A Cross-sectional Study Of Primary And Secondary School Students’ Mathematical Problem-posing Ability

Problem is the core driving force of discipline development and the prerequisite for human thinking.A good problem can promote long-term and profound thinking.In the rapidly changing information age,starting from the foundation and starting from the discipline,developing students’ mathematical problem-posing ability in the real world is a key step in the cultivation of innovative talents.For primary and secondary school students,an ideal educational state is to start with a simple life situation,guide students to experience the process of discovering,posing and deeply exploring problems from the surface phenomenon,and then think about the changes of personal life and even society.However,the actual situation is that with the growth of age,students’ awareness,courage and ability to actively pose problems have not been significantly improved.Therefore,teaching needs to analyze and understand the specific performance of students in the problem-posing process at different stages,reveal the development law of students’ problem-posing ability,and lay a research foundation for establishing a clear ability goal and training system in the future.In this context,starting from the subject of mathematics,this study takes the students of grade 5 of primary school,grade 2 of junior middle school and grade 2 of senior high school as the research object.This study designs the classroom teaching aimed at investigating the students’ mathematical problem-posing ability,and explores the behavior process of students in different stages to find and pose mathematical problems in the real situation and the development law of their thinking ability.The research questions are as follows:How to design classroom teaching to investigate students’ mathematical problem-posing ability in real situations?What are the specific performance and basis of mathematical problem-posing ability of students in Grade 5 of primary school,grade 2 of junior middle school and grade 2 of senior high school?How do the students’ mathematical problem-posing ability in the three learning stages change and develop?This study uses cross-sectional research as the main method,supplemented by literature research,questionnaire survey,classroom analysis,expert discussion and other research means to answer the above three questions.Firstly,by reviewing the literature,this paper defines the connotation of students’ mathematical problem-posing ability in real situations,and deconstructs it into three sub abilities:the consciousness of posing mathematical problems,the ability to generate practical problems,and the ability to mathematicize practical problems.For each sub ability,the corresponding investigation tools and evaluation framework are formulated by analyzing and referring to the experience and results of previous research.Secondly,based on constructivism,situated learning,socio-cultural theory and activity theory,the main investigation tool of this study is designed: "classroom teaching to investigate students’ mathematical problem-posing ability",and three situations of "life under the COVID-19 ","taxi" and "diet and exercise" are selected to design specific teaching cases.Subsequently,based on the above research work,a pilot survey was carried out and the survey tools and capacity analysis framework were revised.Finally,a formal survey was carried out in the natural classes of grade 5 of primary schools,grade 2 of junior middle schools and grade 2 of senior high schools from three cities in two provinces,including: issuing the "questionnaire on the consciousness of posing mathematical problems";carry out classroom teaching;assign homework after class.This study shows that: in general,the mathematical problem-posing ability of primary and secondary school students shows a development trend of "first rising and then falling" from the second school stage to senior high school stage.There are significant differences in the consciousness of posing mathematical problems,the ability to generate practical problems,the ability to mathematicize practical problems and the perception and understanding of problem situations among students in each learning stage,mainly including:(1)the consciousness of posing mathematical problems decreases significantly with the increase of learning stage,and the curriculum may be the key factor to reduce students’ consciousness and interest in posing problems;(2)The ability of students to generate practical problems shows a spiral trend with the rise of the learning stage,and the behavior characteristics of students in different stages are distinct when they generate practical problems;(3)Students have different "perception" of problem situations.Grade 5 students in primary school are the most "sensitive" to situations,followed by grade 2 students in junior middle school,and grade 2 students in senior high school are the weakest in sensing the situations;(4)The students’ ability to mathematicize practical problems is at the medium level.From the second to the third learning stage,the students’ ability has been significantly improved,but there has been a significant decline in the senior high school stage,falling back to the level slightly higher than that of the students in the second stage;(5)The high level and quality of students’ ability to mathematicize practical problems are lack,that is,the cognitive level of mathematical problems is generally low;(6)There are significant differences in students’ ability to mathematicize practical problems in different situations.Students generally perform better in situations with strong personal experience such as "life under the COVID-19".This study suggests that in the cultivation of mathematical problem-posing ability in the future,we should pay attention to the changes of students’ problem-posing behavior characteristics,formulate multi-dimensional goals for students’ ability development,and cultivate students’ quality of "being able to learn and dare to pose problems,being diligent and good at posing problems".When designing teaching,we should pay attention to the multiple attributes of problem situation and develop activities suitable for different students.In addition,teaching and research also need to tirelessly explore the cognitive mechanism of posing problems to stimulate the rapid growth of students’ ability.This dissertation has made some contributions and innovations in design,practice and theory,which provides some empirical support for promoting the development of students’ mathematical problem-posing ability in the future.