Didactical design for distance concept in solid geometry to develop mathematical representation ability in vocational high school

This is qualitative research about the didactical design of distance concept in solid geometry, aiming to develop mathematical representation ability. This research employs a qualitative method with didactical design research (DDR) consisting of three stages of the didactical situation: didactical and pedagogical anticipation, metapedadidactical analysis, and retrospective analysis. Hypothetical didactical design was arranged by learning obstacle and hypothetical learning trajectory with the theory of didactical situations. The research subjects were three students of State Vocational High School in Garut as representatives of 30 students who had experience learning Distance Concepts in Solid Geometry and had been given an identification test for learning obstacles. The study identified that learning obstacles are the didactic and epistemological obstacle, which covered five inaccuracies in (1) Students’ ability in presenting concepts in various mathematical representation; (2) Understanding of the concept orthogonal projection between points on a line in the geometry; (3) construct geometric shapes of space to clarify the problem; (4) Understanding students’ visual representations related to the ability to determine the position of a point or a line perpendicular to a line; (5) Understanding of calculation procedures using the Pythagorean theorem and algebraic concepts.