Briefly describe the characteristics of mathematics core literacy

Characteristics of Mathematics Core Literacy

Mathematics core literacy not only has the attribute of developing students' core literacy, but also has the attribute of mathematics discipline. Lin Chongde believes that core literacy has six characteristics: "core literacy is the most critical and necessary basic literacy that all students should have;" Core literacy is the comprehensive expression of knowledge, ability and attitude; Core literacy can be formed and developed by receiving education; Core literacy has the continuity and stage of development; Core literacy has both personal value and social value; The core literacy of students' development is a system, and its function is comprehensive "[7]. According to the characteristics of the core literacy of mathematics, combined with the understanding of the core literacy of mathematics, the main characteristics of the core literacy of mathematics include comprehensiveness, discipline, criticality, stages and persistence.

We can illustrate several characteristics of mathematics core literacy through an example of "number understanding" teaching.

Teaching fragment of Mathematical Understanding of 1 1-20 [8]:

"1 1-20" is the first time that students formally learn numbers and values on numbers, and it is the beginning of learning decimal counting methods. Although many students have learned these contents before entering school, whether students really understand the representation of decimal numbers and whether students clearly express different numbers on different numbers is related to important mathematical ideas such as "number sense" and number abstraction. In the design of this lesson, teachers focus on the possible confusion of students, and in the process of understanding this knowledge, they highlight the abstraction of mathematics and pay attention to the formation of students' "sense of number". The following passage puts forward a thoughtful question according to students' specific feelings about how the ancients knew numbers and how to express numbers 12 with sticks, which aroused students' discussion and debate.

Teacher: Children, our story continues, remember? Wise ancients used 1 big stone and 1 small stone (1 1). We can also use a bundle of sticks and a stick to represent it (1 1), but the problem is that only two small beads look like this and have the same size.

The following discussion shows that students disagree. Some people think they can, others think they can't. The teacher invited several representatives to the front to discuss and talk about their own ideas. )

Health 1: I think two beads are the same size, which cannot represent 1 1, but only two, that is, two, and cannot represent 1 1. It can also mean 20.

Health 2: When I touch it, it looks like 2, not 20.

Health 3: Use one as a decimal digit and one as a digit, which can represent 1 1.

Health 4: One bead stands for 10 and the other stands for 1.

If you are born as big as 1:, you can't mean 1 1. One is big and the other is small. But are these two beads the same size? Not a big one and a small one. Two beads of the same size, either 2 or 20, cannot represent 1 1.

Teacher: Yes, they all look the same. How do you let everyone know who is 10 and who is 1?

Health 3: Write ten digits on one bead and one digit on the other, which can be distinguished, indicating 1 1.

Teacher: Actually, his idea just now is very similar to that of a mathematician. Mathematicians made counting tools for us. Come and have a look (at the display counter), got it?

Teacher: This is called a counter. Mathematicians helped us invent this. Look, there are many small seats on the counter. From the right, the first one is called "Unit" and the second one is called "Ten".

Teacher: With the help of counter, can it be expressed as 1 1? Let's have a look.

Teacher: Draw a counter on the blackboard and put a small bead on it. What does this mean?

Health: 1 one.

Teacher: Put 1 beads on ten, not 1 one!

Health: This is 1 10.

Teacher: Great. 1 10 and 1 10 add up to 1 1.

In the above teaching clip, the focus of students' argument is whether two identical beads can represent 1 1. The two views are tit for tat. They can express 1 1, but they can't express 1 1. Both of them make sense. In this process, students really think seriously, think with their brains and put themselves into the learning process. Finally, the key to understand this problem is "write ten bits on one bead and one bit on the other", which can be expressed as 1 1. This is the process for students to understand that numbers and numbers on different numbers can represent different values. Starting with the analysis of this teaching clip, we can analyze some characteristics of students' core literacy.

With the help of the above cases, analyze the characteristics of the core literacy of the discipline.

