This research aims to produce a Learning Trajectory Based Instruction (LTBI) that can help the ninth grade students understand the concept of congruence of the two-dimensional shape by examining Lawang Sewu as one of Central Java historical buildings. LTBI is defined as a teaching and learning trajectory that uses Hypothetical Learning Trajectory (HLT) for instructional decisions. The present research uses the design research developed by Gravemeijer and Cobb that consists of three phases; the preliminary design, design of the experiment (pilot experiment and teaching experiment), and  retrospective analysis. In this study, a series of learning activities is designed and developed based on the Realistic Mathematics Education (PMRI) approach. This research produced LTBI that consists of a series of learning processes embodied in three activities of (1) identifying and finding the properties which shapes are congruent shapes by watching Lawang Sewu video, (2) proofing two shapes are congruent through transformation (translation and rotation), and (3) solving problem related to the congruence of two-dimensional shape. The activity can help to improve the students’ understanding of the concept of congruence. Nevertheless, the present study is limited to the first stage of Gravemeijer and Cobb’s design research, namely preliminary design.

This study aims to produce a learning trajectory by using the context of Lawang Sewu in helping students to understand the concept of similarity. The approach used in this research was Realistic Mathematics Education, in Indonesian version is called by PMRI. Subject of the study is the third-grade students of SMP 37 Semarang, Central Java, Indonesia, involving 6 students who were chosen in heterogeneous capabilities. The methodology used is a design research consisting of three phases, namely the preliminary design, the design experiment, and the retrospective analysis. However, this study only shows the results in the design experiment phase, in particular on a pilot experiment. Data collection was done through several techniques, namely: video recordings, photograph, students work result, and students interview during learning. Student learning activities consist of four activities, namely observing the Lawang Sewu video, identifying two similar shapes, identifying the requirements of two similar shapes, and solving a contextual problem related to similarity. The results of this study indicate that through a series of activities that have been designed could help to stimulate students understanding of similarity concept by using Lawang Sewu context.