First, the confusion of inquiry activities in primary school mathematics classroom teaching
(A) explore a mere formality
Area of a circle
1. Before class, the teacher asked each student to prepare two circles and asked them to use the circles in their hands to convert them into the figures they had learned. 2. Students begin to operate.
Analysis: Independent exploration, cooperation and communication, and hands-on practice are important mathematics learning methods advocated by the new curriculum. However, inquiry activities do not mean that students simply carry out teachers' orders. At best, this kind of operation is to get some kind of teaching conclusion, which makes students lack the consciousness of active inquiry, and it is difficult to cultivate students' active learning ability, resulting in inefficient or ineffective exploration process. This operation process is just a label of pursuing the wind of form in curriculum reform, and students just become props of classroom practice reform, losing the main role. In view of the above phenomena and analysis, I think we should guide students to grasp the direction of inquiry, stimulate their desire to explore, create an atmosphere of inquiry, and form a research atmosphere, so that teachers can really get out of the misunderstanding of false inquiry in teaching.
(B) lack of thinking and exploration
Sum of internal angles of triangle
1. Introduction to the problem. Guess: What is the sum of the internal angles of any triangle? (Most students say 180) 2. Can you prove that "the sum of the interior angles of a triangle is 180"? 3. Some students are measuring, some students are cutting corners, but the result is left and right. Even if some students make mistakes, correct them immediately. The sum of the angles in the triangle is 180. The teacher immediately concluded on the blackboard that the sum of the inner angles of the triangle is 180.
Analysis: What is the sum of the internal angles of a triangle? Most students will say. But classroom practice tells us that students just listen and speak, and why it is 180 degrees is not clear to them. Students always use the results to demonstrate in the process of inquiry, which embodies the operation but does not really understand and master the arithmetic. This kind of operation and exploration lacks certain thinking and challenges, and has no meaning.
The survey results exist in name only.
Case 3: Area of Triangle
1. The teacher prepares corresponding material bags for each group before class. After students think independently, try to explore the area of the triangle by themselves. Feedback the original idea. There may be two kinds of defaults: the base multiplied by the height is higher than the area, and the base multiplied by the height divided by 2 equals the area. 2. Discuss and exchange your own thinking process in the group. The teacher said that it is not right to multiply the bottom by the height, but the area of two figures.
Analysis: The area derivation of triangle uses the idea of transformation, which plays an important role in geometry teaching. If students can correctly understand and master this idea, it will play an important role in learning the knowledge of trapezoidal area, circumference, area, cylinder and cone volume.
Second, the strategies of inquiry activities in primary school mathematics classroom teaching
Through analysis, the author thinks that teachers should pay attention to the following points before designing inquiry learning.
(1) The design of inquiry activities should follow the cognitive rules of primary school students, create an equal, harmonious and vivid inquiry atmosphere for students, constantly stimulate students' cognitive conflicts, and let students truly understand and master mathematics knowledge in the process of constantly overcoming thinking obstacles. For example, when teaching cone volume, a teacher designed it like this: 1. Know the cone. 2. Ask students to observe a group of cylinders and cones with equal bottoms and equal heights and guess what the multiple relationship between their volumes is. 3. Experimental verification. This kind of teaching process seems that students explore learning through hands-on operation and draw conclusions through experiments; But why suddenly compare the sizes of cylinders and cones? Why do you want to do this experiment? Obviously, this is the teacher leading the students, and the students passively carry out operational inquiry. Another teacher added such a link: through courseware, let students review the three-dimensional figures formed by the rotation of cylinders and cones into rectangles and right triangles respectively. Then rotate the height of a rectangle with equal base and equal height and a right triangle respectively to get a cylinder and a cone, and then guess and verify. This setting has caused cognitive conflicts among students, and students have realized the necessity of doing experiments. Only in line with students' cognitive laws is the best inquiry activity.
