First, the object, content and method of investigation.
In this survey, we selected physics, chemistry, computer, engineering, machinery, electrician, radio, literature, art, history, politics, agriculture, forestry and fisheries, geography and economics as the main survey objects. See Appendix I for the survey contents. The survey methods include questionnaire survey, interviews and questions, data collection and other forms.
Second, the conclusion of the investigation.
1. Understanding of mathematics.
The survey results show that mathematics is more and more widely used in all aspects of production and life in modern society, and mathematics has penetrated into all walks of life and various professional directions. From satellites to nuclear power plants, from weather forecast to family life, high-tech features such as high precision, high speed, high automation, high quality and high efficiency are all realized through mathematical models and methods and computer control. The design and manufacture of products and engineering, product quality control, prediction and management in economy and science and technology, information processing, resource development and environmental protection, and economic decision-making all need the application of mathematics. In addition, mathematical culture and mathematical thinking methods also affect people's production and life everywhere.
2. Investigation on the use of current high school mathematics teaching content.
In this survey, the current high school mathematics textbooks (compulsory books) used in two provinces and one city and the original high school mathematics textbooks 15 used in ten provinces and cities are divided into four aspects: frequent use, occasional use, occasional use and non-use (see appendix 1). The results of the survey are as follows (all parties disagree, rough statistics).
Commonly used: set and simple logic, analytic formula of function, image, power function, exponential function, nature of inequality, solution of unary quadratic inequality, proof of inequality, solution of arbitrary triangle, general term formula of sequence, arithmetic progression, geometric progression, curve and equation, linear equation, image solution of two-dimensional linear inequality, simple linear programming problem, intuitive drawing of plane graphics, addition principle, multiplication principle, arrangement and arrangement. Formula of combination and combination number, meaning of probability, probability of equal possible events, occurrence probability of mutually exclusive events, occurrence probability of independent repeated test, distribution list of discrete random variables, expected value, variance, sampling method, normal distribution, linear regression, limit of sequence, limit of function, continuity of function, meaning of derivative, derivation of elementary function, maximum and minimum of function, indefinite integral of simple function, and graph.
Sometimes it is used: mapping, inverse function, exponential function, logarithmic function, mathematical induction, operation of plane vector, coordinate representation of plane vector, quantitative product of plane vector, inductive formula of trigonometric function, image and properties of trigonometric function, equation of circle, parabola and its standard equation, plane and its basic properties, space vector and its operation, processing geometric problems with space vector, estimation of overall distribution, derivative of compound function and differential operation. Using derivatives to study the properties of functions, finding definite integrals of simple functions, basic formulas of calculus, other applications of integrals, solving exponential inequalities, and vector representation of complex numbers.
Occasionally used: solving irrational inequalities, solving logarithmic inequalities, the positional relationship between straight lines and planes, polyhedron, prism, sphere, ellipse and its standard equation, hyperbola and its standard equation, simple geometric properties of ellipse, hyperbola and parabola, binomial theorem, complex number operation.
Basically, there is no need for: the positional relationship between planes, straight lines on different planes, the sum and difference product of trigonometric functions, and the triangular operation of pyramids and complex numbers.
3. Investigation on whether it can be included in the new high school mathematics curriculum.
The 24 knowledge items listed in this survey can be investigated from two aspects (see appendix 1), and the results are as follows (opinions from all directions are inconsistent, rough statistics).
It can include: estimation, algorithm, vector and transformation, determinant, algebraic operation of matrix (mainly two-dimensional), logical quantifier, preliminary discrete mathematics, recursion of sequence, conditional probability, probability density, distribution table, expectation and variance of continuous random variables, interval estimation, correlation coefficient, binomial distribution, inquiry problem, problem solving by graphic calculator, and inquiry of computer and mathematical modeling.
It is considered that it cannot include: iterative method for solving equations, matrix and geometric transformation, exponential form of complex number, complex number and trigonometric transformation, regression function, integral of compound function and step-by-step integration.
For other parts of this survey, such as which mathematical thinking methods should be emphasized and which mathematical abilities should be emphasized, the functions and significance of "solid geometry", "analytic geometry" and "trigonometric function" in the current high school textbooks are under investigation. In addition, according to Appendix I and Appendix II, an online survey is also under way.