What problems may be encountered in mathematics teaching in primary schools?

What problems may be encountered in primary school mathematics teaching Abstract: Numbers play an important role in people's mathematics learning. It affects students' study in all subjects, and also lays a foundation for students to continue studying mathematics. Today's society is digital, and numbers play a very important role in people's lives. Numbers can be used to express and communicate, help people understand things around them and help people solve problems in life. Therefore, it is an important task to cultivate students' sense of numbers in primary school mathematics teaching.

Keywords: number sense accumulation, infiltration, formation, mastery

The number sense is put forward as one of the core contents in the<& lt mathematics curriculum standard for the first time, and it is placed at the top of the six core concepts, which shows that the new curriculum standard emphasizes and attaches importance to the number sense. Therefore, we must effectively think and explore a new field of establishing and cultivating students' sense of numbers. Sense of number is a basic accomplishment of human beings, and it is the understanding and feeling of numbers and their operations. This kind of understanding and feeling can help people to put forward useful strategies to solve complex problems flexibly, which is a mental skill of human beings. The purpose of cultivating students' sense of number in primary school mathematics teaching is to make students learn mathematical thinking, understand and explain practical problems with mathematical methods, and consciously establish the relationship between practical problems and quantity. Therefore, every student should establish a certain sense of numbers. How to cultivate students' sense of number in primary school mathematics teaching.

First, accumulate a sense of numbers in life.

Children's learning of mathematics often begins with the recognition of numbers. Therefore, when children begin to know numbers, they should make full use of the mathematics materials around them, create a teaching situation that helps children understand mathematics, and let children accumulate a sense of numbers unconsciously. For example, when teaching "Lovely Campus", students are invited to see the beautiful forest, and the animal school begins. Lovely animals walked into the school happily, which aroused students' interest in counting small animals. The students can't help but count how many rabbits, butterflies, birds and flowers there are in the school ... After counting, let him say a word with these numbers, so that the children can initially realize: If there are no numbers, which one do you want to find out? For another example, guide students to contact specific and interesting things around them. By actively observing and analyzing life phenomena, use numbers to represent things around you, talk about the numbers around you and the numbers used in life, and let the children count: there are several learning tools in the pencil box, and each learning tool has several; Let the students think about it: the house number, the telephone number, mobile phone number, birthday, license plate number, etc. Let students feel the meaning of numbers in colorful activities and understand the role of numbers in expression and communication, so that mathematics can be seen and touched, which has a real role and laid the foundation for cultivating children's sense of numbers.

Second, the infiltration of number sense in the situation

The standard emphasizes: "guide students to contact with concrete and interesting things around them, and feel the meaning of numbers and the role of numbers in expression and communication through rich activities such as observation, operation and problem solving, and initially establish digital consciousness." In teaching, teachers should make full use of real life resources, create teaching situations that help children understand mathematics, awaken students' existing life experience, reproduce the realistic source and practical application of the concept of number, and enable students to master the essence of the concept of number, truly understand the meaning of number and establish a good sense of number. For example, when teaching Counting, students can be guided to observe the theme map in the book. Cheerful, warm and childlike pictures bring happy childhood memories to students, who are eager for colorful primary school life. Because children generally have a learning foundation in kindergarten, they will count with interest: 1 wooden ladder, 2 swings, 3 wooden horses, 4 planes ... all common things in their lives, and mathematics is so ubiquitous; After counting, the students should tell each other what the painting has. So "number" has become an indispensable tool for students to communicate and has a real role.

For example, in teaching "Simple operation of addition and subtraction close to integer hundred and integer thousand", in order to let students understand the difficulty "2" in "345- 198 = 345-200+2" and "345+ 198 = 345+200-2". Student A plays the salesman and student B plays the customer. Student B bought a camera of 198 yuan at the original price of 345 yuan, and paid two bills of 100 yuan, so he should look for 2 yuan, thus explaining the simple calculation process of "348- 198": that is, if you pay more, you should look for it. Then, based on A's original 345 yuan, he sold the goods of 198 yuan, but received 200 yuan and overcharged 2 yuan, so he should take them back to 2 yuan. In this way, the simple calculation process of "345+ 198" is clarified: if you overcharge, you have to pay it back. On this basis, guide students to sum up the law of "simple addition and subtraction algorithm close to integer hundred and integer thousand".

For another example, when teaching division, let students be group leaders and distribute learning tools to group members. Based on this, we can understand the meaning of division and make continuous calculations. When learning "Statistics", combine the class's events and achievements in the sports meeting, and let students find ways to make tables themselves, so as to master the statistical methods. For another example, when teaching the calculation of "nine plus several", create a situation that "the salesperson cleans up the counter, there are nine ping-pong balls in one box and eight in another box, which is more or less a * * *", so that students can find a way to calculate by themselves.

