scholarly journals A LEARNING TRAJECTORY FOR PROBABILITY: A CASE OF GAME-BASED LEARNING

2021 ◽  
Vol 12 (1) ◽  
pp. 1-16
Author(s):  
Ariyadi Wijaya ◽  
Elmaini Elmaini ◽  
Michiel Doorman
Keyword(s):  
Design Research ◽  
Learning Trajectory ◽  
General Level ◽  
Game Based Learning ◽  
Starting Point ◽  
Formal Level ◽  
Formal Concepts ◽  
Sample Points ◽  
Four Levels ◽  
Actual Learning

This research is aimed to describe a learning trajectory for probability through game-based learning. The research employed design research consisting of three stages: preparing for the experiment, design experiment, and retrospective analysis. A hypothetical learning trajectory (HLT) using Sudoku and Snake-and-ladder games was developed by collecting data through documentation, interviews, and classroom observations. The HLT was implemented in the classroom to investigate students’ actual learning trajectory. The results of this research indicate that the games helped students understand the concept of probability. The learning trajectory for probability based on game-based learning is seen from the perspective of four levels of emergent modeling. In the first level – ‘situational level’ – Sudoku and Ladder-and-Snake games were played by students. The second level is the ‘referential level’ where the rules of the games were used as a starting point to learn the concept of probability. Communication during game playing stimulated students' knowledge about random events, sample spaces, sample points, and events. At the third level – ‘general level’ – students used tree and table diagrams to generalize possible outcomes of an experiment and develop an understanding of sample spaces and sample points. Lastly, at the ‘formal level’ students developed their informal knowledge into formal concepts of probabilities.

scholarly journals Facilitating Students’ Multiple Intelligences through RME: A Learning Trajectory of Volume and Surface Area Measurement

2021 ◽  
Vol 3 (1) ◽  
pp. 27-50
Author(s):  
Ahmad Wachidul Kohar ◽  
Achmad Dhany Fachruddin ◽  
Soffil Widadah
Keyword(s):  
Surface Area ◽  
Multiple Intelligences ◽  
Design Research ◽  
Teaching Experiment ◽  
Rectangular Prism ◽  
Area Measurement ◽  
Learning Activity ◽  
Learning Trajectory ◽  
Formal Level ◽  
Formal Concepts

This is a design research which aims to describe the learning trajectory of volume and surface area of rectangular prism by considering the involvement of the multiple intelligences-based activities within the realistic mathematics education (RME) learning activity. A total of 39 students of grade five at an elementary school in Sidoarjo, Indonesia were involved in teaching experiment phase. By collecting data through documentation, interviews, and classroom observations, the Hypothetical Learning Trajectory which was developed in pilot experiment was then revised to get a revised learning trajectory reported in this paper. Such a revised learning  trajectory are the learning activities around drawing the nets of cube and cuboids through rolling activity, comparing surface are and volume of two models with different sizes, finding surface area using the constructed nets, building miniature buildings using cube unit model, predicting the number cube units in a box, constructing various models of cuboids to various sizes using particular number of cube units, rearranging a number of cube units arrangements with different layers to get different volume and surface area, and comparing the volumes of two rectangular prism made from the same rectangular model of paper. Lastly, at the ‘formal level’ students developed their  informal  knowledge  into  formal  concepts  of volume and surface area of rectangular prism, which in this case is cuboid and cube.

scholarly journals Designing Learning Translation Using the Motifs of Anyaman Bambu

2020 ◽  
Vol 3 (2) ◽  
pp. 61
Author(s):  
Maryati Maryati ◽  
Rully Charitas Indra Prahmana
Keyword(s):  
Design Research ◽  
Basic Material ◽  
Learning Trajectory ◽  
Preliminary Design ◽  
Learning Mathematics ◽  
Starting Point ◽  
Formal Level ◽  
Ninth Grade Students ◽  
Is Design ◽  
Design Experiments

Indonesia has many cultures, one of which is in the form of traditional crafts namely Anyaman Bambu. It’s a form of traditional craft in the community that uses bamboo as its basic material. However, people only see these crafts as only a form of traditional craft, even though there are many motifs in these crafts that can be used as a starting point in learning mathematics, namely geometry transformations. Therefore, this research aims also to produce the learning trajectory of students in learning one subject in geometry transformations namely translation, which develops from informal to formal level through the Indonesian Realistic Mathematics Education (IRME) approach. The research method used is design research starting from preliminary design, design experiments, and retrospective analysis. This study explores how the motifs of Anyaman Bambu make a real contribution for ninth-grade students to understand the concept of translation. The results of design experiments show that the context of the motifs of Anyaman Bambu can stimulate students to understand their knowledge of the concept of translation. All the strategies and models that students find, describe, and discuss that show how students' constructions or contributions can be used to help their initial understanding of the translation.

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

2019 ◽  
Vol 10 (3) ◽  
pp. 397-408 ◽  
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.

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 DESAIN PEMBELAJARAN SUDUT MENGGUNAKAN KONTEKS RUMAH LIMAS DI KELAS VII

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.

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 Kemajuan Belajar Siswa pada Penjumlahan Bilangan Desimal Menggunakan Pengukuran Berat

2018 ◽  
Vol 3 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Leni Maimuna ◽  
Darmawijoyo Darmawijoyo ◽  
Ely Susanti
Keyword(s):  
Design Research ◽  
Number Line ◽  
Learning Trajectory ◽  
Design Experiment ◽  
Fourth Grade Students ◽  
Measurement Results ◽  
Formal Level ◽  
Field Notes ◽  
Three Stages ◽  
Is Design

This study was aimed at describing the student’ learning progress on decimals addition by a set of learning activitis based on Indonesian Realistic Mathematics Education. This research  method is design research which contain three stages, namely: preliminary design, design experiment and retrospective analysis. Hypothetical Learning Trajectory (HLT) has been designed to play an important role as learning design and research instrument. HLT was tested to 30 fourth grade students. The data were collected through interview, observation, and field notes. The findings of the research  showed that this instructional design could stimulate students  in the introduction of one digit decimal through the result of weight measurement, the use of the model that the students make themselves (model of) to describe the measurement results at the second level, and marking the result of the measurement to the number line and continued by describing the process of decimals addition from the measurement activity to the number line in the more formal level. Furthermore at the formal level, students are able to solve the problem of the decimals addition using the correct procedure that is the place value rule.

scholarly journals The Hypothetical Learning Trajectory on Addition in Mathematics GASING

2015 ◽  
Vol 5 (1) ◽  
pp. 49-62
Author(s):  
Rully Charitas Indra Prahmana
Keyword(s):  
Retrospective Analysis ◽  
Research Method ◽  
Design Research ◽  
Learning Trajectory ◽  
Preliminary Design ◽  
Hypothetical Learning Trajectory ◽  
Formal Level ◽  
Is Design ◽  
Teaching Experiments

The purpose of this study is to look at the role of using Mathematics GASING (Math GASING) to help students understand and master the addition concept from the informal level (concrete) to the formal level. The research method used is design research with a preliminary design, teaching experiments, and retrospective analysis stages. This study describes how the Math GASING made a real contribution for students understanding of the concept of addition. The whole strategy and model that requires students to discover, to describe, and to discuss during the construction phase demonstrates how students can use their initial understanding of the addition concept. The stages in the learning trajectory have an important role in understanding the addition concept from informal level to formal level and also make the study of mathematics more easy, fun, and enjoyable.

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