Research On The Current Situation Investigation And Cultivation Strategies Of Mathematics Problem-Posing Ability Of High School Students

The General High School Mathematics Curriculum Standards(2017 Edition Revised 2020)stresses that students’ ability to identify and formulate problems from a mathematical perspective should be improved.With the increase in the national demand for innovative talents in the knowledge economy,cultivating students’ problem-posing ability has gradually become a hot spot in the field of educational research.Based on the requirement of improving the current mathematics classroom teaching,it is of far-reaching practical significance to cultivate students’ problem-posing ability.This paper focuses on "What is the status quo of senior high school students’ ability to present mathematical problems?" "What are the main factors that affect students’ ability of presenting mathematical problems in senior one?" And "Teaching strategies and methods to cultivate high school students’ ability of presenting mathematical problems".Firstly,this study draws on the three levels of development of students’ mathematical problem-posing ability,namely,memorization and manipulation(Level 1),understanding and connection(Level 2),and reflection and extension(Level 3),based on three different problem contexts,namely,free,semi-structured and structured,and using the knowledge content of "function" as the content.The questionnaire was developed based on three different problem contexts: free,semi-structured and structured,using the knowledge of functions as the content;and the literature was reviewed to pre-determine the factors influencing senior secondary students’ ability to formulate mathematical problems.Secondly,interviews were conducted with teachers in order to further understand the current situation of students’ problem-posing ability and the factors influencing it from the teachers’ perspective.On the basis of the survey and interviews,an overall analysis of the current situation and the factors influencing the problem-formulating ability of senior secondary students was conducted.Finally,based on the results of the survey,teaching strategies for developing senior secondary students’ problem-formulating ability in mathematics are proposed with specific examples.In this study,204 senior high school students from two schools in urban and county areas of K city in Henan province were selected as the subjects of the survey,The students were selected from three different subject combinations: "Physics + Chemistry + Biology ","Physics + Chemistry + Geography" and "History+ Politics + Geography".Three research methods,namely documentary analysis,survey method(test paper method and questionnaire method)and data analysis method,were used to study the current situation and factors influencing the problem-solving ability of senior students in mathematics.Five high school mathematics teachers of different genders,titles and years of teaching experience were selected for the interviews.The analysis of the data revealed that:(1)the mathematical problem-solving ability of Upper Secondary students was low,with a low proportion of students asking questions at the reflective and extended level(Level 3),indicating that the mathematical problem-posing ability of Upper Secondary students needs to be improved;(2)there were significant differences in the performance of students’ mathematical problem-posing in three different contexts,with students performing better in the liberalised context,less well in the semi-structured context and weaker in the structured context(3)There were significant differences in students’ mathematical problem-posing abilities between classes with different combinations of subjects,with students in the "Physics + Chemistry + Biology"(traditional science combination)class having higher mathematical problem-posing abilities and the "Physics + Chemistry +Geography"(traditional arts and science combination)class having the second highest.(4)There was no significant difference in students’ ability to ask mathematical questions by gender;(5)There were significant differences in students’ ability to ask mathematical questions by district,with students in urban schools being slightly more able to ask mathematical questions than students in the county.This study analyses the factors affecting students’ problem posing ability from both internal and external dimensions,and draws the following conclusions:(1)Among the internal factors,firstly,first-year students have a single learning style and are not able to think deeply about problems,which is not conducive to the development of students’ problem-posing ability.(2)Among the external factors,firstly,in terms of peers,peer communication and peer atmosphere are significantly and positively related to students’ problem-posing ability.Secondly,in terms of teachers,teachers’ teaching styles had a significant impact on students’ problem-posing skills,and in practice,teachers were less likely to integrate problem-posing activities into the mathematics classroom due to the teaching schedule.Finally,in response to the findings of the study,the following development strategies are proposed:(1)create different contexts to develop students’ awareness of problem formulation;(2)inspire students to think deeply about problems through layers of questions;(3)focus on the overall concept to expand the breadth of students’ problem formulation;(4)pay attention to mathematical language and value students’ tools for expressing problems;(5)enrich learning styles to increase students’ opportunities for problem formulation.(6)Teaching students problem-posing methods and skills in the process of problem solving.