scholarly journals KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

2014 ◽  
Vol 3 (3) ◽  
Author(s):  
Irkham Ulil Albab ◽  
Yusuf Hartono ◽  
Darmawijoyo Darmawijoyo
Keyword(s):  
Instructional Design ◽  
Design Research ◽  
Design Stage ◽  
Geometric Transformation ◽  
Learning Trajectory ◽  
Supporting Line ◽  
Hypothetical Learning Trajectory ◽  
Preliminary Design Stage ◽  
Learning Progress ◽  
Transformation Geometry

Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT) berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research,HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT) played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews, observations, and field notes. The findings of the study showed that this instructional design could stimulate students to provide reflection characteristics and other transformation geometry informally, to classify them in the transformation isometry in the second level, and to find the reflection supporting line in the more formal level. In addition, the reflection supporting line was used by the students to draw the reflection image and the mirroring pattern and to understand the rotation and translation shapes as a combination of reflection at the highest level. Keyword: geometric transformation, rotation, translation, and HLT

scholarly journals DEVELOPMENT OF LEARNING TRAJECTORY ON THE SET TOPIC FOR 7TH GRADE IN THE CONTEXT OF SEDEKAH LAUT TRADITION

2021 ◽  
Vol 6 (2) ◽  
pp. 181-194
Author(s):  
Hartono Hartono ◽  
Denti Zaedatul Khaeriyah ◽  
Dina Lita Sari ◽  
Mila Ilfiana ◽  
Farida Nursyahidah
Keyword(s):  
Design Research ◽  
Design Stage ◽  
Learning Trajectory ◽  
Preliminary Design ◽  
Venn Diagrams ◽  
Set Operations ◽  
Preliminary Design Stage ◽  
Three Stages ◽  
Learning Development ◽  
Teaching Experiments

Set is an important topic to be mastered by students because it influences the development of mathematics in daily life. However, many students still have difficulty learning the topic. Therefore, it is necessary to design a learning trajectory using the appropriate approach, context, and media. This research resulted in the learning development using Sedekah Laut context to create meaningful learning and increase students' understanding of sets. The method used in this study was design research proposed by Gravemeijer & Cobb with three stages: preliminary design, experimental design (pilot experiments and teaching experiments), and retrospective analysis. However, this article only presented the results from the Preliminary design stage. The participants involved in this study were 7th-grade students of SMP Negeri 6 Semarang. The resulting hypothetical learning trajectory consists of a series of learning processes: observing context videos to find the concepts of sets, non-sets, empty sets, universal sets, and Venn diagrams; explaining the properties of the set; defining set operations; and solving problems related to sets.

scholarly journals Hypothetical learning trajectory in student’s spatial abilities to learn geometric transformation

2021 ◽  
Vol 6 (3) ◽  
pp. 174-190
Author(s):  
Ricki Yuliardi ◽  
Rizky Rosjanuardi
Keyword(s):  
Private School ◽  
Spatial Abilities ◽  
Geometric Transformation ◽  
Spatial Thinking ◽  
Learning Trajectory ◽  
9Th Grade ◽  
Hypothetical Learning Trajectory ◽  
Thinking Process ◽  
Transformation Geometry ◽  
The Relationship

The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students' understanding, and how to develop HLT (Hypothetical Learning Trajectory)in transformation geometry learning. HLT design consists of three stages: initial design, experimental, and retrospective analysis. The results of HLT are then refined into LIT (Local Instructional Trajectory). Then this paper present the empirical results of the perceptions of twenty  9th grade students in one of Islamic private school in Kabupaten Kuningan, West Java, Indonesia, towards the corresponding geometric and math questions. Literature review analysis was used to analyze the retrieved articles. At the end of the paper, we explain and discuss how to apply mathematical conceptions in learning geometry. This research is expected to be a guidance for teachers to develop learning in accordance with the students' spatial thinking process in studying geometry.

scholarly journals MENGATASI LEARNING OBSTACLE KONSEP TRANSFORMASI GEOMETRI DENGAN DIDACTICAL DESIGN RESEARCH

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Ramdani Miftah ◽  
Lia Kurniawati ◽  
Ticha Putri Solicha
Keyword(s):  
High School ◽  
Design Research ◽  
Geometric Transformation ◽  
Learning Trajectory ◽  
Student Responses ◽  
Hypothetical Learning Trajectory ◽  
Three Stages ◽  
Preliminary Study ◽  
Epistemological Barriers ◽  
Obstacle Analysis