(2) Provide students with sufficient time and space to explore. Inquiry learning is the development of knowledge, skills, emotions and attitudes acquired by students through inquiry activities. In teaching, we should not only provide students with suitable inquiry materials, but also give them some time and space. For example, when teaching the circumference of a circle, first guess what is the relationship between the circumference and diameter of the circle. After guessing, the teacher explained that when studying their relationship, they usually study their "relationship of sum, relationship of difference, relationship of product and relationship of multiple of division". In the process of calculating with a calculator, students understand that there is no certain law in the addition, subtraction, multiplication and division of the circumference and diameter of a circle; Dividing the circumference by the diameter has a certain rule: the circumference is always more than three times the diameter. If teachers don't give students enough time in such a link, it will weaken the effect of inquiry learning. In inquiry learning, only by giving students a certain amount of time and space for full exploration can we achieve the expected purpose and truly implement inquiry teaching.
(3) Pay attention to the extension of inquiry learning to extracurricular activities, and the class ending does not mean the end of all inquiry learning activities. For example, after learning litres and milliliters, ask students to look for them at home and in the classroom. After learning the knowledge of discount, let the students accompany their mother to buy a discounted item; After learning the circle, let the students draw a circle on the playground. Extending the results of inquiry into extracurricular activities can stimulate students' desire for inquiry, feel the close connection between mathematics and life, and enhance students' initiative in learning mathematics.
In short, in classroom teaching, teachers should follow the cognitive rules of primary school students, give students sufficient time and space, let students discover, experience and explore themselves, and make independent inquiry truly become an effective way of classroom teaching.
How to use teaching AIDS in primary school mathematics teaching is an eternal topic for every mathematics educator to pursue efficient mathematics classroom. In the teaching process, the effective way to reduce students' schoolwork burden is actually to improve the efficiency of mathematics classroom. So, how to improve the efficiency of mathematics classroom teaching? In addition to appropriate teaching methods, we should also attach importance to the development and utilization of teaching AIDS for mathematics majors and use them as much as possible in classroom teaching. This paper analyzes the use of underlined keywords in blackboard writing, chalk, multimedia tools, real physical cards and correct use in practical activities, hoping to have certain reference value for primary school mathematics teachers to improve teaching efficiency. ……
How to make students with learning difficulties develop effectively in mathematics teaching in primary schools? In primary school mathematics teaching, we often meet such students: lack of independence, no self-confidence, no goal in learning, study hard, or simply give up learning and give up on yourself. Over time, they got tired of studying and then gave up. This is what we often say about students with learning difficulties. It is precisely because of the lack of initiative in learning that the intellectual development of students with learning difficulties is seriously affected and their learning progress is hindered. Therefore, it is of great significance to pay attention to the transformation of students with learning difficulties to improve mathematics teaching in primary schools in a large area. The formation of students with mathematics learning difficulties in primary schools is mainly manifested in the following aspects: 2. Basic concepts and theorems are vague: concepts, formulas and theorems cannot be reproduced in mathematical language. Without reading textbooks, it is impossible to explain the system of concepts, and concepts cannot be linked. For example: axisymmetric and axisymmetric graphics, they can't tell which concept is to discuss the position and shape relationship between the two graphics and which graphic is to discuss the special shape of the graphics itself; At the same time, they don't understand the symmetry of graphics. 3. Lack of enthusiasm for solving problems in the classroom: In the classroom, teachers are indifferent to the assigned problems and exercises and do nothing. There are no process steps to solve the problem, or the logic is unclear. They lack the motivation to think positively, refuse to use their brains, and are always careless and avoid answering. 5, do not pay attention to the exam, lack of competition awareness. Do not review carefully before the exam, cope with carelessness, lack confidence in the exam, and "improvise" in the examination room. Below, combining my own experience, I talk about my views on the transformation of students with learning difficulties: First, in teaching, we should pay attention to cultivating students with learning difficulties' interest in mathematics learning and stimulating their enthusiasm for learning, which is the premise of changing their learning attitude. Mathematics is a scientific, rigorous and abstract subject. It is precisely because of its abstraction that it is the main reason for the formation of students with learning difficulties. Therefore, when teaching, we should strengthen the intuition of teaching. Through intuition, students can understand the concept and essence of mathematics and establish a mathematical model of what they have learned in their brains. 