First, the understanding of the core literacy of mathematics
Mathematics core literacy is the comprehensive ability that mathematics learners should achieve when learning mathematics or learning a certain field of mathematics. Mathematics core literacy is the basic literacy that should be paid special attention to in the process of mathematics teaching and learning. The Mathematics Curriculum Standard for Compulsory Education (20 1 1 Edition) (hereinafter referred to as the Standard) clearly puts forward the core qualities of 10, namely, sense of number, sense of symbol, sense of space, geometric intuition, sense of data analysis, calculation ability, reasoning ability, model thinking, application consciousness and innovation consciousness. In some textbooks, such as Interpretation of Compulsory Education Mathematics Curriculum Standards (20 1 1 Edition), these expressions have been called core concepts, but strictly speaking, it is not appropriate to call these expressions "concepts". They are the overall understanding and grasp of ideas, methods or mathematics, and the expression of students' mathematical literacy. Therefore, it is appropriate to call this expression 10 as the core literacy of mathematics. The core literacy of mathematics can be understood as the comprehensive ability that students should achieve in learning mathematics. Core literacy does not refer to specific knowledge and skills, nor to general mathematical ability. Core literacy is based on mathematical knowledge and skills, which is higher than specific mathematical knowledge and skills. Core literacy embodies the essence and thought of mathematics, which is formed in the process of mathematics learning and is comprehensive, phased and persistent. Mathematics core literacy is directly related to the goal and content of mathematics curriculum, which is of great significance and value for understanding the essence of mathematics, designing mathematics teaching and carrying out mathematics evaluation.
"Mathematical literacy refers to the knowledge that an individual must possess in order to become a caring and thoughtful citizen in his current or future life, as well as the ability to understand the position and ability of mathematics in natural and social life, make mathematical judgments and participate in mathematical activities." [1] It can be seen that mathematical literacy is the quality that people have when they learn to know, understand and deal with things around them through mathematics, and it is usually the way of thinking and the strategy of solving problems when people interact with the surrounding environment. The problems people encounter may be mathematical problems or they may not be obvious and direct mathematical problems. People with mathematical literacy can look at problems with mathematical eyes, think about problems with mathematical thinking methods and solve problems with mathematical methods. For example, when shopping in a supermarket, people often find a long queue in front of the checkout counter, and people who only buy one or two things are also waiting in line with people who buy all kinds of things. When a mathematician saw this situation, he immediately thought of whether it was possible to set up a separate exit for people who bought less things, so as to avoid these people waiting for a long time and greatly improve efficiency. Then the question comes. What do you mean by buying less? 1, 2, 3, 4 yuan. What is the upper limit? How will setting different pieces affect the overall situation of the cashier? So I will think of using statistical methods to collect the number of people who buy different things at different times, and using these data can help people make judgments. In this process, it is reflected from at least two aspects that in the face of such a situation, having certain mathematical literacy is helpful to help people ask and solve problems. The first is the sense of numbers. People with a sense of numbers will consciously associate something with numbers and quantities, and realize that there is a mathematical problem in queuing for checkout. The number of things people buy is related to the speed of checkout. There is also a long queue to buy a few things. On the one hand, there seems to be a long queue at the checkout counter. On the other hand, these people who only buy a few things will have psychological anxiety. Secondly, solving this problem requires the concept of data analysis, and speaking with specific data will convincingly solve this problem. From this example, we can know that having mathematical literacy may help people find, ask and solve problems in specific situations. There may be no obvious mathematical problem in the situation itself.
These core qualities of mathematics put forward by the standard are generally closely related to the content of one or several learning fields. Some core qualities are related to the content of a single learning field. For example, the sense of number, the sense of symbol and the ability of operation are all directly related to the field of "number and algebra". When learning the understanding, operation and letter representation of numbers, they are directly related to these core qualities. The learning process of digital cognition is conducive to the formation of students' sense of number, which is helpful for students to understand and master logarithm. The concept of space is closely related to the field of "graphics and geometry". When learning the understanding of graphics and the relationship between graphics, we should pay attention to the development of students' spatial concept. Students need the support of the concept of space when exploring how many faces a cube has and how to find the surface area that is easy to pull. The concept of data analysis is directly related to the fields of statistics and probability. The whole process of data collection, collation, presentation and judgment is the process in which students form the concept of data analysis.
