Pembelajaran Operasi Penjumlahan dan Pengurangan Bilangan Bulat Menggunakan Garis Bilangan

Abstract:This study aims at determining the role of the number line media in helping students understand and obtain local instructional theory in learning integer operations in the 4th Grade of Madrasah Ibtidaiyah in Tarakan. This research is design with three stages, namely preliminary design, experimental design, and retrospective analysis. In the preliminary design stage, a number line media along with the hypothetical learning trajectory is made. Then the teaching experiment is conducted to compare the expected learning trajectory with the actual learning trajectory that takes place. In the final stage, a retrospective analysis is carried out by viewing the video recording of learning and evaluation results. From the analysis, it was found that the use of number lines can help students to understand the operations of addition and subtraction of integers. This study also developed local instructional theory related to learning integers using number lines.Abstrak:Penelitian ini bertujuan untuk mengetahui peranan media garis bilangan dalam membantu pemahaman siswa serta mengembangkan teori instruksional lokal (local intructional theory) pada pembelajaran operasi bilangan bulat di kelas IV di salah satu Madrasah Ibtidaiyah di Kota Tarakan. Desain penelitian ini terdiri dari tiga tahap, yaitu desain pendahuluan, desain percobaan, dan analisis retrospektif. Pada tahap desain pendahuluan dilakukan pembuatan media garis bilangan beserta dugaan lintasan belajar, kemudian dilakukan percobaan pengajaran untuk membandingkan lintasan belajar yang diharapkan dengan lintasan belajar yang sesungguhnya terjadi. Pada tahap akhir dilakukan analisis retrospektif dengan melihat rekaman video pembelajaran dan hasil evaluasi. Dari analisis tersebut ditemui bahwa penggunaan garis bilangan dapat membantu siswa untuk memahami operasi penjumlahan dan pengurangan bilangan bulat. Penelitian ini juga mengembangkan teori instruksional lokal terkait pembelajaran bilangan bulat menggunakan garis bilangan.

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DESAIN PEMBELAJARAN MATERI HUBUNGAN ANTAR GARIS YANG MENDUKUNG PEMAHAMAN KONSEP SISWA

PHI: Jurnal Pendidikan Matematika ◽

10.33087/phi.v5i1.128 ◽

2021 ◽

Vol 5 (1) ◽

pp. 60

Author(s):

Rika Firma Yenni ◽

Malalina Malalina

Keyword(s):

Retrospective Analysis ◽

Design Research ◽

Teaching Experiment ◽

Learning Trajectory ◽

Design Experiment ◽

Preliminary Design ◽

Instructional Theory ◽

Pilot Experiment ◽

Starting Point ◽

Hypothetical Learning Trajectory

Peran guru tak lebih dari seorang fasilitator, moderator atau evaluator. sedangkan peran siswa lebih banyak aktif untuk berfikir dan mengkomunikasikan argumentasinya, menjustifikasi jawaban, serta melatih nuansa demokrasi dengan menghargai pendapat atau strategi teman lain. Penelitian ini bertujuan menghasilkan Local Instructional Theory (LIT) dalam pembelajaran materi hubungan antar garis yang mendukung pemahaman konsep siswa di kelas IV Sekolah Dasar. Pada materi ini, menuntut siswa dapat menyelesaikan permasalahan hubungan antar garis secara kontekstual. Subjek penelitian adalah siswa kelas IV MI Fajar Siddiq Palembang. Metode yang digunakan adalah design research terdiri dari tiga tahap, yaitu: preliminary design, design experiment (pilot experiment dan teaching experiment), dan retrospective analysis. Namun pada penelitian ini hanya dilakukan sampai pada tahap pilot experiment. Penelitian ini mengembangkan hasil pembelajaran hubungan antar garis dengan menunjukkan aktivitas dan prosedur serta strategi siswa dalam menemukan ide atau strategi dalam mendeskripsikan materi hubungan antar garis. Pada bagian ini, akan dibahas penggunaan garis lurus sebagai starting point pembelajaran hubungan antar garis dengan Pendidikan Matematika Realistik Indonesia (PMRI) sebagai pendekatan yang mendukung aktivitas dari penggunaan konteks tersebut. Selain itu, perubahan dari Hypothetical Learning Trajectory (HLT) ke Learning Trajectory (LT) melalui aktivitas, dilakukan dengan pengumpulan data menggunakan lembar observasi, wawancara, rekaman video, foto, dan lembar aktivitas siswa

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Pengembangan Learning Trajectory Based Instruction Materi Kerucut Menggunakan Konteks Megono Gunungan

Mosharafa: Jurnal Pendidikan Matematika ◽

10.31980/mosharafa.v9i1.560 ◽

2020 ◽

Vol 9 (1) ◽

pp. 47-58

Author(s):

Farida Nursyahidah ◽

Bagus Ardi Saputro ◽

Irkham Ulil Albab ◽

Fifin Aisyah

Keyword(s):

