The purpose of this research is to develop local instruction theory on triangular and quadrilateral material and examine the improvement of mathematical representation ability by using local instruction theory. The method used in this research is design research method which includes three stages, namely: preliminary design, design experiment and retrospective analysis. The instruments in this study were in the form of tests and non-tests, where the tests used were aimed to determine the improvement of students' mathematical representation ability while non-tests such as interviews and observations were used to develop the local instruction theory. Subjects in this study were 40 junior high school students. The final result of this research is the development of local instruction theory teaching materials that can be used by the teacher to be used as a guide in teaching and the ability of students' mathematical representation in triangular and quadrilateral material is sufficiently increased