately participate in stock issues that many parents are now passionate about; how much rice, how much oil, how much salt, etc. are consumed at home every month, and how much per capita consumption is; this year, there are In flood disasters, the relationship between the upstream water level and the width of the downstream river channel needs to be considered when discharging floods.

In addition, games and activity scenarios can also be used to stimulate students' interest in learning. For example, "Equations in the Calendar", blackboard newspapers on mathematics topics, etc.

3. Turn abstraction into image.

Most students today are interested in computers. It is a good way to guide students to learn mathematics from this point of view. Teacher Liu from a key middle school in Zhengzhou uses geometric sketchpads to let students intuitively experience mathematical knowledge. While students learn geometric sketchpads, their enthusiasm for learning mathematics is also mobilized.

4. Accumulation of successful experiences.

Interest and sense of achievement are often closely related. Every child has an inner desire to be a researcher and discoverer, a need to be recognized and appreciated, and a desire to achieve success and progress. Educators should be good at discovering the little progress of students and setting 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: when lecturing children on a topic, do not finish all the ideas at once. Use questions to guide the children to think independently, or tell half of the topic and leave the other half for the children to think on their own. If the child is not capable of thinking about the next half, at least let the child think independently to the next step.

Of course, parents should also give timely verbal encouragement. On the one hand, they can enhance their children's self-confidence and let them experience the sense of success in solving problems independently. On the other hand, parents will also improve their understanding of their children and cultivate their children in the process of encouraging them. The ability and habit of thinking deeply about the same problem.

Tip: Success Record Book

You can also encourage children to prepare a special notebook to write their own success records. The wrong question book is very important, but with only the wrong question book, children can only pay more attention to their own failure experience, use the success record book to record the process of solving a certain question that is difficult for them, and record today's performance compared with yesterday's. Make progress little by little, enhance your sense of accomplishment, and increase your interest in learning.

5. Create an environment for learning mathematics.

For example, you can put some mathematics-related books on the bookshelf at home, such as "Secrets of Quick Calculation", "Mathematics and Chemistry for Middle School Students", "Fun Mathematics Series", "Mathematics Books for Training Thinking Ability", "Mathematics in Stories", etc. , and recommended reading for children. Such an atmosphere can also be created in schools. A teacher said: "I sit at the door of the classroom every day during recess, pick up a book and read it. There will always be a few students asking me what book I am reading, and they are interested in me as soon as I ask and answer. I am interested in the book in my hand. After a few days, I will find that one or two students will take the lead in borrowing this book. After a while, the book will become popular among the whole class."

Part 2: The foundation of mathematics must be solid

Without a solid foundation, how can a high-rise building come from? There are many questions that children seem to have done incorrectly due to carelessness. After careful analysis, they are all caused by weak basic knowledge. For example, some children will say: "I just can't tell the difference between these two formulas, and I used them wrong during the exam." In fact, if the child not only memorizes the formulas, but also knows how to derive them, on-site deductions in the exam room can also be avoided. of this question. On the other hand, it is necessary for children to master and memorize some of the most basic knowledge, which can also be said to be the most basic tools, such as the square of natural numbers within 30, what are the cubes of 1-9, etc.

Laying a solid foundation can also be achieved by doing questions. This is different from the question-sea tactic. Some students may understand it after doing two questions, then they do not need to do it again. Some students may 20 questions need to be answered. In short, in order to achieve the best understanding and memory effect, students should do 1-2 more questions after they understand the knowledge points by themselves to achieve 150% understanding and memory effect.

Five-step learning method to lay a solid foundation:

A. Do a good job of previewing before class and take the initiative in listening to the class. Everything will be successful if it is foreseen, and it will be ruined if it is not prepared.

B. Listen attentively and take class notes. You need to get into the mood in advance when attending lectures. The quality of preparation before class directly affects the effectiveness of the class.

C. Review in time and turn knowledge into skills. Review is an important part of the learning process. Review should be planned, not only to review the day's homework in time, but also to conduct stage review in time. This past week and last month will be about reviewing, thinking, and summarizing what we have learned this semester. It is best to use the winter and summer vacations to review and consolidate all the content from the previous school year or this school period. If the current stage of study involves content that was not very clear in the past, it is best to check and verify it in time. Students who are not particularly good at mathematics generally lack the confidence to learn mathematics well. If they persist in this way for 2 to 3 years, they can gradually perform outstandingly in daily homework and classroom performance, and their confidence in learning mathematics will be gradually established, and their mathematics performance will naturally improve. Get better.

D. Complete homework carefully, develop skills, and improve the ability to analyze and solve problems. When academician Yang Le, an authority in education, answered the question of how middle school students can learn mathematics well, he gave three short sentences: first, practice more on the basis of understanding, second, accumulate more on the basis of understanding, and third, proceed step by step. The practice mentioned here means doing questions and completing homework. The practice mentioned here, on the one hand, is to do the questions, complete the homework and further reflect on the wrong questions, think clearly, find similar questions and do 3 to 5 questions to achieve complete mastery and consolidate improvement, on the other hand, combine your own life experience , use the knowledge you have learned to analyze and explain some problems in life.

E. Make timely summaries to organize and systematize the knowledge learned. After studying a topic or a chapter, you must summarize it 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 to lectures, review before doing homework, and conduct stage summaries frequently.

When you go home from school every day, you should first review the day's homework, complete the day's homework first, and then preview the next day's homework.

None of these three things can be missing, otherwise it will not be possible to ensure 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, oral arithmetic ability, etc. Many students now cannot do these things. If every student could go through the movie in his mind after going home at night and before going to bed, what would I have learned today? We also use this method when reviewing. Think back to how many chapters there are in a course? How many knowledge points are there in each section? What examples are there for each knowledge point? It is very systematic and effective to learn.