2. The artistic application of teaching language should be strengthened to make teaching lively and interesting. In classroom teaching, teachers should not only observe the learning mood of the whole class at any time, but also pay special attention to the learning mood of students with learning difficulties. Students with learning difficulties are often absent-minded and inattentive in class. They turn a deaf ear to the teacher's lectures in boring language and are not interested in mathematics knowledge. At this time, teachers should properly use artistic teaching language, enliven the classroom atmosphere, and guide each student to enter a positive thinking state, so as to achieve the teaching purpose. 3. Pay attention to emotional education. Although he is a student with learning difficulties, he is full of emotions. They need teachers to give them more care and love, and they need their encouragement and affirmation. Teachers should seize every bright spot in students and praise them in time. As long as students with learning difficulties accept teachers, they will mobilize their enthusiasm for learning and learn independently. Therefore, in actual teaching, it is far from enough for teachers to pay attention to their image in front of students. What is more important is to pay attention to emotional education for students with learning difficulties. We should fully affirm the advantages of students with learning difficulties, affirm their slight progress, and urge them to study actively. Second, cultivating students' good habit of consciously learning, imparting correct learning methods and improving their ability to solve problems are the key to solving the learning problems of students with learning difficulties. 1. Most students with learning difficulties are passive and dependent. Teachers should pay attention to the application of heuristic teaching methods when answering questions, guide them to analyze problems and gradually let them use their brains to answer questions. It is necessary to correct the mistakes they analyzed and solved at any time, and gradually cultivate their habit of completing their homework independently. 2. When assigning homework, teachers should reduce the requirements for students with learning difficulties, and the difficulty of homework should be close to the actual learning level of students. We should pay attention to strengthening the guidance and transformation of students with learning difficulties, adopt the method of gradual induction according to the principle of step by step, patiently guide them to make up lessons from the starting point bit by bit, so that they can gradually improve. For the assigned homework, we should urge them to finish it carefully, and give timely praise and encouragement to the poor students who have done their homework better or made progress in their homework. 3. Students with learning difficulties should not only be concerned and cared for, but also be patiently and meticulously counseled, and should be combined with strict requirements. There are many reasons why students with learning difficulties become students with learning difficulties. Some are because they are weak in learning will and lazy in life; Sometimes I have to copy my homework because I am often distracted and absent-minded in class. The content of this lesson is not mastered, and the content in the future can't be understood, which leads to a vicious circle of plagiarism. Therefore, teachers should pay special attention to poor students' homework completion, put forward strict requirements for them in the teaching process, and urge them to study hard. Third, pass the exam carefully and pay attention to cultivating the self-confidence and self-esteem of students with learning difficulties, which is a powerful weapon to motivate students to learn. In the exam, we should consciously ask some easy questions, cultivate their confidence, let them taste the sweetness, and let them realize that they can learn well. Clear and specific requirements should be put forward for students before the exam, and individual counseling should be given to the weak points of students with learning difficulties. This will also enable some students with learning difficulties to get higher scores through hard work, give them a sense of accomplishment, gradually change their sense of inferiority in their studies, and cultivate their self-confidence and self-esteem. For individual students with learning difficulties, they can take separate papers. In short, teachers should find ways to motivate them to work hard and strive for progress, so as to achieve the goal of transforming students with learning difficulties.
How to deal with the wrong questions in primary school mathematics teaching because students always have some wrong questions in their usual homework and exams, especially in primary school mathematics teaching, these wrong questions will affect teaching efficiency to a certain extent if they are not handled well. Therefore, how to effectively use the wrong questions in primary school mathematics has become the main concern of teachers today. This paper expounds how to make effective use of wrong questions in primary school mathematics.
