Research On The Present Situation And Training Strategy Of Mathematical Problem Posing Ability Of Sophomore Students

With the advancement of education reform in China in the new era,the mathematical problem-posing ability is increasingly regarded as an important mathematical ability,and as an important part of the "four skills",It not only occupies an important part in the mathematics curriculum standards,but also plays a fundamental role in developing students’ core mathematical literacy and their sense of innovation.Therefore,to strengthen the study of problem-posing in mathematics and to measure the quality of students’ thinking and learning in mathematics based on the problems they pose is crucial to the development of students’ innovation abilities.In this study,literature research method,investigation method(test papers,questionnaires,interviews)and quantitative analysis method are used to investigate and study the current situation,influencing factors and training strategy of mathematical problem-posing ability of senior two students in a middle school in K City,Henan Province.Firstly,based on the literature on problem-posing,constructivist theory and SOLO classification theory,a test paper is developed depend on three different situations consist of free situation,semi-structured situation and structured situation,moreover,a questionnaire is developed based on the internal factors(students)and external factors(teachers,environment,teaching materials).A more scientific evaluation framework is attempted to be constructed,and form effective evaluation criteria to measure the questions raised by students from three dimensions: the rate of questions,the types of questions and the quality of questions,so as to reflect the real performance of the students in posing mathematical questions.Secondly,teacher interviews are conducted to find out more of teachers’ perceptions of the mathematical problem-posing activities and the barriers to teaching in practice,and statistical software is used to analyse the findings and data to identify the main factors affecting students’ problem-posing ability.Finally,the results of the test and questionnaires are then evaluated together with the results of the teacher interviews to suggest strategies for their development.In addition,teaching case is designed based on the training strategies.The current status of the mathematical problem-posing ability of sophomore students are based on the following findings:(1)The overall level of sophomore students’ problem-posing ability is low.In terms of the rate of questions,the majority of students are able to ask questions based on the contextual task,but a few did not;in terms of the type of questions,the students raised less comprehensive questions related to other knowledge;and in terms of the quality of questions,the majority of students are able to give U-level questions,but few give E-level questions.In general,although students have the ability to ask questions,the questions they ask are vague,uneven and of poor quality,and their questioning ability is not high.(2)There are differences in students’ mathematical problem-posing ability about different situations,higher ability to ask questions in semi-structured situations and lower to ask questions in free and structured situations.(3)The students’ academic performance in mathematics is positively related to their scores of the posing mathematical questions test but no significant difference in gender.The main factors influencing students’ mathematical problem-posing ability: all dimensions of the questionnaire are positively correlated with students’ test scores,internal factors,such as students’ interest in posing questions and their own awareness of posing questions,are the main influencing factors;external factors,such as teachers’ teaching style,the classroom learning environment and the set of problem situations in the textbook,are the main influencing factors.In addition,no significant differences are found between boys and girls in their perceptions of these factors.Based on the survey results,this study believes that the following strategies can be adopted to cultivate the mathematical problem-posing ability of sophomore high school students: stimulating students’ interest in asking questions by relying on various problem situations;Teach a variety of questioning methods to strengthen students’ awareness of questioning;Using mathematical representation,standardizing students’ questioning expression;Improve the classroom teaching environment,cultivate students’ questioning habits.The specific teaching case "Ellipse and its Standard Equation" is designed according to these strategies for the reference of front-line teachers.