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

Achmad Fahrurozi,Imam Suwanto,Farida Nursyahidah,Suci Maesaroh

doi:10.23917/jramathedu.v3i2.6616

Achmad Fahrurozi, Imam Suwanto + Show 2 more

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https://doi.org/10.23917/jramathedu.v3i2.6616

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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.

Highlights

Geometry is an important material in learning because: (1) it helps humans have an appreciation toward the whole of the world, (2) exploration of geometry can help to develop problem solving skills, (3) it plays a major role in other fields of mathematics, (4) it is useful in daily life, and (5) it is enigmatic and enjoyable (Walle, 1994: p. 35)
The problem in this study is how to develop learning trajectory based instruction of the congruence for ninth grade using central java historical building? the aim of this study is to develop learning trajectory based instruction of the congruence for ninth grade using central java historical building
The prior basic competence that are already owned by students in the second grade namely: describing a line segment by using concrete models of two-dimensional shape and three-dimensional shape, describing two-dimensional shape and threedimensional shape based on their characteristics, identifying a line segment by using concrete models of two-dimensional shape and three-dimensional shape, classifying twodimensional shape and three-dimensional shape based on their characteristics

Summary

Introduction

Geometry is an important material in learning because: (1) it helps humans have an appreciation toward the whole of the world, (2) exploration of geometry can help to develop problem solving skills, (3) it plays a major role in other fields of mathematics, (4) it is useful in daily life, and (5) it is enigmatic and enjoyable (Walle, 1994: p. 35). Chi in Panjaitan (2013) confirmed that the problem faced by students is to understand the concept of congruence such as student’s lack of understanding of the differences between congruence and similarity of twodimensional shape, student’s difficulties to understand that the similarity of triangle is applicable to all types of triangle. Students often experience difficulties in understanding sides and angles. They hardly distinguish that two-dimensional shape and triangle may be similar but not necessarily congruent, while these are congruent must be similar. Kurniati (2010) stated that in solving congruence and similarity problems, most students make errors due to their lack of understanding on the concept, on the concept of congruence (50%)

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