1. Intelligently guide "mistakes" into "bright spots" and promote the effective formation of students' mathematical knowledge.
In primary school mathematics teaching, teachers should skillfully turn students' "wrong questions" into "bright spots", analyze and study them effectively with wrong questions as carriers, guide students to use wrong questions effectively, and let students participate in the application of wrong questions from different angles. Teachers can't blame students blindly when they make mistakes, which will not only hurt students' self-esteem, but also reduce students' learning efficiency and fail to achieve the expected results. Therefore, skillfully turning "wrong questions" into "bright spots" can not only reduce wrong questions in primary school mathematics teaching, but also greatly improve students' research ability on right and wrong issues and promote the effective formation of their mathematical knowledge.
Second, reorganize the wrong questions into a group of wrong questions.
For primary school students, because of their age, they simply correct the problems existing in their usual exercises, without in-depth research, and even without recording the wrong questions. Some students like to have fun. In order to be lazy, they don't even correct the wrong questions pointed out by the teacher, and similar problems will still make mistakes when they appear again. Therefore, teachers should reorganize the wrong questions into a set of wrong questions, record all the students' usual wrong questions, analyze the mistakes and establish a set of wrong questions, which can not only help students understand their mistakes, but also provide effective basis for students to consolidate their mathematics knowledge. In addition, after the completion of the wrong question set, teachers should make periodic revisions, add some new wrong questions that students appear, so as to avoid complacency, and distribute the wrong question set to students for them to read and browse frequently, so as to effectively play the role of the wrong question set. It can be seen that grouping wrong questions into a group of wrong questions can not only reduce students' error rate, but also improve students' correct rate of doing questions and improve teaching efficiency.
Third, cultivate students' habit of writing about math diary.
In the process of mathematics learning, primary school students will always encounter corresponding confusion in solving problems. However, some students are unwilling to use their brains, and most of them just skip and wait for their classmates or teachers to answer. This will not only improve their math problem-solving ability, but also affect their future math learning effect to some extent. Since mathematics learning is one step at a time, we should go down step by step to improve our learning efficiency. Therefore, teachers should cultivate students' habit of writing math diary, so that students can write it down when they are confused and when they solve a difficult problem. In this way, in the future study, students can make reflective learning through their own records, which can not only overcome their own thinking obstacles, but also record and analyze their own gains and losses through math diary, so as to better understand their own problems and correct all kinds of mistakes and bad habits in solving problems, so as to improve their ability to solve problems and make their thinking more profound and rigorous.
To sum up, because the cognitive ability of primary school students is not perfect enough, it is normal to make mistakes in math exercises. As a primary school math teacher, in order to make effective use of wrong questions in primary school math, we should first establish a correct view of wrong questions, regard students' wrong questions as valuable resources, stimulate students' thinking with wrong questions, and guide students to establish self-confidence in learning. In addition, teachers should organize the wrong questions into a set of wrong questions, let students read and browse frequently, and guide them to examine the internal relations of math problems from multiple angles and in all directions, so as to reduce the rate of students' wrong questions, cultivate students' habit of writing math diary, and let students learn reflective through their own records, so as to effectively play the role of wrong questions and lay a solid foundation for students to learn math well.