The first is comprehensiveness. Comprehensiveness means that the core literacy of mathematics is the comprehensive embodiment of basic knowledge, basic ability and basic thought of mathematics. The basic knowledge and ability of mathematics can be regarded as the explicit expression of the core literacy of mathematics. In the teaching process of "Understanding Numbers of 1 1-20", some basic knowledge such as understanding numbers, meaning of numbers and representation of numbers are involved. Students need to understand that the number of sticks can be expressed by numbers, and different numbers can be expressed by different numbers. When the numbers 1 1 and 12 need to be expressed, different expressions are produced, which leads to conflicts in students' thinking. When the teacher suggested that "two identical beads can represent 1 1", two different ideas appeared. In the discussion and debate of the two ideas, students' thinking is constantly inspired, and the original knowledge and methods are gradually combined with the present situation, forming a new understanding and cognition of this issue. This process is a process of comprehensive application of knowledge, skills and design methods, which not only has a deep understanding of the knowledge learned, but also forms important mathematical ideas. Core literacy is always based on basic knowledge and basic ability, and it is externalized in the process of solving problems with basic knowledge and basic ability. In this process, the basic ideas of mathematics, learning attitude and other core qualities are always hidden.

The second is discipline. The core literacy of mathematics always has the subject attribute of mathematics, which is closely related to the subject content of mathematics and the characteristics of mathematical thinking. Mathematical knowledge and skills also include the quality of mathematical thinking and the key ability closely related to it. Therefore, the core literacy of mathematics is always related to one or more learning contents, which embodies the characteristics of mathematics itself. The content in the above example is the understanding of logarithm, which is the core content in the field of "number and algebra", and the core literacy related to it is number sense or mathematical abstraction.

The third is the key. Mathematics core literacy is the thinking quality and key ability that students should achieve in the learning process. The design and implementation of mathematics curriculum and teaching requires students to use different ideas, methods, skills and techniques in the process of understanding and mastering knowledge and skills. Not all methods and abilities in mathematics learning can become the core literacy of mathematics. The core literacy of mathematics reflects the development of mathematics, and it is the thought and ability to understand and solve a kind of mathematical problems, not a method that is only suitable for specific content and specific situation. In the above example, when you know numbers, two numbers, five numbers, etc. Are methods of representing numbers, which are suitable for specific situations. For the understanding of numbers, the common method is decimal counting. Students' mastery of numbers with different digits can represent different numerical values, which is not only valuable for understanding numbers within 20, but also valuable for further understanding larger numbers. Therefore, learning the abstract representation of numbers is an important idea for students.

The fourth is the stage. It is useful for students to form core literacy in the process of mathematics learning, which is gradually formed in different learning stages. The stage of mathematics core literacy means that the core literacy is displayed at different levels, and the core literacy of students in different classes is displayed at different levels. In the above example, the content of learning is the beginning of understanding numbers, and students have initially established digital consciousness and experienced the abstraction of numbers. Here, the meaning and expression of numbers are limited to numbers within 20. With the increase of students' grades, the number of students studying is also expanding, from the number within 20 to the number within 100 and 10000, and then from integers to decimals and fractions. The content of understanding number is expanding, and the abstract level of logarithm is also improving. The basic way of thinking is the same, all abstracted from quantity, but the level of thinking is deepening. Numbers on different numbers represent different numbers for the same reason. It is ten, hundred, thousand and ten thousand in the integer range, and ten, percentile and thousandth when it is extended to decimal. When learning fractions, the numbers are expressed differently. Although the representation of numbers is no longer decimal, and different fractional units represent different fractions, the representation of numbers is the same. From the abstract thinking mode of numbers, different stages have different degrees of abstraction, which reflects the different stages of students' abstract thinking. It is a complex problem to divide the levels and levels of mathematics core literacy, and different core literacy also has its own characteristics.

The fifth is persistence. Persistence means that the core literacy of mathematics is the thinking quality and key ability that pays attention to students' lifelong benefit. It not only helps students to understand and master mathematics knowledge, but also will accompany students to further study and move towards future life and society. In the above example, the sense and abstraction of numbers are the abilities that students need to know numbers in primary schools, and middle schools and even universities also need such abilities. Learning mathematics requires abstract ability, and learning other subjects also requires abstract thinking. Learning beyond mathematics learning, as well as practical problems encountered in life and work, also need abstract thinking. Learning abstract thinking mode will accompany students all their lives. This reflects the persistence of this core literacy.