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The purpose of this research is to know the difference of mathematical representation skill, the result of science learning and its influence on problem-based learning and discovery learning model. The population of this study was 16 students of PGSD FKIP University of Lampung. Among 534 students, there were two experimental classes consisting of 35 students and each was determined through cluster random sampling. The data on mathematical representation skills and learning outcomes of science were obtained through a description test, five questions for assessing mathematical representation skills, and ten questions for assessing science learning outcomes. From the instruments that had been tested to 30 respondents, it was obtained a valid and reliable instrument with a score of 0.505 for mathematical representation skills, and 0.832 for learning outcomes. Furthermore, the data were analyzed by using normality test, homogeneity test, independent sample t-test, correlation test, and simple linear regression test. The results showed that there was no difference in the result of mathematical representation skill and science learning outcomes, between the problem-based learning model and real discovery. But there is a positive and significant linear influence between the mathematical representation skill and the learning outcomes of science, through a problem-based learning model of discovery.