The purpose of the present study is (1) to investigate factors that influence mathematical problem solving competence for elementary students, (2) to understand the current studies regarding the development of mathematical problem solving competence, and (3) to probe background factors that affect the development of mathematical problem solving competence. The subjects of the study included 710 fifth-graders in Tainan city. The surveys of Thinking Style Inventory, Mathematical Learning Perception Check List as well as Mathematical Problem Solving Competence Test were used as instruments for data collection. A total of 710 questionnaires were delivered and 587valid questionnaires were collected, with fairly high 82.60% return rate. The collected data was tested with descriptive analysis, independent t test¡BANOVA¡Bproduct-moment correlation coefficient,multiple correlation and multiple regression. Based on the data analysis, the six findings of this study are summarized as follows: 1. The low satisfaction with mathematics class was revealed from the analysis of students¡¦ Mathematical Learning Perception Check List. It is suggested boosting subjects¡¦ satisfaction with the mathematics class will enhance the development of mathematical problem solving competence. 2. The positive correlation between administration style and mathematical problem solving competence was shown eminently among all types of thinking styles. The result indicated different function of the thinking styles influenced the development of mathematical problem solving competence in a varied degree. 3. From the analysis of students¡¦ background factor and mathematics problem solving competence, the statistic indicated the length of extra curriculum students devoted to does not affect their mathematical problem solving competence. The factors that influence students¡¦ mathematical problem solving competence the most were shown in the following order: administration district, the social status of father, the social status of mother, gender and the size of school. 4. The comparative variance of the mathematics learning achievement and mathematics problem solving competence was 24.3%. It implied the two influences each other. Students with low mathematical learning achievement show low mathematical problem solving competence and vice versa. 5. When predicting students¡¦ development of mathematical problem solving competence via the data of parents¡¦ social status and mathematical learning perception check list, the result showed the prediction via parents¡¦ social status is less significant. Yet the prediction via mathematical learning perception check list gained the highest variance ratio in this case. 6. In terms of the distribution of parents¡¦ social status, East, North and Middle East were of eminent as compared to South, An-Ping and An-Nan district in Tainan city. The finding implied parents¡¦ social status was a major factor that influence students¡¦ mathematics problem solving ability in administration district, as the £b2 ¡]Eta Squared¡^¡×25.3¢H shown in this study.