20 15 Comments on Mathematics Volume of Sichuan College Entrance Examination

20 15 college entrance examination mathematics paper follows the requirements of "Examination Outline" and "Examination Instructions (Sichuan Edition)", which is consistent with the style of examination questions in recent years, conforms to the current mathematics teaching practice, embodies the concept of curriculum reform, conforms to the nature of college entrance examination, and makes innovations on the basis of steady progress. Based on the core and backbone of the subject, the design of test questions fully embodies the scientific value and humanistic value of mathematics, integrates knowledge, ability and quality, deepens the concept of ability, strengthens the intersection of knowledge, focuses on the contents supporting the subject system of mathematics, comprehensively examines the basic knowledge, basic methods and basic ideas, thoroughly examines the candidates' abilities of problem-solving operation, reasoning, abstract generalization, spatial imagination, application consciousness and innovation consciousness, and highlights the examination of mathematical thinking and methods.

The difficulty setting of the whole paper conforms to the current situation of high school students' mathematics learning, attaches importance to the basis of textbook testing, highlights the ability of thinking testing, embodies the exploration of curriculum reform testing, shows the abstraction, logic, application and creativity of mathematics, and highlights the foundation, comprehensiveness, originality and selectivity of test questions. The layout of test papers is reasonable and hierarchical, and the design of test questions is scientific and standardized, which is conducive to accurately testing the learning level of candidates at different levels.

First, attach importance to teaching materials and foundation, and highlight the core content.

The examination questions attach great importance to the exploration and connection of the value of teaching materials. Some questions are directly adapted from the examples or exercises in the textbook, while others are derived from the background of the textbook. The questions of arts and sciences 1-8,11-13,6-19, etc. Because textbooks are higher than textbooks, they give full play to the value of textbooks in understanding mathematics and teaching. This idea and method of writing college entrance examination questions based on textbooks fully guarantees the fairness of the background of the questions, can effectively guide middle school mathematics teaching to attach importance to textbooks and deeply understand them, and has a good guiding role in further promoting curriculum reform and reducing students' excessive academic burden.

The whole volume pays attention to the comprehensive examination of basic knowledge, covering all the knowledge plates of mathematics in the whole high school; The design of test questions is based on the core and backbone of high school mathematics, focusing on functions and derivatives, trigonometric functions, probability statistics, analytic geometry, solid geometry, series, vectors, inequalities and so on. Science 4, 8, 9, 13, 15, 2 1, liberal arts 4, 5, 8, 15, 2 1 etc. , comprehensively examine the basic knowledge such as the concept and properties of functions; Science 5,10,20, liberal arts 7,10,20, etc. It is the basis and main content of analytic geometry to examine the equations of straight lines, circles and conic curves and their simple applications. Science questions 14 and 18 examine the spatial line-plane relationship and the calculation of plane included angle, while liberal arts questions 14 and 18 examine the spatial line-plane relationship, three views and volume calculation; Science 17 questions, liberal arts 3 questions, 17 questions, examine the relevant knowledge of probability statistics; 16 liberal arts and science questions, examining the relevant knowledge of the series; The third question of liberal arts examines the concept of stratified sampling, requiring candidates to understand its essential attributes; Science 14 the calculation of the angle of the inspection space line. If the concept is unclear, even if the operation is correct, the correct result cannot be obtained. This content design not only comprehensively examines the foundation, but also highlights the contents supporting the subject system, attaches importance to the examination of basic knowledge and general methods, focuses on the mathematics foundation and literacy of high school graduates, and ensures the content validity of the test paper, which is conducive to paying attention to the foundation, strengthening the core content and main knowledge, and returning to the essence of mathematics in middle school mathematics teaching.

Second, pay attention to abilities and methods and strengthen mathematical thinking.

The test paper is designed for the purpose of ability, and examines the abilities of operation and solution, reasoning and demonstration, spatial imagination, abstract generalization, data processing, application consciousness and innovation consciousness from multiple angles and levels. On this basis, the comprehensive and profound examination of mathematical thinking is particularly highlighted. A large number of topics fully examine mathematical thinking methods and abilities such as observation, association, analogy, conjecture and estimation, and comprehensively examine mathematical thinking such as functions and equations, combination of numbers and shapes, classification and integration, transformation and transformation, and special and general. The questions of science 15, 16, 2 1 and liberal arts 15, 2 1 not only examine intuitive thinking such as geometric intuition, association, conjecture and estimation, but also require candidates to calculate accurately and reason strictly; Science 13, 17, liberal arts 8, 17, investigated the problem-solving operation ability and application consciousness; Arts 15 questions, examining intuitive conjecture, abstract generalization, reasoning and innovative consciousness, comprehensively examining mathematical thinking, characterized by small calculation and big thinking; Arts and sciences, 16-2 1 and other questions focus on solving the ability of operation and reasoning; 20 questions and 2 1 questions in arts and sciences require candidates to have a high level of abstract generalization ability, reasoning and argumentation ability, operational solving ability, mathematical inquiry consciousness and innovation consciousness, and examine a variety of mathematical thinking methods.