Third, form a sense of number in expression and communication.

Create problem situations for students in teaching, so that students can inspire each other, learn from each other and learn from each other in the process of discussion. Empirical number can be used to express and exchange information, so that students can expand their thinking, enrich their understanding of logarithm and appreciate the value of mathematics when communicating the perception of logarithm, thus promoting the formation of number sense.

For example, when talking about "liters and milliliters", ask students to look at the scale and say the volume of water in practice. The picture shows that one measuring cylinder contains 1000 ml of water and the other 700 ml of water. What's the total? After reading the picture, the students came up with various methods, some said 1 liter 700ml；; Some say 1.7 liters; Some say 1700 ml, etc. Students express the same quantity in many ways, and judge whether these methods are correct through discussion. Description also refers to the integration of water in a painting, which can be expressed by integers, decimals and fractions. In this way, students have established a relationship among fractions, decimals and integers, knowing that they can understand a number from many aspects, enriching the understanding of logarithm and further developing the sense of number.

Learning to listen, finding problems and thinking from others' descriptions of certain quantities is also a kind of communication. For example, in the actual measurement, I led students to the playground to measure the length and width of rectangular flower beds. The students measured the length and width of the flower bed in different ways. In the classroom communication, they showed a variety of measurement methods, and some students measured directly with a tape measure. Some students first measure the length of a brick, then count how many bricks are included in the length and width, and multiply the length of each brick by the number of bricks to get the length of the length and width; Some students measure the rope 1 m length first, and then 1 m 1 m; Other students use the method of step test. In communication, everyone communicates their own ideas with others, and also understands other people's ideas and practices, perceives a certain length from different angles, develops a sense of distance, and enhances a sense of numbers.

The fourth is to master the sense of numbers in practice.

The Standard clearly points out that effective mathematics learning activities can't just rely on imitation and memory, and hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. Primary school mathematics practice activities should let students learn mathematics through personal experience, do and use mathematics with their hands, not just listen to and remember mathematics. Mathematics practice is the sky for students' active development, and the mathematics classroom focusing on practical activities will surely become a paradise for students to explore and a cradle for innovation. Similarly, the cultivation and development of number sense can not be separated from practical activities. First-grade children are curious and active, and simple practical activities such as operation, observation, guessing and communication are very attractive to them. In the first volume of the first grade experimental textbook of the new curriculum standard, many interesting practical activities are designed to cultivate students' sense of numbers. For example, when teaching Statistics, the problem situation is designed according to the theme map in the textbook. "Xiao Ming investigated the class's favorite fruit. Children, guess what kind of fruit you like best? " "What method can you use to let your classmates see at a glance what kind of fruit you like best?" "What method can you use to let students see at a glance what kind of fruit they like best?" Then let each group of students discuss and talk about it, and then put it on the map. And choose the best method from the students' works to derive the fruit statistical chart. In this way, close contact with students' real life in teaching and cultivating students' sense of numbers in specific operation activities can make students have a distinct representation of numbers, and when they encounter similar situations again, they will have a specific reference in their minds and truly establish a good sense of numbers. ?

Fifth, cultivate the sense of number in application.

"Mathematics Curriculum Standard" puts forward: "We should further cultivate students' sense of numbers by solving practical problems". Practice is the only criterion for testing truth. Students' learning mathematics ultimately lies in its application value, and the key experience of application cannot be taught, and it must be experienced by children themselves. Therefore, teachers should guide students to "re-create" knowledge after class to solve practical problems around them. In this process, students should learn from predecessors' experience from the perspective of mathematics, flexibly choose appropriate mathematical methods and strategies to try, and supplement, modify, reflect, summarize and evaluate their rationality at any time. In this way, the mobility of students' learning experience is strengthened and transformed into a learning ability with extensive mobility, thus cultivating a sense of numbers.

For example, after knowing the average, how old is the grandmother and grandfather of each member of the investigation team? Then ask the students to estimate the average age. With the video of the 1 1 National TV Grand Prix for Young Singers, ask students to estimate the final score of each singer according to the score of each judge. Let the students understand why to calculate and what kind of calculation method to choose.

Another example: helping my mother go shopping for food, it is estimated how many vegetarian dishes and meat dishes are needed. How much is the price of each vegetable, and how much do you need to bring?

After learning statistics, ask students to make statistics on family expenses, water consumption, electricity consumption and watching TV programs, and make suggestions to families accordingly.

