Mathematics literacy sounds profound and unfamiliar, but in fact, it permeates our daily life all the time, such as discount information in shopping malls and family investment and financial management.
Primary school students' mathematical literacy includes five kinds of mathematical consciousness, namely, sense of number, sense of symbol, sense of space, sense of statistics and sense of mathematical application, four kinds of mathematical abilities, namely, mathematical thinking, mathematical understanding, mathematical communication and problem solving, and the development of mathematical values.
I will talk to you about my superficial understanding of cultivating students' mathematical literacy from the following three aspects:.
1. Understanding the world from the perspective of mathematics-the cultivation of mathematical consciousness.
What is "mathematical consciousness"? For example, students can calculate "48÷4", which shows that students have the knowledge and skills of division. Students will understand, "there are 48 apples, with an average of 4 apples per person." How many people can you give them? " It shows that students have certain ability to analyze and solve problems, but none of them can show that students have mathematical consciousness. In physical education class, 48 students are jumping long ropes, and the teacher has prepared four long ropes, from which students can think of the formula "48÷4", which shows that students have a certain sense of mathematics.
(1) Understand the meaning of numbers and the relationship between numbers, and cultivate a sense of numbers.
Cultivating pupils' "sense of numbers" is the focus of lower grade teaching. In fact, students already know a lot before entering school, but that's just what they know from their life experience. They have only a very superficial understanding of numbers. Our task is to make these adults look abstract and gradually enrich them in children's minds. The understanding of learning 1 1 ~ 20 in Unit 5, Volume I, Grade One. The teaching focus of this lesson is to let students know the numbers "unit" and "ten" and the counting units "one" and "ten" preliminarily through hands-on operation; Understand that the same number represents different values in different positions. In the first class, I drew the number "1 1" through the guessing game, and then asked the students to put the wooden stick of 1 1 on the desktop, so that others could see it at a glance. When students divide 1 1 root into 10 root and 1 root, then ask them to bind 10 root together. At this time, I will tell you that, like the students, numbers also have their own positions. Show the digital cylinder and you will know the number one and the number ten. 1 branch means 1 branch should be put in a unit cylinder, 1 bundle means 1 ten should be put in a unit cylinder. In addition, students can understand the practical significance of the concepts of "number" and "counting unit" and establish the concepts of "number" and "counting unit" through the mutual conversion process of 1 tens and 10 digits. At the same time, the teaching of "digital cylinder" has also played a very subtle role in the teaching of the concept of "copy". From the analysis of the concept of copy, bundling "10" into 1 bundle means treating 10 as 1. After learning, I asked my classmates, what do you think when you see 20? The student said, "I wear size 20 shoes." 20 is 2 for ten digits and 0 for one digit. I have 20 new pencils. 20 is much greater than 1 1. "If we don't give children the freedom to speak, we probably won't have the opportunity to know that the numbers in their hearts have such rich connotations.
(2) Go through the symbolization process and cultivate the symbolic consciousness.
Students can come into contact with many symbolic situations such as stop signs and Olympic rings in their lives, so they have some symbolic experiences. When I teach "Determining the position by using number pairs", I first activate the existing experience of describing the position of objects in students' minds by presenting the specific scenes of seats that students are familiar with in the classroom. Through communication, students have the need to express their positions in a consistent way. Then, the specific scene diagram is gradually abstracted into a plan diagram such as a circle diagram and a network diagram, and the position is represented by several pairs. In this way, students have experienced the learning process of "concrete things-personalized symbol representation-learning mathematical representation", realized the necessity of introducing symbols and the simplicity and practicability of mathematical symbols, cultivated students' symbol consciousness and developed the concept of space.
(C) the combination of practical operation and mathematical thinking to cultivate the concept of space
In teaching, we should make full use of students' existing life experience and find the fulcrum to develop the concept of space. When studying Direction and Position, I took my students to the playground, and used their existing life experience of "The sun rises in the East" to determine the East first, and then to know the other three directions. In this way, the teaching vision is extended to the living space, and the prototype of life is used to effectively promote the development of students' concept of space.
(d) Experience the whole process of statistical activities and cultivate statistical concepts.
The cultivation of statistical concepts is difficult to form only by training, and students must experience it personally. For example, when the school held the "Sunshine Girls' Day" last semester, our class made a survey on "What color balloons should we buy". Students have experienced statistical activities of collecting data, sorting out data, describing data and making decisions through communication. During the activity, the students realized the necessity and function of statistics.
Modern public media have widely used statistical charts to express information, and understanding the common statistical charts in life is an important mathematical literacy of modern citizens. Therefore, in statistics teaching, we should focus on guiding students to read statistical charts, analyze the data in the charts and make necessary reasoning, rather than making statistical charts. For example, a classmate surveyed five male students in his class, four of whom like playing basketball, so he came to the conclusion that 80% of his classmates like playing basketball. It is necessary to guide students to reasonably question the data sources, data processing methods and conclusions drawn from them, so that students can have a more comprehensive and correct understanding of statistical data.
