The following is what I wrote before. You can refer to:
I. Guiding ideology and basic principles of the proposition
1, guiding ideology
Based on teaching materials and curriculum standards, implement the spirit of quality education and curriculum reform, guide and promote mathematics teaching to fully implement the curriculum objectives set by curriculum standards, and promote the transformation from exam-oriented education to quality education, which is embodied in the following aspects:
(1) Give full play to the role of textbooks in teaching, focusing on basic knowledge, basic skills and basic thinking methods, and checking the achievement of curriculum standards.
(2) Guide teachers to pay full attention to the cultivation of ability, including the cultivation of basic computing ability, logical thinking ability and spatial concept, the ability to analyze and solve problems by using mathematical knowledge, and the cultivation of creative thinking ability; Pay full attention to the teaching and learning of mathematical thinking methods.
(3) Guide teachers to attach importance to developing students' sense of number, symbol, space, statistics, application and reasoning ability in mathematics activities, and guide teachers to improve students' mathematics learning methods and improve students' mathematics learning efficiency.
(4) The test questions are for all students, and the test questions are compiled according to their age characteristics, thinking characteristics and life experience, so that students with different cognitive characteristics and different levels of mathematics development can express their mathematics learning status.
2. Basic principles
(1) The examination content is based on the curriculum standards, ensuring that teachers and students can properly teach and learn basic knowledge and skills.
Highlight the evaluation of students' basic mathematics literacy. The test questions first pay attention to the most basic and core content in the curriculum standard, that is, the most important core concepts, thinking methods, basic knowledge and common skills that all students must master in the process of learning mathematics and applying mathematics to solve problems.
(2) Have a comprehensive application of knowledge, which is in line with the actual situation of students in this grade and the requirements of teaching materials and curriculum standards. Pay attention to and implement application-centered and practical application problems.
(3) Open questions, reading comprehension questions and operation design questions are all reflected in the three grades. According to the situation of the three grades, some questions were sorted, adapted and selected.
(4) The difficulty of the test questions is not reflected in the mastery and proficiency of a specific skill or the complexity of the problem itself, but in the examination of students' mathematical thinking level (such as abstraction, diversification, logicality, visualization, etc.). ) and their ability to understand and apply mathematics (such as whether they can gain insight into profound mathematical relations and characteristics, and the effectiveness of using mathematics to solve problems, etc. ).
(5) The problem-solving process embodies the mathematical activities advocated by the curriculum standards, such as observation, experiment, guessing, verification and reasoning. , not just rote learning, imitation and proficiency.
Second, the basic structure of the test questions
(A) the first test paper
1, type and quantity. There are 3 kinds of questions and 26 small questions in the whole volume * * *, including multiple-choice questions 10, 7 fill-in-the-blank questions and 9 answer questions. The score ratio of the three questions is 10: 1 1: 29.
2. Examination content. This semester, students' learning content consists of four parts: rational number, linear equation, preliminary understanding of graphics and data collection. The proportion of each part in the test paper is 35%, 30%, 22% and 65,438+03% respectively. The mathematics knowledge involved in the whole volume covers the first grade listed in the curriculum standard.
(2) The examination paper of Grade Two.
1, type and quantity.
The whole volume * * * consists of three types of questions and 25 small questions, including 8 multiple-choice questions, 7 fill-in-the-blank questions and 10 solutions. The score ratio of the three types of questions is 8: 7: 25.
2. The content of the exam. This semester, students' learning content consists of five parts: the roots of numbers, multiplication and division of algebraic expressions, Pythagorean theorem, translation and rotation, and understanding of parallelograms. The proportions of each part in the test paper are 1 1%, 30%, 8%, 17% and 28 respectively.
(3) the third grade examination paper
1, type and quantity.
There are 3 kinds of questions and 26 small questions in the whole volume * * *, including 8 multiple-choice questions, 7 fill-in-the-blank questions and solutions 1 1. The score ratio of the three types of questions is 8: 7: 25.
2. Examination content. The content of students' study in this semester consists of five parts: fraction, quadratic equation of one yuan, congruence and proof of circle and figure, sample and population. The proportion of each part in the test paper is 20%, 20%, 65,438+00%, 34%, 65,438+06% respectively. The whole volume is involved.