The whole volume focuses on students' understanding and application of basic concepts and important theorems of mathematics, and focuses on controlling and reducing tedious operations. Science 7,9, 10, 14, 15,20,21,liberal arts 7,9, 10, 14,15. Although arts and sciences 15 requires high thinking, on the basis of deeply understanding the essence of the problem, it does not need special skills and complicated operations to solve the problem through the combination of functions and equations, numbers and shapes. This kind of problem has profound background, ingenious conception, appropriate materials and reasonable and practical problems. It focuses on the examinee's understanding and application of knowledge, emphasizing scientific, rigorous, abstract, exploratory, comprehensive and applied examination, which can effectively test the examinee's ability to transfer knowledge and methods to different situations, thus testing the examinee's thinking breadth, depth and potential for further study.

Third, pay attention to exploration and innovation, and embody the concept of curriculum reform.

The test paper sets the question situation from the height of the whole discipline and thinking value, and pays attention to the internal connection and intersection between knowledge; By properly enhancing the comprehensiveness of the test questions and setting the difficulty of the test questions at different levels, the selection function of the test can be better reflected. The 9 questions of science involve monotonicity of functions, linear programming and basic inequalities, and the 9 questions of arts and sciences 10 involve the idea of parabola, circle, tangent of circle and combination of numbers and shapes, which is comprehensive and difficult. Science 19 is a combination of triangular congruence transformation and triangular solution, with clear conception, novel situation and beautiful form, which tests the flexibility of candidates' thinking; Based on the knowledge of logarithmic function, quadratic function, derivative, zero point of function and inequality, the 2 1 question examines the ability of candidates to comprehensively apply mathematical knowledge, mathematical methods and mathematical ideas. This kind of test questions requires high flexibility, profundity and creativity in mathematical thinking, which is difficult to some extent. To answer these questions, you need to have a strong ability to analyze, explore and solve problems.

The design of test questions closely combines the characteristics of mathematics, and fully embodies the concept of curriculum reform by examining the consciousness of inquiry, application and innovation. The questions of 10, 15, 20, 2 1 examine the consciousness of inquiry. Candidates need to deeply analyze the situation of the question, from special to general, from intuitive to abstract, from different sides to explore, rationally use the corresponding mathematical methods and ideas, and answer accurately and quickly. The 20 questions in science require candidates to explore the existence of fixed points. If it is assumed that the coordinates of fixed points are directly solved, there are many operational obstacles. It is relatively simple to solve general and moving problems by solving special situations and abstractly summarizing specific objects. This kind of question design examines candidates' awareness of inquiry and innovation, and ensures that the questions can distinguish candidates with higher learning level. The questions of science 13, 17, liberal arts 8 and 17 examine the ability of candidates to refine quantitative relations, turn real problems into mathematical problems and build mathematical models to solve them, which embodies the characteristics of application consciousness and practical ability. The 2 1 question of arts and sciences shows the abstraction and rigor of mathematics, and requires candidates to have a high level of rational thinking. Candidates can use the idea of "intuitively connecting geometry, exploring ways to solve problems, making reasonable guesses, constructing auxiliary functions, combining actuarial estimation and reasoning to prove" when answering. The whole process of answering questions is basically the same as that of mathematical research, which can better promote candidates to master mathematical knowledge, explore mathematical problems and discover mathematical laws in the process of mathematical learning. These questions have the characteristics of far-reaching, profound background and ingenious questions, and are full of thinking value, which embodies the concept of curriculum reform and is a good material to test the breadth, depth and learning potential of candidates' rational thinking. This design is reasonable and scientific in evaluating candidates. It encourages active, active and inquiry-based learning, which is helpful to guide middle school mathematics teaching to focus on improving students' thinking ability, developing application consciousness and innovation consciousness, and plays a very positive role in comprehensively deepening curriculum reform and improving middle school mathematics teaching quality.