A case study on the combination of junior high school mathematics and traditional culture

Mathematics is a process in which people qualitatively grasp and quantitatively describe the objective world, gradually abstract and generalize, form methods and theories, and widely apply them.

Since the middle of the 20th century, great changes have taken place in mathematics itself, especially the combination with computers, which makes mathematics in the research field.

The research method and application scope have been expanded unprecedentedly.

Mathematics can help people better explore the laws of the objective world, make appropriate choices and judgments on a large number of complex information in modern society, and provide an effective and simple means for people to exchange information.

Mathematics, as a universally applicable technology, helps people to collect, sort out and describe information, establish mathematical models, and then solve problems and directly create value for society.

The basic starting point of mathematics curriculum in compulsory education stage is to promote students' all-round, sustained and harmonious development.

We should not only consider the characteristics of mathematics itself, but also follow students' psychological laws in learning mathematics, and emphasize that starting from students' existing life experience, students should experience the process of abstracting practical problems into mathematical models and explaining and applying them, so that students can gain an understanding of mathematics and make progress and development in thinking ability, emotional attitude and values.

I. Basic concepts

1, mathematics curriculum in compulsory education stage should highlight the foundation.

Popularization and development make mathematics education face all students and realize.

Everyone learns valuable mathematics; Everyone can get the necessary mathematics; -Different people get different development in mathematics.

2. Mathematics is an indispensable tool for people's life, work and study, which can help people to process data, calculate, reason and prove, and mathematical models can effectively describe natural and social phenomena; Mathematics provides language, ideas and methods for other sciences, and is the foundation of all major technological developments; Mathematics plays a unique role in improving people's reasoning ability, abstract ability, imagination and creativity. Mathematics is a kind of human culture, and its content, thought, method and language are important components of modern civilization.

3. Students' mathematics learning content should be regular, meaningful and challenging, which should be conducive to students' active observation, experiment, guess, verification, reasoning and communication.

Content should be presented in different ways to meet diverse learning needs.

Effective mathematics learning activities cannot rely solely on imitation and memory. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics.

Because of the different cultural environment, family background and their own way of thinking, students' mathematics learning activities should be a lively, proactive and personalized process.

4. Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience.

Teachers should stimulate students' enthusiasm for learning, provide them with opportunities to fully engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication, so as to gain rich experience in mathematical activities.

Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning.

5. The main purpose of evaluation is to fully understand the students' mathematics learning process, motivate students' learning and improve teachers' teaching; An evaluation system with multiple evaluation objectives and methods should be established.

The evaluation of mathematics learning should not only pay attention to students' learning results, but also pay attention to their learning process; Pay attention to students' mathematics learning level.

In mathematics activities, we should pay more attention to their emotions and attitudes to help students know themselves and build up their confidence.

6. The development of modern information technology has a great influence on the value, goal, content and the way of learning and teaching of mathematics education. In the design and implementation of mathematics curriculum, we should attach importance to the application of modern information technology, especially give full consideration to the influence of calculators and computers on the contents and methods of mathematics learning, vigorously develop and provide students with richer learning resources, regard modern information technology as a powerful tool for students to learn mathematics and solve problems, and strive to change students' learning methods so that students are willing and have more energy to put into practice.

Second, the design ideas

(1) About the learning period

In order to reflect the integrity of the mathematics curriculum in the compulsory education stage, the Mathematics Curriculum Standard for Full-time Compulsory Education (Experimental Draft) (hereinafter referred to as the Standard) comprehensively considers the contents of the nine-year curriculum. At the same time, according to the physiological and psychological characteristics of children's development, the nine-year study time is divided into three sections.

The first phase (1 ~ 3 grades), the second phase (4 ~ 6 grades) and the third phase (7 ~ 9 grades).

(2) About the goal

According to the Outline of Basic Education Curriculum Reform (Trial) and the characteristics of mathematics education, the Standard defines the overall goal of mathematics curriculum in compulsory education, and further expounds it from four aspects: knowledge and skills, mathematical thinking, problem solving, emotion and attitude.

The standard not only uses target verbs such as "knowing (understanding), understanding, mastering and using flexibly" to describe knowledge and skills, but also uses process verbs such as "experiencing (feeling), experiencing (understanding) and exploring" to describe the level of mathematical activities, thus better reflecting the requirements of the standard for students in mathematical thinking, problem solving, emotion and attitude.