(5) Pay attention to the connection between mathematics and life, and cultivate the consciousness of mathematics application.
Once, my good friend asked me shyly: When shopping in the supermarket, will you first look at the price of the same product in different packages, and then compare which one is cheaper? In fact, what do we learn knowledge for? Isn't it just for use? What can we learn if we don't let it serve our lives? For example, it is also bright pure fresh milk: large package 1000ml, 8 yuan/barrel; Small package 220ml, 2 yuan/box. By calculating 1000÷8= 1250(ml/ yuan) 220 ÷ 2 = 1 0 (ml/yuan), we can know that the same1yuan, we What is the consciousness of mathematics application? Mathematical application consciousness is a psychological tendency to apply mathematical knowledge and mathematical thinking methods and actively try to think and solve practical problems with mathematical knowledge, methods, strategies and ideas. It seems that my friend's sense of mathematical application is still good. In teaching, we should consciously guide students to pay attention to these mathematical problems in life, let them realize the significance and application value of learning mathematics, and form the habit of observing life with mathematical eyes.
Second, mathematical thinking-the cultivation of mathematical thinking ability.
(A) the combination of numbers and shapes to develop students' thinking in images
Primary school students' thinking is in the transitional stage from image thinking to abstract thinking. Number is the abstraction of shape, and shape is the expression of number. The combination of numbers and shapes can help students produce correct mathematical expressions and promote their mathematical understanding.
For example, the understanding of "kilogram and gram" belongs to concept teaching, and the content is abstract, which is difficult for students to understand. When I was studying kilograms, I designed a link to find 1 kilogram. I asked the students to weigh 1 kg of washing powder in one hand and the contents in the bag in the other. It is estimated that which bag is also 1 kg. In addition to weighing and estimating, a very important way for people to intuitively perceive the quality of objects is to simply infer according to the number of specific objects. Therefore, when evaluating students' knowledge of grams and kilograms, we should always examine students' "five apples weigh about () kilograms" and "1 box of apples 10 ()". We adults can make simple estimates based on general life experience. The primary school students who have just entered the third grade have little life experience, or have experienced it at ordinary times but didn't pay attention to it. When it comes to solving problems, they can only guess. And objects of the same mass have different sizes and quantities. This requires teachers to awaken students' experience through classroom practice activities and remind them to pay attention to the quality of accumulated experience. For example, after weighing 1kg apples and flour, students can count them and find that 4-6 apples weigh about 1kg, 2 bottles of mineral water weigh about 1kg, and several handfuls of 1kg soybeans (about 4,000 grains). Let students associate the abstract mathematical concept 1kg with the quantity and volume of specific things, which can help students effectively establish the quality concept of 1kg and transform the abstract concept into visible mathematical facts.
Graphic language is the main carrier of thinking in images. Solving problems with the method of "combination of numbers and shapes" is to combine the quantitative relationship and spatial form in mathematical problems for thinking. For example, children line up, Xiaoyu counts from the back, and he is the eighth. He is the fifth from the back. How many children are there in this team? Some students are difficult to solve at the moment, so the teacher should guide the students to draw a schematic diagram to solve it, which means: before ○ before ○ before ○ ○ ○ ○ ○ ○ ○ ○ ○ ○.
(2) Grasp the whole, break through the routine and cultivate intuitive thinking ability.
Einstein said: "The truly valuable thinking is intuitive thinking." Intuitive thinking is a form of thinking in which the human brain has some direct comprehension and insight into things, problems and phenomena. In teaching, we should cultivate students' intuitive thinking ability. First of all, we should improve students' overall ability to grasp knowledge. For example, Xiaoming is 8 years old and his mother is 36 years old. In six years, how old will her mother be than Xiaoming? According to the general way of thinking, the formulation of this question is "(36+6)-(8+6)", but students with good intuitive thinking will simplify the distance between information and questions and directly express it as "36-8". Secondly, we should choose appropriate questions and forms to train students' intuitive thinking. For example, 1 Title: Calculation (1+3+5+…+2007)-(2+4+6+…+2006), teachers can guide students to observe the characteristics of data, thus generating intuitive foresight, removing the brackets and reorganizing the formula into1+(. Question 2: In the following time, the one closest to your age is (). A.600 hours, b. 600 days, c. 600 weeks, d. 600 months This topic is multiple choice, which only requires choosing a reasonable answer from four options, omitting the problem-solving process, allowing students to use reasonable guesses, which is conducive to the development of intuitive thinking.
Third, solving problems by mathematical methods-the cultivation of problem-solving ability.