Retrospective Analysis ◽

Interactive Video ◽

Design Research ◽

Teaching Experiment ◽

Design Stage ◽

Learning Trajectory ◽

Preliminary Design ◽

Pilot Experiment ◽

Based Instruction ◽

The Right

AbstrakSebagian besar siswa masih mengalami kesulitan dalam belajar kerucut. Oleh karena itu diperlukan pendesainan lintasan belajar materi tersebut menggunakan konteks dan media yang tepat. Penelitian ini bertujuan untuk menghasilkan Learning Trajectory Based Instruction (LTBI) materi kerucut menggunakan konteks tradisi Syawalan masyarakat Pekalongan yaitu Megono Gunungan yang dikemas dalam bentuk video interaktif. Penelitian ini menggunakan design research yang dikembangkan oleh Gravemeijer dan Cobb yang terdiri dari tiga tahap yaitu: preliminary design, design of the experiment (pilot experiment and teaching experiment), dan retrospective analysis. Namun, artikel ini memaparkan hasil pada tahap pertama, yaitu tahap preliminary design. Subjek penelitian ini adalah siswa kelas IX SMP N 38 Semarang. Dalam penelitian ini dihasilkan LTBI yang terdiri dari serangkaian aktivitas pembelajaran, yaitu: (1) mengidentifikasi bagian-bagian kerucut melalui video interaktif Megono Gunungan, (2) menemukan luas permukaan kerucut dengan menggunakan jaring-jaring kerucut, (3) menemukan volume kerucut dengan menggunakan media beras, dan (4) menyelesaikan masalah kontekstual yang berkaitan dengan kerucut. Selanjutnya, siswa diharapkan dapat lebih mudah memahami materi kerucut melalui beberapa aktivitas yang telah didesain. Development of Learning Based on Trajectory Material Cone Middle School Using Megono Gunungan AbstractMost students still experience difficulties in learning cones. Therefore it is necessary to design the learning trajectory of the material using the right context and media. This study aims to produce Learning Trajectory Based Instruction (LTBI) cone material using the context of the Pekalongan community's Syawalan tradition, Megono Gunungan, which is packaged in the form of interactive video. This study uses design research developed by Gravemeijer and Cobb which consists of three stages: preliminary design, design of the experiment (pilot experiment and teaching experiment), and retrospective analysis. However, this article presents the results of the first stage, the preliminary design stage. The subjects of this study were students of class IX SMP N 38 Semarang. In this study LTBI produced consisting of a series of learning activities, namely: (1) identifying cone sections through interactive video Megono Gunungan, (2) finding the surface area of the cone by using cone nets, (3) finding the volume of the cone by using rice media, and (4) resolve contextual problems related to cones. Furthermore, students are expected to more easily understand the cone material through several activities that have been designed.

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A Proposed Instructional Theory for Integer Addition and Subtraction

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.43.4.0428 ◽

2012 ◽

Vol 43 (4) ◽

pp. 428-464 ◽

Cited By ~ 49

Author(s):

Michelle Stephan ◽

Didem Akyuz

Keyword(s):

Number Line ◽

Teaching Experiment ◽

Learning Trajectory ◽

Realistic Mathematics Education ◽

Instructional Theory ◽

Education Theory ◽

Addition And Subtraction ◽

Support Students ◽

Grade Classroom ◽

Viable Model

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional sequence, which was based on a financial context, was designed using the Realistic Mathematics Education theory. Additionally, an empty, vertical number line (VNL) is posited as a potentially viable model to support students' organizing their addition and subtraction strategies. Particular emphasis is placed on the mathematical practices that were established in this setting. These practices indicate that students can successfully draw on their experiences with assets, debts, and net worths to create meaning for integer addition and subtraction.

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

Jurnal Pendidikan Matematika RAFA ◽

10.19109/jpmrafa.v3i1.1444 ◽

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.

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Stadion Gelora Sriwijaya Jakabaring dalam Pembelajaran Segitiga

Kreano Jurnal Matematika Kreatif-Inovatif ◽

10.15294/kreano.v6i2.4830 ◽

2015 ◽

Vol 6 (2) ◽

pp. 147 ◽

Cited By ~ 2

Author(s):

Nyiayu Fraisa Fatiyah ◽

Ratu Ilma Indra Putri ◽

Ely Susanti

Keyword(s):

