This design research aims to design and develop an intervention as a solution to solve the problem of students' understanding of the topic of geometric transformation and to advance knowledge about the characteristics of the intervention in it to develop or validate local learning theories. The research procedure refers to the design research phase which consists of a preliminary design consisting of a literature review and designing a learning trajectory plan (HLT) with a realistic mathematics education approach (RME), a design experiment consisting of teaching experiments and pilot experiments, and a retrospective analysis phase. This study uses a population of 11th  grade students of SMA ABBS Surakarta who have been and are currently taking the topic of geometry transformation in their mathematics learning. The data obtained in this study were analyzed retrospectively to evaluate the learning activities carried out, observing student learning progress, and describing the findings and learning progress. The sample selected through snowball sampling in this study was analyzed in stages consisting of data analysis, interpretation of findings, and formulation of recommendations for the next design cycle and future research.

The conclusions are: 1) Mathematics can be developed from situational into formal, and vice versa. An approach linking the situational and the formal will be a great bridge in learning. Designing learning activities with the RME approach and using batik as the context in this study will make batik a suitable context for helping students understand the concept of transformation geometry. Thus, the role of batik is used in designing student activities to make progress in student understanding, 2) The process of students in understanding geometric transformations starts from determining the main pattern of a complete batik to know that the batik consists of an object that is transformed (and duplicated), from which the basic understanding of transformation is formed. Furthermore, students will be given the components used in the transformation with activities carried out directly by them, here they understand the transformation of geometry according to mathematical concepts in its use on informal objects. Next, students transform these informal objects into more mathematical objects through modeling or independent determination, from here students step on to understand the correlation between the use of transformations in informal and formal objects. Finally, students will use their understanding fully in the formal transformation geometry and solving problems.