The purpose of this study was to identify learning obstacle precisely on students' epistemological barriers to the concept of geometry transformation. Furthermore, researchers overcome these obstacles by developing mathematical learning concepts in the concept of geometry transformation in high school. This research was conducted at one of the senior high school in Tangerang Selatan. The research method used is Didactical Design Research. This method is carried out in three stages, the analysis of didactic situations before learning (prospective analysis), metapedidactic analysis, and retrospective analysis. Based on the results of the preliminary study, of the 20 students who took the obstacle learningidentificationtest,82.35%ofthetotalstudentsexperiencedepistemologicalbarrierstotheconceptofgeometry transformation. In overcoming the epistemological obstacles students in the concept of geometric transformation requires the design of learning developed based on learning obstacle analysis, repersonalization, and recontextualization so as to produce hypotheses consisting of Hypothetical Learning Trajectory which contains various activities and predictions of student responses and anticipations and produces Student Worksheets. The results show that the didactic design provided can overcome student barriers. It can be seen from the effectiveness of anticipation given during learning that reaches 90% of the difficulties that arise based on predictions of response and anticipated didactic pedagogical.

scholarly journals THE CONTEXT OF ARCHIPELAGO TRADITIONAL CAKE TO EXPLORE STUDENTS’ UNDERSTANDING IN INTEGERS DIVISION CLASS VII

2019 ◽  
Vol 14 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Elis Muslimah Nuraida ◽  
Ratu Ilma Indra Putri
Keyword(s):  
Junior High School ◽  
Design Research ◽  
Mathematics Learning ◽  
Learning Trajectory ◽  
Mathematics Problems ◽  
Learning Path ◽  
Starting Point ◽  
Hypothetical Learning Trajectory ◽  
Integer Division ◽  
Division Operation

This study aims to explore the students’ mathematical understanding in integer division operation through the context of archipelago traditional cakes in class VII. This research is related to the Indonesian Realistic Mathematics Approach (PMRI) as a learning approach used. The methodology used in this study is Design Research consisting of three stages: preliminary design, experimental design, and retrospective analysis. The study was conducted on VII grade students of Palembang 1 Junior High School. The learning path (Hypothetical Learning Trajectory) in design research plays an important role as a research design and instrument. The Hypothetical Learning Trajectory (HLT) was developed together with a series of activities using the context of archipelago traditional cakes such as: omelette roll, bakpia, milk pie, etc. The medium used in this study was the Students’ Activity Sheet. The results of this study indicate that exploration using the context of traditional archipelago cakes can help students understanding in multiplication and division of integers. The conclusion of this study is the use of archipelago traditional cakes as starting point in mathematics learning in integer division operation material helps the students to explore their understanding in solving mathematics problems.

scholarly journals DESIGNING LEARNING ROTATION USING THE CONTEXT OF BAMBOO WOVEN MOTIF

2020 ◽  
Vol 4 (2) ◽  
pp. 100
Author(s):  
Maryati Maryati ◽  
Rully Charitas Indra Prahmana
Keyword(s):  
Design Research ◽  
Learning Trajectory ◽  
Realistic Mathematics Education ◽  
Preliminary Design ◽  
Realistic Mathematics ◽  
Formal Level ◽  
Three Stages ◽  
Transformation Geometry ◽  
Ninth Grade Students ◽  
Design Experiments

An essential part of learning transformation geometry is rotation. Before learning more about other parts of the transformation geometry topic, such as translation, dilation, and reflection, firstly, students are required to understand well about rotation. However, several students have not been able to understand this subject properly due to the stages of learning in the rotation has not been appropriately arranged. Thus, this study aims to design a student learning trajectory in learning rotation, which develop from informal to formal level through the Indonesian Realistic Mathematics Education (IRME) approach. Furthermore, researchers used a design research method divided into three stages, namely preliminary design, design experiments, and retrospective analysis. This study describes how the bamboo woven motif contributes significantly to 31 ninth-grade students understanding the rotation concept. As a result, the woven bamboo motif's context can stimulate students' understanding of rotation. It is proven based on the strategies and models of students during their learning process which contributes to their fundamental knowledge of rotation.