Knowledge and skill objectives

Recognizing can recognize or explain the relevant characteristics (or meanings) of the object from specific examples; According to the characteristics of the object, the object can be identified from the specific situation.

Understanding can describe the characteristics and origin of objects; Can clearly explain the difference and connection between this object and related objects.

Mastery can apply objects to new situations on the basis of understanding.

Flexible application can comprehensively use knowledge and flexibly and reasonably select application-related methods to complete specific mathematical tasks.

Program objective

Experience (feel) in specific mathematical activities and get some preliminary experience.

Experience Participate in specific mathematical activities, get a preliminary understanding of the characteristics of objects in specific situations, and gain some experience.

Explore and actively participate in specific mathematical activities, and discover some characteristics of objects or differences and connections with other objects through observation, experiment, reasoning and other activities.

(3) About learning content

In each learning section, the standard covers four learning fields: number and algebra, space and graphics, statistics and probability, practice and comprehensive application.

The study of course content emphasizes students' mathematical activities and cultivates students' sense of number, symbol, space, statistics, application and reasoning.

The sense of number is mainly manifested in: understanding the meaning of number; Numbers can be expressed in many ways; Be able to grasp the relative size relationship of numbers in specific situations; Able to express and exchange information with numbers; Can choose the appropriate algorithm to solve the problem; Can estimate the result of operation and explain the rationality of the result.

The sense of symbol is mainly manifested in: it can abstract the quantitative relationship and changing law from specific situations and express it with symbols; Understand the quantitative relationship and changing law represented by symbols; Will be converted between symbols; Can choose appropriate programs and methods to solve the problem of symbol representation.

The concept of space is mainly manifested in: you can imagine the geometric figure from the shape of the object, imagine the shape of the object from the geometric figure, and transform the geometric body into its three views and expanded drawings.

Can make three-dimensional models or draw graphics according to conditions; Can separate basic graphics from more complex graphics, and can analyze basic elements and their relationships.

Can describe the movement and change of physical objects or geometric figures; Can describe the positional relationship between objects in an appropriate way; Can use graphics to describe problems vividly and use intuition to think.

The concept of statistics is mainly manifested in: being able to think about problems related to data information from the perspective of statistics; Be able to make reasonable decisions through the process of collecting data, describing data and analyzing data, and realize the role of statistics in decision-making; Can reasonably question the source of data, the method of processing data and the results obtained from it.

The application consciousness is mainly manifested in: recognizing that there is a lot of mathematical information in real life and that mathematics has a wide range of applications in the real world; In the face of practical problems, we can actively try to use the knowledge and methods we have learned from the perspective of mathematics to find strategies to solve problems; When faced with new mathematical knowledge, we can actively look for its actual background and explore its application value.

Reasoning ability is mainly manifested in: being able to obtain mathematical guesses through observation, experiment, induction and analogy. , and further proof, proof or counterexample; Be able to express your thinking process clearly and methodically, and be reasonable and well-founded; In the process of communicating with others, I can discuss and ask questions logically in mathematical language.

In order to reflect the flexibility and selectivity of mathematics curriculum, the standard only stipulates the basic level that students should reach in the corresponding learning period. Textbook editors, schools, especially teachers should teach students according to their learning desire and the possibility of development.

At the same time, the standard does not stipulate the presentation order and form of the content, and the teaching materials can be arranged in many ways.

(iv) Recommendations on implementation

The Standard puts forward some suggestions on teaching, evaluation, textbook compilation and the utilization and development of curriculum resources.

For the reference of relevant personnel, so as to ensure the smooth implementation of the standard.

In order to explain and explain the corresponding curriculum objectives or curriculum implementation suggestions, the standard also provides some cases for reference.

The second part of the curriculum objectives

First, the overall goal

Through mathematics study in compulsory education, students can:

● Obtain important mathematical knowledge (including mathematical facts and experience in mathematical activities) necessary to adapt to future social life and further development, as well as basic mathematical thinking methods and necessary application skills;

● Initially learn to observe and analyze the real society by using mathematical thinking mode, solve problems in daily life and other disciplines, and enhance the awareness of applied mathematics;

Experience the close relationship between mathematics and nature and human society, understand the value of mathematics, enhance the understanding of mathematics and the confidence to learn mathematics well;

● Have the initial innovative spirit and practical ability, and fully develop their emotional attitude and general ability.

Details are as follows:

Knowledge and skills

Experience the process of abstracting some practical problems into numbers and algebra, master the basic knowledge and skills of numbers and algebra, and solve simple problems.

