### Developing Learning Trajectory Based Instruction of the Congruence for Ninth Grade Using Central Java Historical Building

Achmad Fahrurozi^{(1*)}, Suci Maesaroh

^{(2)}, Imam Suwanto

^{(3)}, Farida Nursyahidah

^{(4)}

(1) Department of Mathematics Education, Universitas PGRI Semarang

(2) Department of Mathematics Education, Universitas PGRI Semarang

(3) Department of Mathematics Education, Universitas PGRI Semarang

(4) Department of Mathematics Education, Universitas PGRI Semarang

(*) Corresponding Author

#### Abstract

*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.*

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