Some core qualities are closely related to several fields and do not directly point to a single field, including geometric intuition, reasoning ability, model thinking and so on. Geometric intuition will be used to learn graphics and geometry, numbers and algebra. When solving specific mathematical problems, drawing can be used to help understand the quantitative relationship between numbers and algebraic problems. Reasoning ability will be used in several learning fields. Reasoning is often used in geometry, especially in the proof of plane geometry in junior high school. Reasoning is also often used in numbers and algebra. Induction is a common way of thinking in primary school mathematics teaching. Deduction is also often used. The simplest way to express the logic of some operations is actually to use alternative reasoning. For example, when learning "abdication subtraction within 20 years", "looking at subtraction and thinking of addition" is calculated by the method of addition, subtraction, multiplication and division. This process is usually expressed as "because 9+6= 15, 15-9=6". In fact, the premise of "reciprocal operation between addition and subtraction" is not stated here. This premise is a complete deductive reasoning process.
The model idea is also used in Numbers and Algebra, Graphics and Geometry, Statistics and Probability. Such as "hours, minutes, seconds" can be understood from the perspective of establishing a time model. Equation learning is a modeling process. Both number axis and rectangular coordinate system are models to describe spatial position. "The simplest one-dimensional geometric model is a straight line. If the origin, unit and direction are marked on a straight line, such a straight line is called the number axis. "
"Practice consciousness" and "innovation consciousness" are comprehensive and holistic, and they have outstanding performances in the field of "synthesis and practice", but they are not limited to this aspect, but should run through the whole process of primary school mathematics education.
Second, the characteristics of the core literacy of mathematics
According to the above understanding of the core literacy of mathematics, the core literacy of mathematics has the characteristics of comprehensiveness, stages and persistence.
We might as well use an example related to "geometric intuition" to illustrate several characteristics of mathematics core literacy. 20 13 in the teaching of "fractional multiplication" in the 11th national primary school mathematics observation class, the problem to be solved is "How many meters do you knit a scarf every hour 1/5m, 1/2h?" . Teachers instruct students to use graph method to solve 1/5* 1/2=. The teacher guides the students: "If a rectangle is used to represent a scarf with a length of 1 m, what should we draw first, and then what?" Draw pictures in pairs to show this quantitative relationship. Then show the students different representations. There are two typical methods:
The difference between the two methods lies in the second step. Method 1 divides a small rectangle into two parts, just like the first time. Method 2 is divided by drawing a small horizontal line. There seems to be no difference between the two methods, but when the teacher asks why the result is 110, the second method is clearer than the1method. A boy said the key word "add an auxiliary line", which formed the following situation.
In this diagram, we can see that 1/2 of 1/5 is110, that is,1/5 *1/2 =1/kloc-.
With the help of the above cases, let's analyze the characteristics of mathematics core literacy.
The first is comprehensiveness. Comprehensiveness means that the core literacy of mathematics is the comprehensive embodiment of basic knowledge, basic ability, mathematical thinking and mathematical attitude. The basic knowledge and ability of mathematics can be regarded as a comprehensive embodiment. The basic knowledge and ability of mathematics can be regarded as the explicit expression of the core literacy of mathematics. In the process of intuitively expressing fractional multiplication with geometry, we need to use basic knowledge and skills such as the meaning of fraction, the meaning of multiplication, multiplication operation, and expressing fraction with graphics. At the same time, students should think about how to better express this quantitative relationship. This is a comprehensive ability. Core literacy is always based on the basic knowledge and ability of mathematics, and it is externalized in the process of solving problems with basic knowledge and ability. At the same time, the core literacy of mathematics also promotes the profound understanding of basic knowledge of mathematics and the improvement of basic ability of mathematics. Implicit characteristics of mathematical thinking and attitude as the core literacy of mathematics. The formation of core literacy requires a deep understanding and comprehensive application of various relationships between mathematics and mathematics. In this process, mathematical thinking ability, thinking mode and mathematical attitude play an important role, which are often not directly seen, but implied in the process of solving problems. In the above example, the teacher has reminded the students in advance that a scarf with a length of 1 meter is represented by a rectangle, and rectangular paper is prepared for the students to do in advance, and what to draw first and then what to draw. If the teacher does not use such hints, students may make various geometric intuitive representations. This will show students' different ways of thinking and attitudes in the process of learning mathematics.
