Constructivism holds that the essence of learning is an active construction process based on one's existing knowledge and experience. In the initial stage of the cultivation of number sense, because the junior students lack life experience and observation ability, the mathematical language has not been effectively developed, and they lack the knowledge and experience to absorb new content. At this stage, group cooperation and communication can be strengthened, so that junior children can inspire and complement each other in cooperative learning, and then form a preliminary sense of numbers. This initial number sense training is very valuable and needs patient training. At the same time, due to the different cultural environment and family background, students' mathematical thinking mode will also show great differences, so the meaning and function of logarithm have their own life brand. Through cooperation and communication, students' imagination and enthusiasm for communication are stimulated, so that students can feel that numbers are everywhere and enjoy the progress and success of mathematics learning. For example, in the teaching of "carry addition within 20", we can first organize cooperation and exchange, design novel exercises, and guide students to draw different oral calculation methods, such as "point method", "number method", "decimal method", "decimal division", "exchanging the position of addend" and so on. Through the communication of oral calculation methods, students can also feel the relative size of numbers and further understand the diversity of algorithms.
Finally, it is worth emphasizing that as a basic quality of mathematics, the cultivation of number sense must run through the whole process of mathematics learning. It is particularly important for primary school students who lack common sense of life to learn how to transform abstract data into useful and perceptible mathematical information. Therefore, we must actively explore diversified teaching methods in mathematics classroom teaching, effectively help students sort out their own knowledge and experience, and cultivate a good sense of numbers in the process of developing mathematical thinking. For example, guide students to learn to observe and explore numbers in nuances; Guide students to learn to change and perceive numbers in change; Help students learn to quote and feel numbers in comparison; Help students organize in an orderly way and express numbers intuitively; Help students learn to experience, touch numbers in practice and so on. This can help students reveal the hidden secrets of all kinds of numbers, so that students can effectively enhance their sense of numbers and constantly improve their mathematical literacy.
How to cultivate junior students' sense of numbers? 3 1. Establish a sense of numbers based on life experience.
Mathematics comes from life, and the cultivation of number sense can not be separated from students' life. Teachers should fully tap students' living resources in teaching activities, be good at combining classroom teaching content, guide students to collect "life examples", and actively create learning scenarios closely related to students' living environment and knowledge background, extending from indoor to outdoor, from school to society, so that students can feel the meaning of numbers in real life background, understand the role of numbers, deepen their understanding of logarithm, and let students talk about the numbers around them, the numbers used in life and how to use them in the process of knowing numbers. For example, when teaching the understanding of grams and kilograms, students can find and weigh 1 gram and 1 kilogram, and find out which objects use grams and kilograms respectively. For example, a penny weighs 1 g, and four bags of soybean milk weigh about 1 kg. For example, when I know large numbers, I use multimedia (using statistical charts and tape recorders) to teach students how many people there are in our city, which is probably several times the number of students in our school; How big is the land area of our province, and the area is equivalent to how many cities. By guiding students to observe and experience the scene of large numbers, students are trained to feel the quantitative significance of the world around them, so as to gradually feel the number. In the teaching of the concept of numbers, we should pay attention to guiding students to talk about numbers around them, numbers used in life, and how to express things around them with numbers. Let students feel that the number is around and deal with it every day. Many phenomena can be expressed simply and clearly with numbers. For example, when buying school supplies, you should look at the price tag, pay with specific figures and change; Your birthday, height, weight and shoe size are all specific figures; How many words are there on a page, how much 10 thousand grains of rice weigh, etc. are all made up of numbers. Providing students with sufficient perceptual background to express numbers in different ways through their perception and experience of specific numbers can help students deepen their understanding of logarithmic meaning and lay a good foundation for building a sense of numbers. These activities are deeply loved by students, who are very interested in learning and have accumulated a sense of numbers unconsciously.
2, according to the characteristics of thinking, cultivate a sense of number.
The main feature of the thinking development of lower grade students in primary school is the transition from concrete thinking in images to abstract thinking in logic. Although there are abstract elements in the thinking of lower grade students in primary schools, they are still based on concrete thinking in images. For example, most of the concepts they master are concrete and can be directly perceived, and it is difficult for them to distinguish the essential attributes and non-essential attributes of concepts, while middle and high school students can distinguish the essential attributes and non-essential attributes of concepts, master some abstract concepts, and use concepts, judgments and reasoning to think. There is a turning point in the transition of primary school students' thinking from concrete image thinking to abstract logical thinking, which usually appears in the fourth grade. With proper education and training, this transition period can be advanced to the third grade.
When we teach "the subtraction of 7" in senior one, it is divided into three levels:
2. 1 The teacher first designed a beautiful courseware, in which there were 7 birds, 3 of which just flew away for students to fully observe. The courseware is lively and interesting. Then ask the students to say what mathematical information they find in the picture.
2.2 Inspire and guide students to express this picture with their favorite and familiar graphics. The students have spoken the meaning of using cubes, squares, circles, etc. To represent this painting.
2.3 Let the students use numbers and expressions to represent this picture. There are seven birds, three of which have flown away, and there are four left. Use the expression: 7-3 = 4 (only).
The above-mentioned instructional design designs the learning process from physical graphics to abstract graphics and then to abstract symbols, and follows the development characteristics from concrete image thinking to abstract logical thinking, so students can easily accept and master this knowledge, thus achieving the teaching purpose and naturally expressing their wishes with numbers, that is, creating a sense of numbers.
3. Cultivate a sense of numbers according to specific problems.
Mathematician Friedenthal thinks: "Mathematics comes from reality, exists in reality and is used in reality." The purpose of learning operation is to solve practical problems, not just to calculate. Cultivate students' sense of numbers by combining specific practical problems. Therefore, teachers should let students know more about practical problems, consciously establish the relationship between practical problems and quantitative relations, guide students to learn to turn a problem in life into a mathematical problem, and learn to deal with practical problems with mathematical methods and viewpoints, so as to construct mathematical models related to specific things.
For example, in fifth grade mathematics, students are required to circle multiples of 4 and 6 in the table, so that students can go through the process of finding the least common multiple. Reveal the meaning of common multiple, thus leading to the concept of minimum common multiple. This enumeration method is a common mathematical thinking method to solve problems, which is easy for students to understand. In addition, at present, the number of times to find the least common multiple is limited to 10, and it is not complicated to solve it by enumeration, which also reflects the idea and method of solving problems with knowledge as the carrier in the textbook. The commonly used "short division" is actually to find out all the factors of two or three numbers, which is too skillful. Many students can't easily understand the arithmetic involved in "short division". If students are required to master it, it will increase their burden and cause embarrassment. It is also not conducive to students' mastery of common multiples and minimum common multiples.
For another example, there are three clothes and two pants in the "collocation" problem of second-grade mathematics. * * * How many ways can I wear it? In order to solve this problem, the teacher first instructed the students to put pictures, and found that there are six ways to wear * * *; Then inspire students to use the method of connection. Clothes and trousers are connected together, and there are six lines, that is, six ways to wear them. Finally, guide students to use numbers to represent 2+2+2=6.
3+3=6 2×3=6. When solving this collocation problem, students have experienced the thinking process from physical diagram to connection and then to number, knowing that there are three solutions to this problem, and developing a sense of number in the process of solving this complex problem.