| dc.description.abstract | Motivating students to enjoy learning math is one of the main objectives of compulsory education in Taiwan. A recent assessment conducted by the Trends in International Mathematics and Science Study (TIMSS) shows that primary school students in Taiwan are at a top-performed level, but their level of confidence in math is lower than most of other countries. This result implies that primary school students in Taiwan may not enjoy solving math problems even though they are able to apply their knowledge in a variety of relatively complex math problems. To further understand this challenge facing the students, this study adopts the free math problem-posing curricular – specifically, the one problem, many revised versions – activities in two classrooms and explores the transition of psychological ownership during the problem-posing.
The fieldwork, the free math problem-posing activities (10 classes, total 400 minutes to each class), was conducted in two 5th grade classrooms that comprise 56 students (the subjects) of a primary school in Northern Taiwan. Using mixed research methods, this study first explores the difficulties at the stage of posing, suggesting, and modifying during the problem-posing activities. Data was collected from the answered questionnaire, feedback notes, fieldwork memos, and it was analyzed mainly through the transcriptions from the interviews. Open coding system based on the grounded theory was adopted for the transcriptions. The second inquiry of this study is to examine the transition of psychological ownership during the free math problem-posing activities. Data analyzed was collected from the surveys of individual and collective psychological ownership during the problem-posing activities. As for the quantitative analysis, the dependent sample t-test and the one-way repeated measures ANOVA were conducted.
The main findings from this study: 1) Difficulties of problem-posing , students encountered difficulties in posing advanced math problems and embedding mathematic concepts into the questions they posed as well as in solving the problem they posed, even they have understood well those concepts; 2) Difficulties of making good suggestions, students were not able to give constructive suggestions especially when they encountered math problems that have large numbers for calculation, they lack of confidence to solve, have long descriptions as well as have a lot of sub-questions and need more steps to solve; 3) Difficulties of making the modifications, students faced difficulties to harmonize disagreements due to the lack of confidence, adding contents of the problems, difficult posed-questions, changing of numeric arrangements, consideration of the completeness of the problems, and useless feedback; 4) During the problem-posing, collective psychological ownership was significantly higher than the individual psychological ownership; 5) Individual psychological ownership significantly increased since phase three but collective psychological ownership remained unchanged throughout the posing activities.
In summary, as the main contribution, this study shows that although students experienced difficulties and challenges at the stage of posing, feedback and revision, they were still enthusiastically participating in the activities of generating and solving math problems. This finding is opposite from implication according to TIMSS that primary school students in Taiwan may not enjoy solving math problems, and can also serve as a reference for practitioners teaching the related subjects. It is also unavoidable of the research limitation in this study. For future study, it is suggested to improve and further examine the application of the questionnaire regarding psychological ownership as well as the research design for inquiring suggestion, and modification during the problem-posing. | en_US |