Didactical design of mathematical reasoning on three dimensional in high school

Mathematical reasoning ability can be obtained through the process of understanding students in learning mathematics. However, not a few students experience learning barriers, one of which is in studying three-dimensional material. The purpose of this study is to identify the epistemological obstacle focused to Reasoning and Proof indicator in the three dimensional and overcome them by developing mathematical learning designs in high school. This research was held at SMAN 9 Tangerang. The reasearch method is Didactical Design Research. This method is consist of three stages, namely analysis before learning (prospective analysis), during learning (metapeda didactic), and after learning (retrosfective). Based on the results of the preresearch, 80,48% of 38 students who took the identification of student obstacle test had epistimological obstacles in the concepot three dimensional. To overcome the epistemological obstacle in the concept of three dimensional, are needed learning design that are developed based of student’s learning obstacle, repersonalization, and recontextualization, so that it results the hypothetical learning trajectory which composed the various student activities and predictions of student responses follows with the anticipation, and result the generates student worksheet. The results of the study show that the design can be used to overcome student difficulties, it can be seen from the effectiveness of anticipation given to overcome student difficulties during learning.