This study, based on the subject from the fifth and sixth graders of elementary schools in Kaohsiung County and District, conducts the ¡§Correlations of Cognitive Style (CS), Self-Concept (SC) and Mathematics Achievements (MA)¡¨. The purpose of this study is: 1. To understand the state of play of the CS, SC and MA of the fifth and sixth graders in elementary schools. 2. To analyze the effect of the different background variables of the fifth and sixth graders in elementary schools to the CS, SC and MA. 3. To research the correlation of the fifth and sixth graders in elementary schools among the CS, SC and MA. 4. To analyze the predictable situations of the fifth and sixth graders in elementary schools among CS, SC and MA. 5. To advance specific suggestions based on the research conclusion, in order to give the references for the teachers in the aspects of teaching, consulting and further study. This study adopted the questionnaire approach. The subjects were the fifth and sixth graders from Kaohsiung County and District. A total of 611 received questionnaires from the 640 questionnaires (received rate was 95.46%), canceled the null 9 ones, thus, we get the available 602 questionnaires. After the statistics of descriptive statistics, Independent-Samples T Test, one-way ANOVA, Pearson product-moment correlation, stepwise multiple regression, we concluded that: 1. The CS of the kids from high social-economic status family tended to be the analyzed model. 2. The MA of the kids from high and media social-economic status family was higher than those from low social-economic family. 3. The SC and MA of the kids with Field Independence convergent contemplative and verbal CS had significant difference. 4. The CS, SC and MA of fifth and sixth graders in elementary schools revealed media and low positively correlation. 5. The correlation between CS and MA of the fifth and sixth graders in elementary schools was stronger than the correlation between SC and MA of the fifth and sixth graders in elementary schools. 6. The CS and SC can predict efficiently the MA of fifth and sixth graders, especially the SC with convergent. Based on the research conclusion, this study provide the following implications: 1. For the teachers: A. During the period of mathematics solving, the teachers should lead the students to develop the CS of convergent. B. To advert the kids¡¦ biological development of SC, consult timely and to reinforce them. C. To understand completely the CS of the kids, and provide the most institutionalized teaching and consulting approaches. D. To advert the individual difference of the kids, and to develop positive SC through the concrete feedbacks and suitable reinforcements. E. To reinforce the parents education 2. For the further study: A. Aspects of the research subjects: This research is based on the matrix of the fifth and sixth graders of elementary schools in Kaohsiung County and District. If we can expand the subjects to those kids in other county and district, we probably understand more about the situations and features of CS and SC for the kids in elementary schools. Furthermore, we can discuss the influences of the both to MA. B. Aspects of variables: There are many factors that affect MA, including the teachers¡¦ cognitive teaching strategies, the students¡¦ solving strategies, mathematics learning attitudes¡Ketc. We can incorporate these factors into research scope or conduct other correlation variables study, thus, we may understand different relationships among CS, Sc and MA. C. Aspects of the research methods: The further research may adopt other approaches, for examples, the Cognitive Styles Analysis (CSA), Q-sorts or Q-technique, Self-Performance, or other instruments, thus, we may enhance our understandings of CS and SC. If we can apply other instruments based on the qualitative study, interview and gather information about the school¡¦s environment, we would understand more about the correlations among CS, SC and academic achievements.