Research On Mathematics Test Questions Of College Entrance Examination From High Viewpoints ——Taking The Background Of Mathematical Analysis And Advanced Algebra As An Example

Since the issuance of the "General High School Mathematics Curriculum Standards(2017 edition revised in 2020)",the reform of mathematics curriculum has been deepening,which puts forward higher requirements for teachers' mathematical expertise and requires them to understand the nature of mathematical knowledge in middle schools from a high perspective.In addition,the frequent examination questions with advanced mathematics background also put forward higher requirements for students' cognition.Based on this,this thesis takes the examination questions as the carrier and studies the following three questions under the guidance of the idea of high viewpoint:(1)What is the background of mathematics(mathematical analysis,advanced algebra)in the entrance examination questions in China?What is the theoretical basis of background knowledge?(2)What are the strategies for solving the higher mathematics test questions under the high viewpoint?(3)How to compile the mathematics examination questions under the high viewpoint?In order to solve the above problems,we adopt literature analysis,statistical analysis and case analysis.After sorting out and analyzing the reference materials,this thesis selects the mathematics examination questions of the college entrance examination in Fujian and Hubei from 2006 to 2015,and the mathematics examination questions of the national college entrance examination in Zhejiang from 2006 to 2021 as the research objects.From the symbolic language high viewpoint,knowledge content high viewpoint,high level of understanding and solution high viewpoint these four aspects of the collection of test questions,and the following conclusions were drawn:In terms of the background knowledge of advanced mathematics(mathematical analysis,advanced algebra)presented in the college entrance examination mathematics questions from a high perspective.Through horizontal comparison,it is found that there are differences between different regions in the five dimensions of question type distribution,location,primary knowledge points,background knowledge points and the changing trend of the number of questions in the examination of mathematics questions in the high view.After longitudinal comparison,it can be found that the number of math questions in college entrance examination under high viewpoint increased significantly before and after the release of the new curriculum standard.In terms of the theoretical basis of background knowledge of mathematics examination questions in the college entrance Examination from a high perspective,according to the statistical analysis,it is found that the theoretical basis of the background knowledge of mathematical analysis and higher algebra mainly includes five aspects,namely,higher symbol language,basic defining properties,important theorems or formulas,important inequalities and important ideas,presenting the theoretical basis corresponding to the background knowledge and illustrating it with specific examples.In terms of the solving strategies of college entrance examination mathematics questions from a high viewpoint,four solving strategies are given:"pioneering and innovating,looking for relevance","paying attention to concept,understanding essence","accumulating conclusions,proving before using" and "forming intuition with the help of number form".In the aspects of setting high viewpoints test questions,Firstly,the thesis points out that the compilation of high viewpoint examination questions should follow four principles of scientific nature,innovation,selection and appropriateness,and then four methods of direct introduction,specialization,deduction and deformation,and innovation could be used in the preparation of high viewpoint questions.