Mathematical representation ability is a cognitive ability that must be possessed by students. However, the reality on the field is in contrast to that. Students' mathematical representation ability are still relatively low, so special measures are needed to improve them. Therefore, the application of connecting-organizing-reflecting-extending (CORE) learning models with an open-ended approach is chosen as a particular action to improve mathematical representation ability. The purpose of this study is to compare the improvement and attainment of mathematical representation ability and selfefficacy mathematics between conventional, core, and core class students with an open-ended approach. This research is quasi-experiment research using a modified pretest-postest design. The population of this study is all grade X students in Pondok Melati Senior High School, Bekasi. The sample of this study was students of Grade X of Sandikta High School and Nasional I High School who were taken in a cluster random sampling. The data collection techniques used are test and nontest techniques. Data analysis is conducted using the One Way Anova test. Based on data analysis, it is shown that: (1) there are significant differences in the improvement and attainment of mathematical representation ability between conventional, core, and core class students with an open-ended approach; and (2) there are significant differences in self-efficacy mathematics attainment between conventional, core, and core students with an open-ended approach.