High School Students ◽

Retrospective Analysis ◽

Teaching Experiment ◽

Learning Trajectory ◽

Design Experiment ◽

Preliminary Design ◽

Seventh Grade ◽

School Students ◽

Pilot Experiment ◽

Starting Point

Penelitian ini bertujuan untuk menghasilkan lintasan belajar pada materi sifat-sifat segitiga berdasarkan panjang sisi dan besar sudutnya menggunakan konteks Stadion Gelora Sriwijaya Jakabaring di kelas VII. Desain pembelajaran yang digunakan terdiri dari tiga tahap yaitu preliminary design, design experiment (pilot experiment dan teaching experiment), dan retrospective analysis. Dalam penelitian ini, serangkaian aktifitas pembelajaran didesain dan dikembangkan berdasarkan pendekatan PMRI. Penelitian ini melibatkan 29 orang siswa kelas VII SMP Negeri 2 Indralaya Utara. Penelitian ini menghasilkan Learning Trajectory (LT) yang memuat serangkaian proses pembelajaran dalam 3 aktifitas yaitu menentukan jenis-jenis segitiga berdasarkan panjang sisi dan besar sudutnya, hubungan panjang sisi dan besar sudut pada segitiga dan menyelesaikan masalah yang berkaitan dengan sifat-sifat segitiga berdasarkan panjang sisi dan besar sudutnya. Hasil dari percobaan pembelajaran menunjukkan bahwa konteks Stadion Gelora Sriwijaya Jakabaring dapat digunakan sebagai starting point pada materi segitiga di kelas VII SMP.This research aims to produce a learning trajectory on the material properties of triangles based on the side and angle using the context Stadion Gelora Sriwijaya Jakabaring in class VII. Instructional design used consisted of three stages: preliminary design, design experiment (pilot experiment and teaching experiment), and retrospective analysis. This study used learning activities are designed and developed based on PMRI approach. Subjects were 29 seventh grade students of SMP Negeri 2 Indralaya Utara. This research resulted Learning Trajectory (LT), which contains a series of learning processes in the three activities that determine the types of triangles based on the side and angle, relationship side lenght and angle of the triangle and resolve problems related to the properties of triangles based on side length and angle. Results of the experiments showed that the Stadion Gelora Sriwijaya Jakabaring could be used as a starting point by seventh grade senior high school students to learn triangle.

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DESAIN PEMBELAJARAN SUDUT MENGGUNAKAN KONTEKS RUMAH LIMAS DI KELAS VII

JINoP (Jurnal Inovasi Pembelajaran) ◽

10.22219/jinop.v2i2.3489 ◽

2016 ◽

Vol 2 (2) ◽

pp. 437

Author(s):

Wiwik Widyawati ◽

Ratu Ilma Indra Putri ◽

Unsri Somakim

Keyword(s):

Design Research ◽

Video Recording ◽

Teaching Experiment ◽

Learning Trajectory ◽

Research Approach ◽

Angle Data ◽

Instruction Theory ◽

Actual Learning ◽

Support Students ◽

Analysis Of Teaching

The aims this study are to produce Learning Trajectory use Rumah Limas as context. The approach used is Pendidikan Matematika Realistik Indonesia (PMRI). The subjects were 26 students of class seventh of SMPN 1 Keluang. This study was using design research approach, the hypothetical Learning Trajectory was developed from a set of activities using Rumah Limas as context. In theory the development carried through the interactive process comprise of preliminary design, teaching experiment and restrospective analysis to contribute to Local Instruction Theory (LIT) to supporting students learn of angle. Data collected by making video recording about incident in the class, collecting students worksheet, giving pretest and postest, interviewing students. The designed HLT compared with Actual Learning Trajectory (ALT) during teaching experiment to analyze whether the students learned or didn't learn from what we had designed in the instructional sequence. Retrospective analysis of teaching experiment showed that by using Rumah Limas as context can support students learning of angle.

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PEMANFAATAN KONTRIBUSI SISWA SEBAGAI ALAT TRANSISI MENUJU PEMAHAMAN KONSEP OPERASI PECAHAN

Refleksi Edukatika Jurnal Ilmiah Kependidikan ◽

10.24176/re.v9i1.2813 ◽

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.

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

KALAMATIKA Jurnal Pendidikan Matematika ◽

10.22236/kalamatika.vol6no2.2021pp181-194 ◽

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.

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Belajar Pencerminan dengan Menggunakan Permainan Bom-Boman di Kelas VII

Jurnal Review Pembelajaran Matematika ◽

10.15642/jrpm.2018.3.1.49-61 ◽

2018 ◽

Vol 3 (1) ◽

pp. 49-61

Author(s):

Sri Hartati ◽

Zulkardi Zulkardi ◽

Yusuf Hartono

Keyword(s):

Retrospective Analysis ◽

Design Research ◽

Analysis Data ◽

Teaching Experiment ◽

Learning Trajectory ◽

Design Experiment ◽

Research Approach ◽

Three Stages ◽

Transformation Geometry ◽

Actual Learning

This study produces a learning trajectory in transformation geometry, specifically on reflection using a game called “bom-boman”. This study using PMRI, the Indonesian version of realistic mathematics education. Subjects of this study are 36 seventh grade students of SMP Negeri 24 Palembang. This study using a design research approach with conducted in three stages: preliminary design, the design experiment (pilot experiment & teaching experiment), and retrospective analysis. Data were collected by observations, interviewing the student, collecting student worksheet, and documentation of classroom event and group works. Hypothetical Learning Trajectory (HLT) has been designed then compared to Actual Learning Trajectory (ALT) during the learning process. Retrospective analysis shows that student’s learning trajectories using the game help students to understand transformation geometry in reflection.

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