Experience the process of exploring the shape, size, position relationship and transformation between objects and graphics, master the basic knowledge and skills of space and graphics, and solve simple problems.

● Having experienced the process of asking questions, collecting and processing data, making decisions and forecasting, mastering the basic knowledge and skills of statistics and probability, and being able to solve simple problems.

Mathematical thinking

Experience the process of describing the real world with mathematical symbols and figures, establish a preliminary feeling of numbers and symbols, and develop abstract thinking.

Enrich the understanding of real space and graphics, establish a preliminary concept of space, and develop thinking in images.

● Experience the process of describing information, inferring and developing statistical concepts with data.

● Experience observation, experiment and guess.

Prove and other mathematical activities, develop the rational reasoning ability and deductive reasoning ability in the first step, and be able to explain your point of view in an orderly and clear way.

solve problems

● Initially learn to ask and understand questions from the perspective of mathematics, and can comprehensively use the knowledge and skills learned to solve problems and cultivate application awareness.

● Form some basic problem-solving strategies, experience the diversity of problem-solving strategies, and cultivate practical ability and innovative spirit.

● Learn to cooperate with others and communicate the process and results of thinking with others.

● Initially form a sense of evaluation and reflection.

Emotion and attitude

● Be able to actively participate in mathematics learning activities, and have curiosity and thirst for knowledge about mathematics.

● Get a successful experience in mathematics learning activities.

Exercise the will to overcome difficulties and build self-confidence.

● Understand the close relationship between mathematics and human life and its role in the development of human history. Experiencing mathematics activities is full of exploration and creation, feeling the rigor of mathematics and the certainty of mathematical conclusions.

● Form the attitude of seeking truth from facts and the habit of questioning and thinking independently.

The goals of the above four aspects are a closely linked organic whole and play a very important role in human development. They are realized in colorful mathematical activities.

Among them, the development of mathematical thinking, problem solving, emotion and attitude can not be separated from the learning of knowledge and skills, and the learning of knowledge and skills must be based on the premise of being conducive to the realization of other goals.

Second, the goal of the learning period

The third stage (grades 7-9)

Knowledge and skills

● Experience the process of abstracting numbers from daily life, and know numbers, decimals, simple fractions and common quantities within 10,000; Understand the meaning of four operations and master the necessary operation skills (including estimation).

Experience the process of intuitive understanding of simple geometry and plane graphics, understand simple geometry and plane graphics, feel the phenomenon of translation, rotation and symmetry, can initially describe the relative position of objects, and gain the skills of preliminary measurement (including estimation), map recognition and drawing.

● Experience in data collection, sorting, description and analysis, and master some simple data processing skills; I felt uncertain at first.

Experience the process of abstracting the relationship between numbers and simple numbers from real life, know the numbers within 100 million, and understand the meanings of fractions, percentages and negative numbers.

Master the necessary calculation (including estimation) skills; To explore the hidden laws in a given thing, we can use equations to express simple quantitative relations and solve simple equations.

Experience the process of exploring the relationship between the shape, size, movement, position and graphics of an object, understand the basic characteristics of simple geometry and plane graphics, transform simple graphics, initially determine the position of the object, and develop skills such as measurement (including estimation), map recognition and drawing.

● Experience the process of collecting, sorting, describing and analyzing data, and master some data processing skills; Experience the equal possibility of events and the fairness of game rules, and you can calculate the possibility of some simple events.

● Go through the process of abstracting symbols from specific situations and know rational numbers, real numbers, algebraic expressions, equations, inequalities and functions; Master the necessary calculation (including estimation) skills; Exploring the quantitative relationship and changing law in specific problems can be described by algebra, equations, inequalities and functions.

Experience the process of exploring the basic properties, transformation and positional relationship of objects and figures, master the basic properties of triangles, quadrilaterals and circles, as well as the basic properties of translation, rotation, axial symmetry and similarity, initially understand projections and views, and master basic skills such as map reading and drawing; Knowing the necessity of proof can prove the basic properties of triangles and quadrangles and master the basic reasoning skills.

● Engaged in the activities of collecting, describing, analyzing data, making judgments and communicating, feeling the necessity of sampling, understanding the idea of using samples to estimate the population, and mastering the necessary data processing skills; If we further enrich the understanding of probability and know the relationship between frequency and probability, we will calculate the probability of some events.

Mathematical thinking

● Be able to use life experience to explain relevant digital information, and initially learn to describe simple phenomena in the real world with specific numbers.