scholarly journals Instructional design of integration factor based on reciprocal teaching approach

2019 ◽  
Author(s):  
Misdalina
Keyword(s):  
Instructional Design ◽  
Retrospective Analysis ◽  
Research Design ◽  
Design Method ◽  
Teaching Approach ◽  
Reciprocal Teaching ◽  
Learning Trajectory ◽  
New Knowledge ◽  
Hypothetical Learning Trajectory ◽  
Field Notes

Conventional learning are given by lecturer, make the students passive and just receive the new knowledge without a meaningful thingking process. Therefore it is required an instructional design, which invites students to understand the knowledge of their own efforts through Reciprocal Teaching approach. The method which used in this study is the research design method that include: preparing for the experiment, experimenting in the classroom, and retrospective analysis. Learning is designed for two meetings. Data collecting is made by documentation, field notes, and tests. The results is Hypothetical Learning Trajectory (HLT) for the material integration factor based on Reciprocal Teaching approach.

scholarly journals Desain Pembelajaran Luas Lingkaran dengan Konteks Explore Dapur Berbasis Realistic Mathematics Education (RME) di Kelas VIII Sekolah Menengah Pertama (SMP)

2019 ◽  
Vol 1 (4) ◽  
pp. 37-44
Author(s):  
Asep Budiyono ◽  
Widya Kusumaningsih ◽  
Irkham Ulil Albab
Keyword(s):  
Mathematics Education ◽  
Design Research ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Realistic Mathematics Education ◽  
Pilot Experiment ◽  
Realistic Mathematics ◽  
Hypothetical Learning Trajectory

Penelitian ini bertujuan untuk mengetahui peran Hypothetical Learning Trajectory(HLT)dalam membantu siswa dalam memahami konsep luas lingkaran serta mengetahui strategi yang digunakan oleh siswa terhadap Hypothetical Learning Trajectory(HLT) yang diberikan. Penelitian ini dilaksanakan di SMP Negeri 3 Petarukan, Kabupaten Pemalang. Subjek penelitian adalah siswa kelas VIII, dengan melalui 2 tahap yaitu pilot experiment melibatkan 6 siswa dari kelas VIII C dan dilanjutkan teaching experiment yang melibatkan 30 siswa dari kelas VIII B. Penelitian ini menggunakan metode design research yang didalamnya terdapat HLT yang memegang peranan sangat penting sebagai desain dan instrumen penelitian. Pembelajaran dalam penelitian ini menggunakan konteks peralatan dapur yaitu gelas, piring dan mangkuk sesuai dengan karakteristik dari RME. Hasil Penelitian menunjukkan bahwa Hypothetical Learning Trajectory (HLT) dapatmembantu siswa 1) membuat potongan juring lingkaran dan mengubahnya menjadi sebuah bangun datar baru yaitu trapesium, 2) menemukan sendiri konsep luas lingkaran dengan pendekatan trapesium, 3) menyelesaikan permasalahan dalam kehidupan sehari-hari yang berkaitan dengan konsep luas lingkaran. Adapun strategi yang digunakan siswa yaitu 1)mensketsakan permukaan perlatan dapur berupa lingkaran, 2) membandingan keliling dan diameter lingkaran untuk memperoleh nilai phi, 3)menyusun juring menjadi trapesium dan memformulasikan konsep luas lingkaran, 4) menerapkan konsep luas lingkaran.

scholarly journals DESAIN PEMBELAJARAN MATERI PERBANDINGAN MENGGUNAKAN KONTEKS RESEP EMPEK-EMPEK UNTUK MEDUKUNG KEMAMPUAN BERNALAR SISWA SMP

2017 ◽  
Vol 3 (1) ◽  
pp. 103-121
Author(s):  
Rahma Siska Utari
Keyword(s):  
Design Research ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Preliminary Design ◽  
Hypothetical Learning Trajectory ◽  
Actual Learning

