Developing And Refining The Developing Progressions For Mathematics Problem Posing In Grades10-11

Developing progressions for mathematics problem posing are empirically grounded and testable hypotheses about how students’understanding of, and ability to pose mathematics problem and explanations and related problem posing activities grow and become more sophisticated over time, with appropriate instruction. These hypotheses describe the pathways students are likely to follow to the mastery of mathematics problem posing.The research on developing progressions was based on revised Bloom’s Taxonomy of Educational Objectives, put the design research as methodological guideline, learned from the research paradigm of learning progressions, and adopted some research methods including literature analysis, questionnaire investigation and teaching model. The research process of developing progressions included how to propose, validate and revise the hypotheses about mathematics problem posing, finally obtaining the revised developing progressions for mathematics problem posing. The main purpose of this dissertation was to make up the shortfall in research on domestic mathematics problem posing to improve the valid integration of mathematics competency evaluation system, educational research and teaching practice of mathematics competency, where the mathematics problem posing was vague in definition and unclear in evaluation index.The research was mainly composed of three parts:The first one was to pose the hypotheses of developing progressions for mathematics problem posing in grades10-11. The hypotheses include the target performances or developing goals, progress variables, levels of achievement and developing performances. First of all, the progress variables and levels of achievement were designed by literature analysis of the national curriculum standards and related research on mathematics problem posing. And then, the real levels of achievement and developing performances of students were decided by the questionnaire survey, which was performed among grades10-11students from3different schools. The target performances or developing goals were specified by the integration of literature analysis and questionnaire survey results. The hypotheses of developing progressions also embraced the corresponding instruction advice about mathematics problem posing.The second one was to validate the hypotheses of developing progressions for mathematics problem posing in grades10-11. Under the methodological guideline of design research, the research process of validating the hypotheses went through design prototype of design research, specific the prototype, design and implement the teaching in grade11that focused on the mathematics problem posing during a four-week period. The results of analyzing the teaching videos, pretest, interim test, posttest and the interview to the teacher and students were used to validate the hypotheses of developing progressions for mathematics problem posing in grades10-11, and also revised the teaching model for improving students’ mathematics problem posing.The third one was to revise the hypotheses of developing progressions for mathematics problem posing in grades10-11. Based on the hypotheses and its validation of the developing progressions for mathematics problem posing in grades10-11, revising the hypotheses mainly involved the target performances or developing goals, developing performances and instruction advice.The key findings of this research contributed to the revised developing progressions for mathematics problem posing in grades10-11and the revised teaching model for improving students’ mathematics problem posing. The research also found that students increasingly posed the understanding problem and reflecting problem from the structured situation with the growth of students’ grade.The research drew lesson from learning progressions research, which was a new method of assessing mathematics competency, and it would be a start for the future competency study.