Tip 1: Use the wrong question book skillfully

Guide the children to take the teacher's sections and exercises seriously, especially the exercises they have done wrong. They must think over and over again, and in addition Find similar subjects and do 3 to 5 more questions to achieve a full understanding and mastery of the knowledge that is not well mastered. Be able to think about why you have not thought of the teacher's problem-solving ideas and methods, and how you can think of them in the future. Consider this What methods are commonly used for similar problems.

In addition, it is also necessary to frequently borrow the wrong question papers of classmates. When borrowing, please note:

First, borrow the wrong question papers of students who are higher than yourself, so as to enrich and broaden your knowledge field.

Second, read the wrong question papers of students who are lower than yourself so that you can often sound the alarm for yourself.

While borrowing, you should make your own reading notes for your daily reference. At the beginning, repeat reading at least twice a week, and after two weeks, it can be one week, and so on. This method can be applied to various other disciplines.

Tip 2: Break the obsession with reviewing the past and learning the new It was shelved, and slowly, more and more issues were shelved, which became difficult to return to. Therefore, it is best if the problem that you do not know can be solved immediately. If conditions do not allow it, then you must write it down and solve it in the future. Solutions can include checking information, asking others for advice, etc.

On the other hand, you should also review the solved problems and some important knowledge points regularly. When reviewing, you must think: Based on the knowledge and skills you currently have, is this question better? method? Do it often and always be new.

Part 3: Thinking training should be done well

1. One question with multiple solutions, exercise children’s alternative thinking

Cultivate students’ alternative thinking, We must let students dare to innovate and become accustomed to innovation. Teachers can deliberately make mistakes during lectures and let students think and correct them. In this way, students will not be in a passive acceptance state during 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 use the following methods: only teach one question in one class, and solve multiple problems for one question, and the method will become better and better; teach one question today and teach it again tomorrow, and always teach new things. On the one hand, it allows students to fully experience the fun of mathematics; on the other hand, it can cultivate students' awareness and ability of alternative thinking. This awareness and ability are of great benefit to children's future life development.

In variant thinking, symmetrical thinking is a very important one. Symmetrical thinking can often solve many problems. To give a real-life example, a Japanese company that produces MSG has been unable to increase profits for a while, so it held an internal company seminar. At the meeting, everyone came up with many methods, such as reducing costs, etc., but because the effects were not obvious, they were not adopted. Later, when conducting consumer research, a housewife said that MSG comes in bottles with many small holes on them. The holes can be enlarged so that people can use more when cooking. If you use more, the sales volume will increase. Just went up. This suggestion was adopted and implemented, and it worked very well. In fact, employees think about problems from the source of production, while housewives think about problems from the consumer side. This is the symmetry of thinking.

In the process of learning mathematics, the symmetry of thinking is reflected in the fact that a question moves from the known to the result, and from the result to the known. There is a very classic question: 1/2+1/4+1/8+…+1/256. You can calculate from front to back, 1/2+1/4=3/4, 3/4+1/8=7/8... Once you discover the pattern, you will know that the final answer is equal to 255/256, or it can be expressed in Eq. Add 1/256 at the end (this is also the embodiment of structural thinking), count from back to front, get the number 1, and then subtract the excess 1/256. These are all manifestations of the symmetry of thinking.

2. Solve multiple problems at once and practice inductive thinking

There are actually several mathematical methods used in each stage of schooling. The method of solving multiple problems can often be used to guide students to understand a certain mathematical method. For example, this class will only teach the idea of ??equations, and the next class will teach another topic.

3. Use a developmental perspective to teach students questions

In other words, we need to use a developmental perspective to teach students questions, and it is still the same old question: 1/2+1/ 4+1/8+…+1/256. Students can be encouraged to use the method of general division to do it, and in the process of doing it, they can extend to the knowledge points learned in high school such as arithmetic difference and geometric sequence. The child will learn easily in the future.

4. Explain to each other and spark ideas

A student said: "My mathematics academic performance is based on the topic. Because I am patient and good-tempered, so Many students would ask me for advice. During the explanation process, I gradually found that my knowledge had been consolidated and my thinking ability had improved. "In addition, I argued with students who were at a similar level or slightly higher than me about what I had mastered or not. Knowledge is also very important, and it often achieves the effect of getting twice the result with half the effort. Even the knowledge learned through arguments is profound and unforgettable.

Part 4: Habits and persistence are important

Good habits make life successful, and the same is true for mathematics learning. The five-step learning method mentioned above is also a good learning habit. In addition, children also need to develop the following study habits:

Review the questions carefully. A famous mathematics teacher said: The depth of a question is limited. If you think more, you will write less and faster; if you think less, you will write more and more complicated. It is easy to make mistakes if you rush through the questions and start working on them. It is recommended that students develop the habit of reading the questions carefully before doing them. If the student is careless, you can suggest that he read the questions carefully three times and think about the known conditions and ideas. Do the questions again. The more you practice, the more you will develop the habit of carefully reviewing questions.

Check carefully. This is also the method that many teachers tell their students. After completing the questions, take a rough look to see if the result is in line with convention (mainly life experience and common sense). If you have enough time, you can use different methods to check to see if the result is correct. If time is limited, just follow the original idea and check it out. Of course, every small calculation step of a question can also be checked by calculating forward and backward.

If there is a problem, it must be solved. When you encounter problems and confusions, you must find ways to solve them by looking up information. This is a habit you need to learn any course and even achieve success in your entire life.