Developing And Refining The Developing Progressions For Mathematics Problem Posing In Grades 6,8 And 11 ——Take "Average" As An Example

Problem posing research is an important direction of international mathematics education research and China's education reform.The research on developing progressions put the design research as methodological guideline,took the “average”content with the three grades in elementary school,junior high school and high school as the content carrier,and used certain research methods including literature analysis,interview,questionnaire investigation and classroom observation.Finally,the research would clarify the current state of students' capability in mathematics problem posing about average content.The main purpose of this dissertation was to provide an assessment method that could help teachers understand the process of students' ability development,clarify the current situation of students' ability in each stage of basic education,put forward the goals of students' ability development and corresponding teaching strategies in each stage,and made up the shortfall in research on cross learning stage comparative research and statistics problem posing.The research was primarily composed of three parts,which were hypothesis,validation and revision of developing progressions for mathematics problem posing about average in grades 6,8 and 11.The hypothesis stage included the construction of the evaluation system of students' capability in mathematics problem posing about average content,the preparation of the test papers for students' capability in mathematics problem posing about average content,and the assumptions about the development characteristics of the students' capability in mathematics problem posing about average content.The evaluation system of students' capability in mathematics problem posing about average content was designed by literature analysis of the national curriculum standards and related research on mathematics problem posing.On the basis of grasping the development context of the average content as a whole,an evaluation system was constructed from two aspects: evaluation dimension(process variables)and level division(development levels);Secondly,designed the capability test paper of mathematics problem posing about average content(development evaluation);Finally,combined with the existing research on the current situation of the capability in mathematics problem posing and the results of classroom observations to form a process hypothesis,describe the possible development characteristics of students' capability in mathematics problem posing about the average content,and then clearly verify the hypothesis from four aspects: the learning stage,situation,gender,and academic performance.The validation stage included preresearch and formal investigation.The reliability and validity of the questionnaire were test by the pre-research.Then analyzed the results of the formal investigation to obtain the relationship between learning stage,problem situation,gender,academic performance and students' performance in mathematics problem posing.The revision stage included formulation of development goals and the formulation of teaching suggestions.Based on the investigation results,the development process was revised and a number of teaching recommendations were finally made.The main findings of this research include: 1.Students in semi-structured and free situations showed a decrease in the dimensions of mathematics characteristics that were significantly related to the learning stage.2.There is a critical period for the development of dimensions that are significantly correlated with learning stage.3.With the growth of the learning stage,the comprehensiveness of the mathematical content elements presented in the questions raised by students continues to improve,but the differences between students within the same learning stage also continue to increase.4.In structured,semi-structured and free situations,the performance of students' problem posing showed a gradual decline in essential characteristics and linguistic characteristics,but there was no such trend in mathematical characteristics.5.The relationship between gender,academic performance and students' performance in problem posing is affected by the learning stage.