So far, there is no strict and unified definition of mathematical literacy. Some people think that "mathematical literacy" is a relatively stable psychological state in which people acquire mathematical knowledge, skills, mathematical thinking methods, mathematical ability, mathematical concepts and mathematical thinking quality on the basis of congenital and influenced by acquired environment and mathematical education. In the words of Professor Gu Pei of Nankai University, "mathematical literacy" is what remains after all the mathematical knowledge you have learned has been discharged or forgotten. 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. Understand the world from a mathematical point of view. Second, think in a mathematical way. Third, use mathematical methods to solve problems. First of all, look at the first aspect: 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. There is a display board in the beijing museum of natural history: "1983, in the navigation survey conducted in the northeast, only two tigers were found in the forest of 7,000 square meters, so the Northeast Tiger was listed as a first-class protected animal." Xiao Yang of university of international business and economics thinks that a standard playground is bigger than 7,000 square meters. If there are two tigers in 7000 square meters, the number of tigers should be very large. How can they be listed as first-class protected animals? So why do so many tourists turn a blind eye to this explanation, while Xiao Yangcan finds the problem? On the one hand, I think Xiao Yang is good at observing and thinking, on the other hand, it shows that Xiao Yang has a good sense of numbers. "Sense of number" is the understanding and feeling of logarithmic essence. The essence of numbers is "more and less" or "big and small", thus transitioning to the order of numbers. The problem of "number sense" can be traced back to animal perception. For example, a dog may dare to fight with a wolf, but if there are two wolves, it will be afraid. If faced with a pack of wolves, it will run away. This shows that animals also know "more and less". In Book Number: The Language of Science, it is recorded that a crow built a bird's nest on the watchtower of a manor. The owner of the manor was very angry about this and decided to kill the crow. However, whenever the manor owner enters the watchtower, the crow leaves the nest until the manor owner walks out of the watchtower. The owner of the manor thought of a way. He found a friend, they went in together, and then came out alone, hoping to leave one person to kill the crow, but the crow was not fooled. Then three people go in, two people come out, four people go in, three people come out, it's still the same. It was not until five people went in and four people came out that the crow could not tell the difference and returned to its nest. This shows that crows can understand numbers at least to 4 or 5. If people can't count, how much can they say? Experiments show that people can only distinguish 4 or 5. It can be inferred that in mathematics, after the invention of counting, there is an essential difference between human beings and animals. Only with the concept of "how much" can human beings understand the concepts of "order" and "successor number" Starting from l, with the help of "successor number", a natural number system is formed; The rational number system is formed by four operations of natural numbers; Through algebraic operation of rational numbers, the real number system is finally formed. Therefore, the concept of "how much" and the natural number generated naturally instead of through operation are the most essential concepts of mathematics and the foundation of primary school mathematics. Therefore, cultivating primary school students' "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? Liu Yujie said, "I wear size 20 shoes." Liu Xiangyu said; "Twenty is two in ten digits and zero in one digit." Du Yumeng said, "I have 20 new pencils." Ding Zhonglan said: "20 is much bigger than 1 1." If we don't give children the freedom to speak, we probably won't have a chance to know that the numbers in their hearts have such rich connotations. (2) Go through the symbolization process and cultivate the symbolic consciousness. Russell, a famous British mathematician, said, "What is mathematics? Mathematics is symbols plus logic. " Symbol consciousness mainly refers to the ability to understand and use symbols to express numbers, quantitative relations and changing laws; Knowing symbols can be used for general operations and reasoning. 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 studied "Counting our shoe sizes" last semester, I used students' existing symbolic experience to encourage them to make statistics in their favorite way. Some students write numbers, some draw "√", and some use "○, △" and other graphics to express them. I remember that when Mr. Wang was teaching "Determining the position with number pairs", he first activated 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. Of course, the emergence and development of mathematical symbols are not smooth sailing. For example, the birth and use of Arabic numerals is a long process. We can introduce the history of the birth of numbers to students in combination with the teaching of understanding numbers, so that students can understand the development history of digital symbols and feel the infinite charm of mathematical culture.