(A) let the use of strategies become a habit of thinking of students.
The problems in life are varied and changeable, so it is impossible for us to let students try to solve all the problems one by one. Therefore, the learning value of "problem solving" lies in enabling students to accumulate basic ideas and common methods to solve problems, accumulate experience to solve problems, and form basic strategies to solve problems. According to the age characteristics of primary school students, drawing, arranging, guessing, verifying and hands-on operation should be used as common strategies in teaching.
Using "graph" can solve many problems or find ideas. "Drawings" include line drawings, schematic diagrams, etc. Line graph is a common pattern representation. When I find out the problem that one number is more (less) than the other in senior one, I guide the students to reveal the quantitative relationship with line graphs, so that the problem is intuitive and easy to solve.
Sketch refers to the process of simulating the movement of a specific situation or thing with pictures, such as a problem: the ship first sailed from the south bank to the north bank, and then sailed back to the south bank from the north bank, and kept going back and forth. After ferry crossing 2 1 time, is the ship on the south bank or the north bank? Why?
Under the guidance of the teacher, the students drew a schematic diagram. Through observation, it is concluded that after passing through an odd number of ferries, the ship is on the north shore; After several ferry trips, the ship stopped at the south bank. Because 2 1 is odd, the ship is on the north shore. Drawing is intuitive and clear, and students can easily find ideas to solve problems.
In addition, while guiding students to master and use these methods and strategies, they should also infiltrate some basic mathematical ideas with appropriate materials, such as the transformation thought just mentioned. The most basic form of mathematical problem solving is transformation: transforming unknown problems into known problems, transforming atypical problems into typical problems, and transforming unconventional problems into standard problems. There are also function ideas, set ideas and so on.
(2) Effectively realize two changes in the process of solving problems.
1. Pay attention to the guidance of "problem representation" methods and strategies, and promote the transformation from "problem situation" to "mathematical problem"
For example, when you see "one * * *", you use addition, and when you see "less", you use subtraction; Students who use the problem model strategy will represent each piece of information, understand the relationship between each piece of information, and then build a situational model. For example, there are 30 basketballs in the school gymnasium, 20 basketballs are borrowed from Class 4 (1) and 8 basketballs are returned. How many basketballs are left in Class 4 (1)? If the student thinks that "* * * has 30 basketballs, borrowed 20, and returned 8, so the formula is' 30-20+8'", it shows that he has used the direct conversion strategy; If a student thinks that "because he borrowed 20 and returned 8, the number of returned basketballs is' 20-8', and 30 is redundant information in this question", then the student uses the problem model strategy. In teaching, teachers should give targeted guidance to improve students' ability to use "problem model strategy" to represent problems.
2. Pay attention to the guidance of quantitative relationship analysis and promote the transformation from "mathematical problems" to "solving problems by mathematical methods"
When solving problems, analyzing the quantitative relationship is a "bridge" from "mathematical problems" to "solving problems by mathematical methods". The construction of quantitative relationship should be combined with specific problem situations. In addition to the common mathematical models such as "speed, time, distance" and "unit price, quantity and total price", there is no need to make unified requirements for other quantitative relations. For complex quantitative relations, teachers should guide students to analyze them by drawing and listing. Let's watch a teaching clip: Solving the Problem of Repeated Numbers in the Corner: How many pieces do you need at least if you put 6 pieces on each side of a square? The teacher encourages students to illustrate their ideas by drawing pictures. Results: 1: 6× 2+(6-2 )× 2 = 20 (pieces). I first figured out that the number of pieces on both sides is 12, and the other two sides only need to increase by 4. Health 2: The four pieces on the corner are repeated once each, and I only count one piece on each side, so it is 5×4=20 (pieces). Health 3: The pieces in the corner are repeated once, so it is 6×4-4=20 (pieces). Health 4: The pieces in the corner can be ignored first, so it is 4×4+4=20 (pieces). After the feedback, the second question was raised: How many pieces of 100 should be placed on each side of a square? Let the students put the pictures in their heads first, try to calculate them continuously, and finally draw pictures to verify them. In the above cases, teachers guide students to think with diagrams from simple to complex, from concrete to abstract, and combine mathematical calculation methods, graphs and mathematical language descriptions, which promotes students' understanding of methods and improves their ability to solve problems by using drawing strategies. Of course, the strategies to solve the problem are diversified. Students should be encouraged to choose appropriate methods and strategies according to different problems, and the problem-solving strategies should be internalized into personal mathematical literacy, making it a habit of thinking about problems.
In fact, don't think that elementary school mathematics knowledge is simple. Without the basic theoretical knowledge of mathematics and the vision of advanced mathematics, this seemingly simple work can't be done well. I look forward to studying with you in the future work and making the college questions of primary school mathematics pediatrics!