The research is motivated by the finding result that the purpose of elementary school mathematics learning have not been achieved optimally. This can be seen from the many students who have difficulty in mastering mathematical ability. The mathematics learning that has been implemented has not facilitated in developing mathematical ability, one of them is critical thinking mathematics. So there is need an alternative mathematics learning which can develop student's critical thinking mathematics ability, is by using CORE model for mathematics learning. The purpose of this research is to determine the effect of the CORE model, the difference of critical thinking mathematics student's ability which obtain learning by using CORE model and critical thinking mathematics student's ability which obtain convensional learning. This research is a quantitative research, with quasi experimental research method. The sample in this research is the students of V-A grade and V-B grade SDN Sukamiskin. The result showed that critical thinking mathematics student's ability were higher after obtaining learning using CORE model and critical thinking mathematics student's ability were higher using CORE model rather than stundent's who obtain convensional learning. The result are based on the result of pretest and posttest data analysis in the experimental class and control class. Critical thinking mathematics student's ability were higher because the learning use CORE model extend opportunity for student to develop their critical thinking ability by interaction with their group and transfer their knowledge to take some way in solve the problem. Thus, CORE learning model can be used as an alternative learning for developing critical thinking mathematics ability elementary school student's.