China Students' Core Literacy and Its Cultivation

2015165438+1October 17 08:53

Source: "Primary and Secondary School Management" 20 15 No.09 Author: Chutian Yizihao

Abstract: Since 1990s, international organizations, the United States, Singapore and other countries have successively constructed the framework of students' core literacy. China should determine the core literacy according to the requirements of human development and social development, highlight the "key minority" literacy, and concretize the core literacy into a phased requirement for the specific quality development of students of different classes. To cultivate students' core literacy, we need to start with the development of curriculum system, the improvement of teaching methods, the improvement of teachers' quality and the reform of evaluation.

Keywords: core literacy "2 1 century literacy" PISA test interdisciplinary literacy "teacher education 2 1 framework"

National quality determines national competitiveness, and national core literacy determines a country's core competitiveness and international status. Since the 1990s, "core literacy" has become an important topic in the fields of educational policy, educational practice and educational research in various countries around the world, and international organizations and many countries or regions have successively constructed the framework of students' core literacy. Core literacy has become the leading concept of educational reform in all countries, leading and inspiring key educational activities such as curriculum reform, teaching method reform, teachers' professional development and teaching quality evaluation.

First, the core literacy framework for foreign students

Since 1997, international organizations such as the Organization for International Economic Cooperation and Development (OECD), the United Nations Educational, Scientific and Cultural Organization (UNESCO) and the European Union (EU) have successively carried out research on core literacy. Influenced by it, the United States, Britain, France, Germany, Finland, Japan, Singapore, and Taiwan Province Province of China are also actively developing core literacy frameworks. This paper mainly introduces the core literacy framework formulated by several representative international organizations and the United States (representatives of western countries) and Singapore (representatives of Asian countries with the same Confucian cultural background as China).

1. The framework of students' core literacy of three international organizations

From 1997 to 12, OECD launched the project "Definition and Selection of Literacy: Theoretical and Conceptual Basis", and identified nine literacy in three dimensions. (1) You can use tools interactively. Including three qualities: the interactive use of language, symbols and texts; Interactive use of knowledge and information; Interactive use of (new) technologies. (2) Being able to interact in heterogeneous groups. Including three qualities: understanding the external environment, predicting the consequences of one's actions, and being able to determine one's specific actions in a complex environment; Form and implement personal plans or life plans; Knowing your rights and obligations can protect and safeguard your rights and interests, and you also know your limitations and shortcomings. (3) Be able to act independently. Including three qualities: building a good relationship with others; Teamwork; Managing and resolving conflicts. [1] This framework has a direct impact on PISA testing, and then it has an important impact on the core literacy framework formulated by many countries and regions.

From June, 5438 to February, 2006, the European Union passed a proposal on core literacy, which includes eight fields: mother tongue, foreign language, mathematics and scientific literacy, information literacy, learning ability, civic and social literacy, entrepreneurship and artistic literacy, and each field is composed of three dimensions: knowledge, skills and attitude. As the overall target system of EU education and training system, the core idea of these core qualities is to enable all EU citizens to have lifelong learning ability, so as to realize the ideal of personal success and social and economic development in the challenge of globalization and knowledge economy.

20 13 February, UNESCO released the report "Towards lifelong learning-what every child should learn". Based on humanism, the report puts forward the core literacy, that is, the transformation from "instrumental goal" (training students as tools to improve productivity) to "human goal", so that people's emotional, intellectual, physical and psychological potential and quality can be developed through learning. In the basic education stage, we pay special attention to the core literacy in seven dimensions: physical health, social emotion, culture and art, written communication, learning methods and cognition, numbers and mathematics, and science and technology.

2. Core literacy framework of American students

The United States formulated the framework of "2 1 century literacy" in 2002, and released an updated version of this framework in 2007, which comprehensively and clearly presented various literacy and their relationships (see figure 1).

