Learning trajectory of a student with learning disabilities for the concept of length: A teaching experiment

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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THE INNOVATION OF LEARNING TRAJECTORY ON MULTIPLICATION OPERATIONS FOR RURAL AREA STUDENTS IN INDONESIA

Journal on Mathematics Education ◽

10.22342/jme.10.3.9257.397-408 ◽

2019 ◽

Vol 10 (3) ◽

pp. 397-408 ◽

Cited By ~ 12

Author(s):

Heris Hendriana ◽

Rully Charitas Indra Prahmana ◽

Wahyu Hidayat

Keyword(s):

Basic Concept ◽

Research Method ◽

Design Research ◽

Teaching Experiment ◽

Learning Trajectory ◽

Preliminary Design ◽

Student Difficulties ◽

Design Learning ◽

Teaching Design ◽

Formal Level

The rural area's student difficulties in learning the concept of number operation had been documented by several studies, especially for the case of multiplication. The teacher typically introduces the multiplication concepts using the formula without involving the concept itself. Furthermore, this study aims to design learning trajectory on multiplication operations in the Mathematics of GASING (Math GASING) by focusing more on the concept itself than the formula and by starting from the informal to a formal level of teaching. Design research used as the research method to solve this problem consisting of three phases, namely preliminary design, teaching experiment, and retrospective analysis. The research results show that the Math GASING has a real contribution for students to understanding and mastering in the concept of the multiplication operations. This research also explains the strategy and the model discovered by students in learning multiplication that the students used as a basic concept of multiplication. Finally, the students were able to understand the concept of multiplication more easily, and they showed interest in using this learning trajectory.

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

Imajiner: Jurnal Matematika dan Pendidikan Matematika ◽

10.26877/imajiner.v1i4.3854 ◽

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.

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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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Desain Pembelajaran Penjumlahan dan Pengurangan Bilangan Menggunakan Konteks Bangka Belitung untuk Mendukung KBKM Siswa

Jurnal Pendidikan Matematika (JUDIKA EDUCATION) ◽

10.31539/judika.v2i1.718 ◽

2019 ◽

Vol 2 (1) ◽

pp. 11-24

Author(s):

Rajab Vebrian ◽

Yudi Yunika Putra

Keyword(s):

Design Research ◽

Pacific Islands ◽

Teaching Experiment ◽

Learning Trajectory ◽

Learning Context ◽

Design Learning ◽

The Pacific ◽

Addition And Subtraction ◽

Support Students ◽

Research Type

This study aims to produce learning trajectories of addition and subtraction of material numbers using the context of Bangka Belitung, also to find out whether the use of these learning designs can support students' Critical Thinking Abilities (KBKM). The research method, this research is a validation study design research type involving 6 students in the pilot experiment stage, and 25 students in the teaching experiment stage. The alleged learning trajectory was developed from a series of learning activities using the context of the Pacific Islands, such as sahang / pepper seeds as a model in learning the addition and subtraction of numbers. The results showed the use of trajectories in the context of Bangka Belitung provided different assessment results between the students' pretest and posttest scores. Most students have been able to solve the problem of addition and subtraction and provide arguments in answering the problems encountered. In conclusion, the use of instructional design using the context of Bangka Belitung in the learning of addition and subtraction of numbers can support student CBCS. Keywords: Numbers, Design, Learning Context

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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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Sixth-Grade Students’ Mathematical Abstraction Processes in a Teaching Experiment Designed Based on Hypothetical Learning Trajectory

TED EĞİTİM VE BİLİM ◽

10.15390/eb.2020.8464 ◽

2020 ◽

Author(s):

Faik Camci ◽

Dilek Tanışlı

Keyword(s):

Sixth Grade ◽

Teaching Experiment ◽

Learning Trajectory ◽

Sixth Grade Students ◽

Hypothetical Learning Trajectory ◽

Mathematical Abstraction

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The Data Package in Learning Mean Using LSLC and PMRI

Jurnal Pendidikan Matematika ◽

10.22342/jpm.15.1.9431.61-70 ◽

2021 ◽

Vol 15 (1) ◽

pp. 61-70

Author(s):

Poppy Trianti Rahayu ◽

Ratu Ilma Indra Putri

Keyword(s):

Learning Community ◽

Lesson Study ◽

Design Research ◽

Teaching Experiment ◽

Learning Trajectory ◽

Literature Study ◽

Field Notes ◽

Design Type ◽

Written Test ◽

Research Type

This study aims to produce statistical learning designs in the introduction of the concept of average values and knowing student learning outcomes in learning average values by previously learning about the presentation of data consisting of tables and diagrams through learning trajectories and what happens during the learning process. This learning is based on Lesson Study for Learning Community (LSLC), the approach of Indonesian Realistic Mathematics Education (PMRI). This study uses a type of Design Research method research design type of validation study, which involves in MTs 1 in Palembang. There are three stages in design research type validation studies namely Preparing for the experiment in the form of literature study and the design of the Hypothetical Learning Trajectory (HLT); Design experiment in the form of a Preliminary Teaching Experiment (Pilot Experiment) and Teaching Experiment; and Restrospective analysis. The instruments used were written test, video and field notes. The results of learning experiments show that the design of learning provided has helped students understand the concept of Mean.

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