In short, the process of cultivating students' sense of numbers is gradual. Cultivating students' sense of numbers can make them have more opportunities to get in touch with society, experience reality, express their views on problems and think and solve problems in different ways, which will undoubtedly help to cultivate students' innovative spirit and practical ability. With the establishment, development and strengthening of number sense, students' overall mathematical literacy will also be improved.

What are the problems in primary school mathematics teaching? Primary school mathematics is a highly instrumental subject. If students do not master this tool firmly, the foundation of primary school mathematics will be very poor.

First, all kinds of operational calculus rules are not firmly mastered, and the calculation speed is slow and the accuracy is poor.

Second, serious mathematical thinking, lack of flexibility, single problem-solving method and lack of divergent and innovative thinking;

Third, the thinking of solving problems is not clear, mathematical language cannot be formed, logical reasoning ability is poor, and formulas, laws and theorems cannot be skillfully used;

Fourth, the poor application ability of mathematics is mainly manifested in the process of solving application problems.

First, the problem of students' learning enthusiasm.

At present, students' initiative in learning in and out of the classroom is poor. What the teacher says in the classroom, he will do. Once they leave the classroom, their knowledge will be forgotten. This way of learning is not only inefficient, but also prone to teaching fatigue for both teachers and students. Maybe some classes know how to improve students' interest in learning through some jokes and situations, but this is not a long-term solution. Over time, students will get used to it, and even concentrate on it, forgetting learning itself. This kind of problem is not uncommon, and it is also the place where most teachers are confused.

Second, the problems existing in teachers' teaching concepts

Many teachers of the older generation, who have been teaching for decades, may have produced excellent students by the same method, but today, it may not work. Their teaching methods are old and closed, and even some teachers are still cramming, which is contrary to the original intention of curriculum reform and not suitable for modern comprehensive quality teaching. Or maybe some teachers ask students questions in order to find answers and use their brains to solve problems, but in essence, this has not changed the bondage of thinking. Students still follow the teacher's path, so teaching can't start with scattered innovative thinking.

Third, the question of "can you learn to do" in the learning process.

As soon as the teacher spoke, he understood that once he changed his form, he would quit. Such problems are very common. I believe many teachers have faced such troubles. Obviously, they have made it very clear in class, but some students just can't write when practicing after class. Some students have reflected this problem, and some teachers have thought about it specially, but when they really meet it, it often makes people feel embarrassed. How to make students understand, draw inferences from others and learn to do problems?

Fourth, the problems brought by the classification of "excellent and poor students"

Some students in the class have good grades, while others have poor grades. The difference in scores caused students to be divided into two groups-"excellent students" and "poor students". This is also presupposed by many teachers. They think that "top students" should get together to discuss their studies, and "poor students" should just teach and not affect "top students"

This distinction is distorted and wrong. In the teaching practice of the new curriculum reform, teachers and students are a whole and there is no gap between them. Equality between teachers and students in class and democratic thinking in teaching are good atmosphere for teachers and students to complement each other.

First, the calculation of addition and subtraction within 100 is not skilled.

Second, the integer mixed operation, the operation order is easy to make mistakes.

Third, the multiplication formula is not skilled.

Fourth, understand the angle: the size of the angle has nothing to do with the length of the side, but with the size of the mouth on both sides.

5. Time, minutes, seconds, unit conversion is easy to make mistakes.

Six, measuring length, ruler is not standardized, reading scale is not accurate, unit conversion is easy to make mistakes.

Ying Sheng observed that the current primary school mathematics knowledge can make children have a basic understanding of numbers, and only from the fifth grade can they cultivate their logical thinking ability and pay attention to problem-solving ideas. The existing problems need to be found from the teaching achievements of different teachers.

The concept of logarithm has remained unchanged for many years, so it is difficult to cultivate children's interest in exploring the mathematical world. Therefore, the most unpopular things in universities are high numbers, line generation and generalized mathematical statistics. Mathematics textbooks deliberately magnify the difficult side of mathematics, but do not show its interesting side. The other is practical ability and personal thinking ability. We pay attention to how many dozens of children wrote the so-called standard answers in the first time, but we don't advocate a child to find another way. To some extent, it stifles enthusiasm.

What are the most common problems in primary school mathematics teaching? First, all kinds of operational calculus rules are not firmly mastered, and the calculation speed is slow and the accuracy is poor.

Second, serious mathematical thinking, lack of flexibility, single problem-solving method and lack of divergent and innovative thinking;

Third, the thinking of solving problems is not clear, mathematical language cannot be formed, logical reasoning ability is poor, and formulas, laws and theorems cannot be skillfully used;

Fourth, the poor application ability of mathematics is mainly manifested in the process of solving application problems.