How to use mathematical tools in primary school mathematics teaching? How to make good use of mathematical tools in primary school mathematics teaching 1. Common learning tools and their functions According to the content of primary school mathematics textbooks and the age characteristics of children, the common learning tools are as follows: 1, physical pictures, mathematics, symbols, geometric graphics cards (or plastic sheets). 2. stick. 3. Counter or counting table. 4. Oral practice card. 5, round oral arithmetic practice board. 6. Clock face and puzzle. 7. Nail board. 8. Quezon color-resistant stripes. Second, the main use of learning tools In the mathematics teaching of the lower grades of primary schools, there are many types of learning tools, and different structures have different functions. How to make good use of these learning tools can we really help students master mathematics knowledge and develop their abilities? The following is a brief introduction to the main methods of using some school tools. For the convenience of narration, it is simply described according to the mathematical content. 1. Understanding and calculation of numbers In the teaching of the concept and calculation of low-order series, plastic sheets, numbers, symbol cards, wooden sticks and Quezon color-resistant strips with various geometric shapes can be selected. There are also counters, counting tables, oral arithmetic practice cards and oral arithmetic practice boards. When teaching reading and writing numbers within 100% and 10000%, it is more effective to combine the counting table with Quezon color fastness bar, which is convenient for students to learn confusing concepts such as counting units and numbers in a short time, and at the same time master the basic rules of digital reading and writing. 2. Application problems In the initial stage of learning application problems, in order to let students understand the quantitative relationship in the problems, the learning tools used are generally plastic pieces (or cards) of various geometric shapes, wooden sticks, Quezon color-resistant strips, etc. The activities of operating with cards and sticks have been introduced in the teaching reference book. Through operation, students can understand the abstract quantitative relationship from the concrete mathematical model, and gradually learn the analytical method to solve the application of phase difference relationship. 3. Basic knowledge of geometry When learning basic knowledge of geometry in the lower grades, you need to prepare graphic cards and objects of various shapes. Such as rectangular, square, triangular and circular objects or cards; Objects or models of cuboids, cubes, cylinders and spheres; There are Quezon colored strips, nail boards and puzzles. 4. The use of computer-assisted instruction is conducive to attracting students' attention; It is beneficial to cultivate students' spatial concept; Strengthening intuitive teaching and practical operation activities has become the trend of mathematics teaching reform in primary schools. Due to the need of operation activities, learning tools have entered the classroom with textbooks and become one of the tools for children to learn mathematics knowledge.
How to cultivate students' sense of numbers in primary school mathematics teaching should combine mathematics teaching with real life and life scenes, so that students can learn to express and explain the methods and means to solve practical problems and the answers to these questions in mathematical language. Mathematics curriculum standards, as a method to cultivate number sense, regard number sense as an important learning content in compulsory education. Sense of number is a general understanding of logarithmic sum operation, which can help people make mathematical judgments and put forward useful strategies to solve complex problems. It is an attitude and consciousness to solve and use numbers actively, consciously or automatically. So how to cultivate students' sense of numbers in our daily classroom teaching? I talk about some superficial methods based on my own teaching practice. First, contact life Life is the source of mathematics. If mathematics learning in the primary stage leaves students' lives, it will be even more difficult to move. The life of new school children is colorful. Games, fairy tales, animals and stories ... are not necessarily the whole of their lives, but at least they account for a large proportion. In the teaching of number recognition, teachers should make full use of mathematical materials around students, try to awaken students' existing life experience, show children the realistic source and practical application of the concept of number, and create a teaching situation that helps children understand mathematics, so as to help students 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 students generally have a learning foundation in kindergarten, they will count with interest: 1 slide, 2 swings, 3 wooden horses, 4 planes ... all common things in their lives, and mathematics is so ubiquitous; After counting, students have to tell each other what is on the picture, so mathematics has become an indispensable tool for students to communicate, because it is almost impossible to explain what is on the picture without counting. For another example, when teaching "Understanding of 10", students are also guided to observe the theme map of ethnic minorities in children dance. After counting, there are 10 children, and the number "10" is obtained. There is also an understanding of "0", which not only makes students realize that "0 has no meaning" with the help of the situation that the white rabbit pulls radish, but also makes students realize that "starting from here" with the help of the meter scale, and also arranges "0 in life" in "thinking and doing", which enriches