This study aims to examine the difference in Realistic Mathematics Education (RME) increase with students who obtain Autograph assisted discovery leaning, 2.The interaction between learning models and students initial mathematical abilities to students’ mathematical problem solving abilities. This type of research is quasi-experimental. The population in this study were all the students of class IX SMA Alwashliyah 3 Medan totaling 90 students. The sample selection is determined by randomly selecting two classes. Instrument used in data collection consisted of tests of problem solving abilities, students’ initial mathematical abilities and self- efficacy questionnaries. The results of the study indicate there are diffrences in the improvement of problem solving abilities provided by mathematics learning with the RME approach and Autograph Assisted Guided Discovery learning.