What problems should be paid attention to in primary school mathematics teaching? Primary school mathematics is an important subject in compulsory education. How to teach this subject well? The author believes that we should first pay attention to the following issues:

First, cultivate students' habit of thinking seriously.

Tolman's S-O-R theory tells us that brain (O) is the key "intermediary" variable in the chain from knowledge input (S) to knowledge output and ability transformation (R). Without thinking, new knowledge cannot be exported, and knowledge cannot be transformed into ability. Therefore, in mathematics teaching, students should be guided to make simple judgments and inferences through operation, observation, abstraction and generalization on the basis of perceptual materials. For new knowledge closely related to old knowledge, students can be inspired to extrapolate on the basis of existing knowledge. Put forward your own independent opinions and gradually cultivate students' habit of thinking seriously.

Second, to teach students the learning methods

As the old saying goes, "It is better to teach people to fish than to teach them to fish", and the German educator Dostoevsky said, "Education is guidance" and "not to give up the truth, but to teach people to discover the truth". Bloom's Mastering Learning Strategies also points out that "learning how to learn is more important than learning what". In mathematics teaching, teachers always keep in mind the learning methods taught to students and attach importance to the guidance of students' learning methods. For example, teach students how to remember, how to preview and how to analyze the quantitative relationship of application problems.

Third, implement the "heuristic" teaching principle

Teaching and learning are bilateral activities between teachers and students, and whether teachers can fully mobilize students' positive thinking in teaching is the key to successful teaching. Confucius emphasized that coaching should start from the students' learning mentality, and advocated that "if you don't get angry, you won't get angry. If you can't take a turn, you can't do it again." Zhu believes that "angry people want to communicate, but not reach"; Obviously, students will be enlightened by "opening their hearts" at critical moments and induced to "speak their own words" when students are always too mature to express themselves. Students will be suddenly enlightened and suddenly realize that only in an angry psychological state can they be inspired and induced to mobilize.

In mathematics teaching, the core of teacher's inspiration and guidance is to inspire and induce students' thinking and cultivate students' ability to analyze and solve problems.

Fourth, carefully create problem situations.

Psychological research shows that doubt easily leads to students' directional inquiry reflection, and students' thinking activities also emerge as the times require. Therefore, mathematics teachers should carefully design interesting question situations to promote students' positive thinking. For example, a teacher said in the Law of Addition and Association: "When Mr. Gauss was a child, the teacher had a problem on the blackboard: many students didn't solve it for a long time, but Gauss solved it at once. Do you know how gauss worked it out? After learning the law of addition and association today, everyone knows that "the students in this class are immersed in the problem situation created by the teacher and their thinking activities are very active." "

Fifth, pay attention to the cultivation of students' practical ability.

Practical activities are the basis of thinking. According to the characteristics of primary school students' activities, first, make full use of and create conditions to guide students to master basic mathematical knowledge through activities such as observation, measurement, piecing together, drawing, making, experimenting with objects and models; Second, carefully design math activity classes that are entertaining and entertaining; Thirdly, extracurricular activities in mathematics should be diversified and vivid, so that students' thinking and innovation ability can be well developed.

Sixth, pay attention to the cultivation of students' non-intelligence factors.

In the process of students mastering knowledge, their intellectual factors and non-intellectual factors are coordinated, and they closely cooperate and promote each other. In mathematics teaching, we should organically unify students' intelligence factors and non-intelligence factors in the teaching process. Non-intellectual factors include many things, but it is important to have the following two points:

(A) interest as a non-intellectual factor is very important. Interest is our understanding of something or our tendency to like an activity, which is associated with certain emotions. If a person has a strong interest in something, he will bravely and persistently pursue it to achieve his goal. So some people say, "Interest is the best teacher". In teaching, teachers should use appropriate teaching methods and means to stimulate and cultivate students' interest in learning mathematics.

(2) We should attach great importance to the positive role of emotional factors in achieving teaching objectives and cultivating students' good psychological quality. In teaching, teachers should fully mobilize all kinds of emotional factors in the teaching content and process, and dedicate their love to teachers. Creating an emotional teaching atmosphere with students can not only reduce students' learning psychological pressure, but also make students' thinking active and their intellectual activity level greatly improved, thus improving classroom teaching efficiency.

It is not easy to teach primary school mathematics well, but as long as teachers follow the teaching rules, seriously study the above problems and gradually form their own unique teaching style, they can also teach primary school mathematics well.