students' understanding of the meaning of 0. It is precisely because of the connection with students' lives that mathematics has become visible and tangible, and has played a real role. Second, to cultivate students' sense of number In the cognitive teaching of number, I cited examples of close contact with students in life, which made students find that mathematics is around them, and life is full of mathematics, so that students can observe and know things around them with a mathematical eye and feel the interest and role of mathematics. For example, when studying hours within 10, when learning "1", students are required to observe the things represented by "1" in real life. Students cite: 1 book, 1 bird, 1 tree, 1 stick, 1 country, 1 bunch of grapes, 1 bunch of sticks ... and then guide students to count a bunch of grapes. How many are there in a bundle? Help students understand that "1" can represent 1 individual (1 branch) or 1 set of such individuals (1 branch); It can represent very large objects (1 country) or very small objects (1 bird). Another example is to teach the separation and combination of 2 ~ 9. One of the contents is: 5 can be divided into 2 and 3 (or divided into 1 and 4). It is not very efficient for students to understand and master this knowledge point through boring and mechanical memory or recitation. At this time, you can play a "clap game", so that the total number of times for teachers and students to clap their hands is 5. For example, the teacher shoots 3 times, the student shoots 2 times, the teacher shoots 1 time and the student shoots 4 times. Although this is a very simple game, after the introduction of the game, students' interest increased sharply, and they really participated in the learning process and experienced the formation of knowledge. This example shows that simple games not only enliven the classroom atmosphere, but more importantly, students experience the division and combination of numbers in "playing", which enhances the understanding of the transformation relationship between logarithm and number, that is, develops the sense of numbers. Another example is in the teaching of "Understanding Numbers from 1 1 to 20". I asked the students to count after grabbing a school stick, and also asked them to estimate according to the number axis: 1 1 or 20? 15? In this way, the cultivation of number sense is implemented in specific activities and linked with students' real life, so that students can have a vivid representation of number. When they encounter similar situations again, they will have a specific reference in their minds and truly establish a good number sense. Third, hands-on practice "learning from time to time is fun!" The original meaning of "learning" means that young eagles practice flying. In this sense, mathematics learning can be regarded as children's own practical activities. Primary school mathematics practice activities emphasize that students learn mathematics through personal experience, that is, doing and using mathematics by hand, rather than just listening to and remembering mathematics. Mathematics practice is a free world for students to actively develop, and the mathematics classroom that pays attention to practical activities will 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-year experimental textbook of the curriculum standard of Jiangsu Education Press, in order to cultivate students' sense of numbers, many interesting practical activities such as "knowing equal, greater than less than" were designed to guide students to truly grasp the relationship between rows and pairs of numbers in combination with the scene of "forest game". For another example, when "knowing numbers and numbers", ask students to look at the pictures of small animals climbing mountains in the book and say, "How many animals are climbing mountains? Number one? Who is the second place? How many animals are there under the mountain? Who is the first? Who is the second? " Enable students to deepen their experience of "Ji and Ji" in communication. For another example, when you know the number from 1 1 to 20, ask the students to grab a small stick and count how many there are; Guess how many strawberries there are in a pile first, and then count them out; According to the number axis, "18 is close to 1"
How to use practical activities to cultivate students' ability in mathematics teaching in primary schools? Students' experience of mathematical activities is slow in the process of experiencing operation and practical activities.
Slowly accumulated. Therefore, in the process of classroom teaching, teachers should let students do it.
Imagine, operate and practice, and cultivate and develop your own thinking ability while accumulating experience in mathematical activities.
How to cultivate gifted students in primary school mathematics teaching can make them do more problems and copy some application problems for them to do (because in the exam, the most points lost are application problems), so that they can be impressed!
How to make primary school mathematics teaching full of life interest? I think asking more questions and interacting more. Send them some sugar for the holidays. They will like you very much. And try not to miss class. You will be more successful.
The new round of teachers put forward that teaching should change the single learning mode of teaching and accepting, pay attention to students' knowledge and ability, and pay more attention to students' emotions, attitudes and values, which requires teachers to pay attention to abstract mathematics problems from students' lives, start from students' existing life experiences, dig out life materials that students are interested in and show them to students in colorful forms. Think of math class as a stage for students to show their wisdom and personality. Specifically, we can start from the following aspects: