Investigation And Research On The Ability Of High School Students To Pose Mathematical Problems On Function

The study of posing mathematical problems is highly valued in mathematics education in various countries.In the curriculum objectives of the "General High School Mathematics Curriculum Standards(2017 Edition,2020 Revision)" in China,it is pointed out to improve students’ ability to pose problems from a mathematical perspective.In the quality description of the three academic quality levels,high school students are also required to be able to abstract mathematical problems in familiar mathematical contexts;Identify problems and propose or transform mathematical problems in related contexts;Propose mathematical problems in a comprehensive context.Professor Silver,a mathematical educator,believes that the ability to solve mathematical problems is highly correlated with creative thinking.Therefore,the ability to pose mathematical problems is not only a requirement for academic quality,but also closely related to creative thinking.Function is the most fundamental concept in modern mathematics and the main thread that runs through high school mathematics curriculum.Studying the ability to pose mathematical problems in the function section is of great significance for the development of students’ problem-solving ability.This study is based on the content of high school mathematical functions.Through literature analysis,the relevant concepts,research status,and existing evaluation models of mathematical problem-solving ability were summarized and analyzed.Based on the SOLO classification evaluation theory,an evaluation model for high school students’mathematical problem-solving ability in the functional part was developed.Based on the model,a survey and research on the mathematical problem-solving ability of high school students in the functional part was conducted.A test questionnaire for the ability to pose mathematical problems in the functional part and a subjective questionnaire for students’ability to pose mathematical problems were developed.A survey was conducted on 217 high school students from 4 classes in two high schools in WZ district.The evaluation perspective covers the mathematical problem-solving ability of students of different genders,classes,and academic achievements.Through setting problem situations to distinguish factors,classroom observation,teacher interviews,and other methods,the factors that affect students’ ability to pose mathematical problems are analyzed,and the following results are obtained:1.Students have a low ability to pose mathematical problems in the function section and are generally at a single structural level.2.There is a significant statistical difference in the problem-solving ability of students with different math grades.The problem-solving ability of students in low to high groups gradually increases,and there is a positive correlation between their math problem-solving ability and math grades.3.There is a significant difference in the ability to solve mathematical problems between the two classes,with experimental class students outperforming ordinary class students.4.There are slight differences in the quantity and quality of mathematical problems posed by students of different genders,with boys outperforming girls in both quantity and quality,but there is no statistical difference.5.There are certain differences in students’ ability to pose problems in different types of situations and representation methods.The ability to pose mathematical problems is highest in both mathematical and real-life situations,and the number and quality of questions raised in problem situations containing charts are higher.Through the analysis of subjective questionnaires,it was found that most students are afraid to ask mathematical problems due to their fear of making mistakes,and the proposed mathematical problems are disconnected from reality.Only a few students will ask mathematical problems from extracurricular resources.The students as a whole are in a dilemma of "high motivation and low behavior".Based on the research results of this article,the author provides corresponding suggestions:(1)establish a formative teaching evaluation mechanism;(2)Returning to the essence of knowledge and constructing a knowledge structure;(3)Strengthen awareness,guide methods,and practice;(4)Strengthen practical connections and focus on the application of knowledge.