● Develop the concept of space in the process of exploring the shape, size, positional relationship and movement of simple objects and figures.

● With the help of the teacher, initially learn to select useful information for simple induction and analogy.

● Be able to think simply and methodically in the process of solving problems.

● Be able to reasonably explain the digital information related to real life, and describe and solve simple problems in the real world with numbers, letters and charts.

● Further develop the concept of space in the process of exploring the position relationship of objects, the characteristics of graphics, the transformation of graphics and the design of patterns.

● Be able to collect useful information according to the needs of solving problems, conduct induction, analogy and speculation, and develop initial rational reasoning ability.

● In the process of solving problems, be able to think methodically and make a convincing explanation for the rationality of the conclusion.

● Be able to reasonably explain and infer large digital information in specific situations, and describe the relationship between things with algebraic expressions, equations, inequalities and functions.

● In the process of exploring the essence of graphics, the transformation of graphics and the mutual transformation between plane graphics and space geometry, the concept of space is initially established and geometric intuition is developed.

● Ability to collect, select and process mathematical information, and make reasonable inferences or bold guesses.

● Some mathematical conjectures can be tested by examples, so as to increase the credibility of conjectures or overturn conjectures.

● The necessity of experience proof.

Develop primary deductive reasoning ability.

solve problems

● Be able to find and ask simple math problems from daily life under the guidance of teachers.

There are different solutions to understand the same problem.

● Experience in solving problems in cooperation with peers.

● Initially learn to express the general process and results of solving problems.

● Be able to find and put forward simple mathematical problems from real life.

● Be able to explore effective methods to solve problems and try to find other methods.

● Can solve problems with the help of a calculator.

● Initially learn to cooperate with others in problem-solving activities.

Can express the process of solving problems and try to explain the results.

● Have the consciousness of reviewing and analyzing the problem-solving process.

● Be able to find and put forward mathematical problems in combination with specific situations.

Try to find solutions to problems from different angles and solve problems effectively, and try to evaluate the differences between different methods.

● Understand the importance of cooperation with others in solving problems.

● Be able to clearly express the problem-solving process with words, letters or charts, and explain the rationality of the results.

● Gain experience in solving problems through reflection on the process of solving problems.

Emotion and attitude

● With the encouragement and help of others, I am curious about some math-related things around me and can actively participate in vivid and intuitive math activities.

With the encouragement and help of others, I can overcome some difficulties in math activities, gain successful experience, and have the confidence to learn math well.

Understand that some phenomena can be described by numbers and shapes, and feel the close connection between mathematics and daily life.

Experience the process of learning mathematics such as observation, operation and induction, and feel the rationality of thinking about the mathematical process.

● Under the guidance of others, be able to find mistakes in mathematics activities and correct them in time.

I am curious about some things related to mathematics in the surrounding environment and can actively participate in mathematics activities organized by teachers.

With the encouragement and guidance of others, I can actively overcome the difficulties encountered in mathematics activities, have successful experience in overcoming difficulties and using knowledge to solve problems, have a certain grasp of the correctness of my own results, and believe that I can make continuous progress in my study.

● Experiencing mathematics is closely related to daily life. I realize that many practical problems can be solved by mathematical methods and expressed and communicated in mathematical language.

Through observation, operation, induction, analogy, reasoning and other mathematical activities, we can experience the exploration and challenge of mathematical problems and feel the order of mathematical thinking process and the certainty of mathematical conclusions.

● Be conscious of asking questions about places you don't understand or different viewpoints, be willing to discuss mathematical problems, and correct mistakes in time when found.

● Willing to contact with mathematical information in the social environment, willing to talk about some mathematical topics, and able to play an active role in mathematical activities.

Dare to face the difficulties in mathematics activities, have successful experience in overcoming difficulties independently and solving problems with knowledge, and have confidence in learning mathematics well.

Experiencing numbers, symbols and figures is an important means to effectively describe the real world, recognizing that mathematics is an important tool to solve practical problems and communicate, and understanding the role of mathematics in promoting social progress and developing human rational spirit.

Understanding can be obtained through observation, experiment, induction, analogy and reasoning. Experiencing mathematics activities is full of exploration and creativity, feeling the necessity of proof, the rigor of proof process and the certainty of conclusion.

On the basis of independent thinking, actively participate in the discussion of mathematical problems, dare to express their own views, respect and understand the opinions of others; Can benefit from communication.