<![CDATA[It is necessary to emphasize the ability to conceptual understanding of geometry (CUG) for each student to support the formation of mathematical competence. In forming, it is important to carry out a lesson by prioritizing interaction between students in conveying ideas known as sociomathematical norms. The construction CUG is very important for learning by prioritizing interaction between students in conveying ideas known as socimathematical norms. The aims of study to analyze the implementation of the discovery learning (DLM) in developing achievements of CUG based on aspects of socio mathematical norms in learning plane geometry. This study used a quasi-experimental method by following a nonequivalent control group design. The sample involved in this research was 70 students of the mathematics education study program. This study concludes: 1) Achievement of students' CUG by implementing DLM is better than achievement of students' CUG by applying the conventional model (CM). 2) there is are significant differences between the achievement of students' CUG using DLM and students applying CM based on the socio mathematical norm level; 3) there is an interaction effect between DLM and sociomathematical norm factors on achievement of students' CUG; 4) the contribution of DLM implementation to student CUG achievement includes: (a) Student Worksheets with DLM syntax make it easier for students to deepen geometry material; (b) a discussion process that gives rise to students' freedom of expression; (c) the diversity of alternative problem solving strengthens students in determining the best choice and analysis of problem solving; (d) classical presentation activities motivate students to understand the concepts in each lesson.]]>
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