Bernalar dalam perbandingan merupakan salah satu topik penting pada pembelajaran matematika SMP. Penelitian ini bertujuan menghasilkan lintasan belajar materi perbandingan menggunakan konteks resep empek-empek dan bagaimana konteks tersebut dapat mendukung kemampuan bernalar siswa. Pendekatan pembelajaran yang digunakan adalah Pendidikan Matematika Realistik Indonesia (PMRI). Subjek penelitian adalah 45 siswa kelas VII SMPN 55 Palembang. Metode penelitian yang digunakan adalah design research, dugaan lintasan belajar (Hypothetical Learning Trajectory) dikembangkan dari aktivitas pembelajaran menggunakan konteks resep empek-empek. Pengembangan secara teoritis dilaksanakan melalui proses interatif meliputi merancang aktivitas pembelajaran (preliminary design), melaksanakan pembelajaran (teaching experiment) dan melakukan analisis retrospektif (restrospective analysis) dalam rangka memberi kontribusi terhadap teori pembelajaran lokal (Local Intructional Theory) untuk mendukung siswa bernalar dalam perbandingan. Pengumpulan data dilakukan melalui beberapa hal meliputi membuat rekaman video tentang kejadian di kelas dan kerja kelompok, mengumpulkan hasil kerja siswa, dan mewawancarai siswa. Hypothetical Learning Trajectory (HLT) yang telah dirancang kemudian dibandingkan dengan Actual Learning Trajectory (ALT) siswa yang sebenarnya selama pelaksanaan pembelajaran (teaching experiment) untuk menganalisis apakah siswa belajar atau tidak belajar dari apa yang telah dirancang dirangkaian pembelajaran. Analisis retrospektif terhadap pelaksanaan pembelajaran menunjukkan bahwa penggunaan konteks resep empek-empek dapat mendukung kemampuan bernalar siswa SMP.

scholarly journals PEMANFAATAN KONTRIBUSI SISWA SEBAGAI ALAT TRANSISI MENUJU PEMAHAMAN KONSEP OPERASI PECAHAN

2018 ◽  
Vol 9 (1) ◽  
Author(s):  
Gregorius Sebo Bito
Keyword(s):  
Retrospective Analysis ◽  
Learning Process ◽  
Design Research ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Fourth Grade Students ◽  
Hypothetical Learning Trajectory ◽  
Three Stages ◽  
Actual Learning ◽  
Is Design

The purpose of this study was to describes the use of student’s contribution as a transition tool at each level of learning the fraction operation concept. This study involved fourth grade students of an elementary school in Ngada East Nusa Tenggara. The type of this research is Design Research with three stages, namely: initial design, teaching experiment and retrospective analysis. This research begins conduct a hypothetical learning trajectory (HLT) of fraction operations concept. The HLT has been tested before the actual learning process (ALT). The results of the retrospective analysis obtained an overview of the Actual Learning Trajectory (ALT) show that the use of various student’s contribution at each level of learning can lead to understanding the fraction operation concept.

scholarly journals DESAIN PEMBELAJARAN UKURAN PEMUSATAN DATA MENGGUNAKAN KONTEKS GAME RATING

JIPMat ◽  
2019 ◽  
Vol 4 (2) ◽  
Author(s):  
Widya Kusumaningsih ◽  
Irkham Ulil Albab ◽  
Septian Dwi Angga
Keyword(s):  
Design Research ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Pilot Experiment ◽  
Hypothetical Learning Trajectory

Penelitian ini bertujuan untuk mengetahui peran Hypothetical Learning Trajectory (HLT) dalam membantu siswa memahami konsep ukuran pemusatan data. Penelitian ini dilaksanakan di SMPN 3 Ungaran. Subjek penelitian adalah siswa kelas VIII, dengan 2 tahap yaitu pilot experiment yang melibatkan 6 siswa dari kelas VIII B dan dilanjutkan teaching experiment yang melibatkan 25 siswa dari kelas VIII C. Penelitian ini menggunakan metode design research yang menggunakan HLT. HLT memegang peran yang sangat penting sebagai desain dan instrumen utama dalam penelitian. Kegiatan pembelajaran dalam penelitian ini menggunakan konteks game rating. Hasil penelitian menunjukkan bahwa HLT dapat membantu siswa 1) menemukan sendiri bagaimana menghitung mean, median dan modus melalui bentuk representasi matematis, 2) menemukan sendiri konsep ukuran pemusatan data, 3) menyelesaikan permasalahan dalam kehidupan sehari-hari yang berkaitan dengan konsep ukuran pemusatan data. Hasil dari penelitian ini menunjukkan bahwa melalui serangkaian aktivitas yang telah dilakukan membantu siswa dalam pembelajaran ukuran pemusatan data.

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