The American "2 1 century literacy" framework takes core disciplines as the carrier and establishes three skill fields, each of which contains several literacy requirements. (1) Learning and innovative skills. Including critical thinking and problem solving, creativity and innovation, communication and cooperation. (2) Information, media and technical skills. Including information literacy, media literacy, information exchange and scientific literacy. (3) Life and vocational skills. Including flexibility and adaptability, initiative and self-guidance, social and cross-cultural skills, work efficiency and ability, leadership and sense of responsibility. [2]

3. Core Literacy Framework for Students in Singapore

20 10 in March, the Ministry of Education of Singapore promulgated the framework of "2 1 century literacy" for Singaporean students (see Figure 2). Among them, the core values include respect, responsibility, honesty, care, persistence and harmony. Social and emotional management skills include self-awareness, self-management, social awareness, interpersonal relationship management and responsible decision-making. Civic awareness, global awareness and cross-cultural communication skills, including active community life, national and cultural identity, global awareness, cross-cultural sensitivity and awareness. Critical and innovative thinking includes rational reasoning and decision-making, reflective thinking, curiosity and creativity, complexity and fuzziness. Communication, cooperation and information skills, including openness, information management, responsible use of information and effective communication.

The teaching of all subjects in the school is to cultivate these qualities, and finally cultivate people who are full of confidence, who can take the initiative to learn, who are actively dedicated and who care about the motherland.

Second, how to determine the core literacy framework of Chinese students?

It is a huge research project to determine the framework and specific indicators of China students' core literacy. On the basis of drawing lessons from the above-mentioned international organizations and national student core literacy frameworks, some principled suggestions are put forward.

1. Determine the core literacy according to the requirements of human development and social development.

The Outline of the National Medium-and Long-Term Education Reform and Development Plan (20 10-2020) proposes to "establish a scientific concept of quality, and take promoting students' all-round development and adapting to social needs as the fundamental standard to measure the quality of education", and also take promoting people's all-round development and adapting to social needs as the standard to formulate the framework of students' core literacy.

Core literacy is a collection of personal qualities necessary for lifelong development, integration into the mainstream society and full employment. These qualities are necessary for children and adults to live a responsible and successful life in a modern democratic society and for society to meet the current and future challenges of technological change and globalization. The purpose of developing core literacy is to cultivate people with work skills and core competitiveness in the 2 1 century, to ensure that the skills learned by students in school can fully meet the needs of subsequent university study or social employment, and to become competent social citizens, employees and leaders in the 2 1 century.

The determination of the core literacy framework must be contemporary and forward-looking. From a global perspective, the selection of core literacy reflects the latest requirements of the development of social economy and scientific and technological informatization, emphasizing innovation and creation, information literacy, international perspective, communication and exchange, teamwork, social participation and social contribution, self-planning and management, etc. Although the contents are different, they are all designed to meet the challenges of 2 1 century. These are all worth learning from.

The determination of core literacy framework should have both personal value and social value, and combine them organically. Personal cultivation can not be divorced from the specific social environment, but should adapt to and promote social change and social progress.

2. Highlight the literacy of "key minority"

Many foreign core literacy frameworks are different, and some take the "comprehensive route", which covers almost all the literacy of students; Some take the "simple route" and only involve some key and high-level literacy. For our country, we think the latter is more suitable.

It is called "core literacy" because these qualities are not ordinary, but "core literacy". The definition of core literacy should be: the "necessary" character and "key" ability needed to adapt to personal lifelong development and social development, and it is the most critical and necessary literacy that all students should have. In other words, core literacy is the "core" knowledge, ability and attitude that students should have in the 2 1 century.

Under the background of globalization, the scope of core literacy will be certain, such as the requirements for information literacy; However, due to different national conditions (such as different key issues facing national development), the content will also be different. As far as China is concerned, there are two core qualities that must be strongly emphasized. The first is the ability to innovate. This is the biggest shortcoming of education in China. The second is democratic literacy. All-round social progress in China requires speeding up the process of political democratization, and further requires cultivating students' democratic literacy.