Third, the source of the test questions
There are three main categories: the adaptation of textbook topics, self-compiled questions and the adaptation of questions in some areas, which are the analogy, transformation, extension and expansion of textbook example exercises and questions in the senior high school entrance examination.
Fourth, the characteristics and proposition intention of the main questions
1. The design of the test questions takes into account the differences of students' cognitive styles and thinking personalities, and provides opportunities for candidates with different mathematical thinking characteristics and different mathematical expression tendencies to express their understanding of mathematics through multiple solutions to one question. For example, the 25 questions in the first grade examination paper can be solved by the same angle and complementary angle or the sum and difference of angles. Different spatial concepts determine different thinking levels and different problem-solving methods. It also produced different answering effects. For example, for the six questions in junior high school papers, students with flexible thinking only need to consider whether the sum of the numbers at both ends of the cross box is equal when doing this question, which will save some time when answering questions, and students with average thinking level can also complete it according to the rational number addition rule, which will take a little more time. For example, the 25 questions on junior high school papers better examine students' different thinking levels. Students with good thinking level and strong spatial concept can adopt the method of direct spelling, while students with good thinking level will also have a clear thinking direction-solving by area method, which shows that students have a good grasp of the mathematical thought of combining numbers with shapes. The thinking direction of this problem has been mentioned in the introduction of the first section of chapter 12. There are also different solutions to 23 questions (1) in the third grade examination paper.
2. Improve the discrimination of test questions through the examination of mathematical thinking methods.
All parts of the world have realized that in many industries in today's and future society, there are not too many opportunities to directly use school mathematics knowledge, and it is not fixed, but more influenced and enlightened by mathematical ideas, so as to solve the practical problems faced.
At present, there are two basic ways to deal with mathematical thinking methods in primary and secondary schools: first, students should gradually master mathematical thinking methods, especially some specific and technical methods, such as method of substitution and formula method, mainly through the study of pure mathematical knowledge; Second, by solving practical problems, students can master the required mathematics content and form a basic thinking method that can promote people's quality. Such as experiment, guess, modeling, rational reasoning, system analysis, etc. These two ways of thinking have different orientations. The former tends to be technical, and more is to help students learn the skills to solve specific problems. The latter is more of a general way of thinking and has a wider range of applications.
The requirements of mathematical thinking methods are not mentioned in the curriculum standards. One of the important reasons is that the accumulated research results are not sufficient in defining and describing the mathematical thinking methods suitable for students to understand and master in compulsory education. Mathematical thinking method is the understanding of the knowledge content of mathematics and the essence of the methods used, and it is some viewpoints extracted from some specific mathematical understanding processes. Its correctness has been proved repeatedly in the follow-up research and practice, and it has a certain mathematical thinking method, which should be an important purpose of mathematics curriculum. With the deepening of the research on mathematical thinking methods, it will be strengthened in the curriculum standards.
(1) The examination of mathematical thinking methods combining numbers and shapes, such as 5 questions in Grade One, 16 questions in Grade Two, 22 questions and 25 questions in Grade Three, not only examines students' consciousness of combining numbers and shapes, but also examines their ability to solve problems by combining numbers and shapes.
(2) Discuss the examination of mathematical thinking in different situations. For example, 15 in Grade One and 24 in Grade Three not only examine students' ability to read images, spatial concepts and mathematical intuition, but also examine students' mastery of mathematical thinking methods when discussing problems in different situations. The estimation difficulty coefficient is relatively low, which can better distinguish different thinking levels.
(3) The examination of mathematical thinking methods of functions and equations, such as 25 questions in the third grade examination paper, allows students to experience the mathematical representation process of real questions, examines students' sense of symbols, and examines students' mastery of functions and equations through answering questions.
(4) The examination of the undetermined coefficient method, such as Grade One 13 and Grade Two/4.
(5) Examination of the overall concept, such as questions 15, 22 and 24 in the second grade, and questions 10 and 15 in the third grade.
(6) Examination of statistical concepts, such as 7 questions in Grade One, 17 questions, 2 1 questions, 6 questions in Grade Three, 17 questions and 20 questions. The examination of probability emphasizes the students' understanding level. Traditional probability evaluation often focuses on probability calculation. The probability test in grade three is from qualitative to quantitative.