The second is stage. Stage means that students' mathematical core literacy is manifested in different levels and stages. In the above example, students showed the process of fractional multiplication in different ways. The way and order of dividing a rectangle are different, which shows students' different levels of intuitive application of geometry. Grade five students can show two different quantitative relationships in a picture and understand the relationship between them. Students in lower grades may not reach this level. A picture only represents a quantitative relationship. In junior high school, students can express quantitative relations in more complicated ways, and the level of geometric intuition will be higher. This reflects the different stages of geometric intuition. It is a complex problem to divide the levels and levels of mathematics core literacy, and different core literacy also has its own characteristics. This will be a problem worthy of in-depth study.
Finally, stick to it. Persistence refers to the cultivation of mathematics core literacy, which not only helps students understand and master mathematics knowledge, but also accompanies students to further study and move towards future life and work. In the above example, the ability to express complex quantitative relations in intuitive forms such as charts, as a student's mathematical literacy, can always accompany his study and life. When students go to middle school, university and even life and work, they will consciously use geometric intuitive methods to solve problems, including mathematical problems and problems other than mathematics. This reflects the persistence of this core literacy.
Third, the relationship between mathematics core literacy and related concepts
There are also some concepts closely related to the core literacy of mathematics, such as the basic ideas of mathematics, mathematical thinking methods and so on. According to the above understanding of the core literacy of mathematics, we can try to analyze the relationship between these concepts.
The basic idea of mathematics is one of the "four basics" proposed by the standard, and it is also one of the important goals that students should achieve in the compulsory education stage. The basic idea of mathematics is the reflection of the essential characteristics of mathematical science and the cornerstone of mathematical science. Shi Ningzhong thinks that the basic idea of mathematics "is the idea on which the development of mathematics depends". [3] The basic idea of mathematics is an indispensable idea in the study of mathematics science, and it is also the goal that should be pursued and achieved in learning mathematics, understanding and mastering mathematics. "The development of mathematics essentially depends on three ideas: abstraction, reasoning and model, of which abstraction is the core. Through abstraction, we can get the concepts and operation rules of mathematics in real life, get the development of mathematics through reasoning, and then establish the connection between mathematics and the outside world through models. " [3] Taking abstraction, reasoning and model as the basic ideas of mathematics is in line with the basic characteristics of abstraction, rigor and extensive application of mathematics. Abstraction is the embodiment of abstract thinking, and rigor comes from logical reasoning. Its wide application is precisely to establish mathematical models, link mathematics with practical problems, and solve a wider range of practical problems. For mathematics education, it is necessary and the most basic goal to understand the basic ideas of mathematics on which the development of mathematics science depends. This reflects the basic understanding and grasp of mathematics and the understanding of the basic thinking mode of mathematics.
Mathematical thinking method is used to learn mathematics, especially to solve mathematical problems. Generally speaking, these methods are operable and embody some ideas of mathematics, which are not concrete methods in the general sense. In the process of learning and solving mathematical problems, people have formed some important mathematical thinking methods, such as transformation thinking method, combination thinking method of numbers and shapes, equivalent substitution thinking method, specialization method, exhaustive method and so on. In primary school mathematics education, these thinking methods are often used to solve a kind of mathematics problems. For example, if you learn the area formula of a parallelogram by transformation, you can convert the parallelogram into a rectangle. From the area of the rectangle = length * width, you can know that the area of the parallelogram = bottom * height. Solving equations by equivalent substitution, etc.
From the above understanding, we can try to analyze the relationship between these three concepts. The basic idea of mathematics is the idea that dominates the whole mathematics and mathematics education, which is of great guiding significance to those who study mathematics and study mathematics. Similarly, the basic ideas of mathematics are superior and instructive to the core literacy of mathematics. Or we can understand that the core literacy of mathematics is the concrete expression of the basic ideas of mathematics in learning one or several fields. Mathematical thinking method is a method or ability to realize the core literacy of mathematics and embody the basic ideas of mathematics from the operational level.