scholarly journals A Learning Trajectory of Indonesian 12-years Old Students Understanding of Division of Fractions

2017 ◽  
Vol 7 (2) ◽  
pp. 41-52
Author(s):  
Achmad Nizar ◽  
Siti Maghfirotun Amin ◽  
Agung Lukito
Keyword(s):  
Design Research ◽  
Learning Goals ◽  
Learning Trajectory ◽  
Experimental Phase ◽  
Division Of Fractions ◽  
Hands On ◽  
Concrete Materials ◽  
Design Research Methodology ◽  
School Yard ◽  
Support Students

The purpose of this study was to describe mathematical hands-on activities that can support students to gain better understanding of dividing fractions. This preliminary research phase was started by testing, analyzing, and refining the initial hypothetical learning trajectory (HLT), then in the pilot experimental phase the revised HLT was implemented, and ended with the teaching experimental phase by developing a learning trajectory for 12-year old students in understanding division of fractions. In developing the trajectory, a design research methodology was employed by using four contextual-based learning series (sharing biscuit, sharing remaining chocolate bar, arranging bedroom mats, and running around school yard), including providing some concrete materials or pictorial models as manipulative tools. Seven mathematics experts and twenty five 12-year old students were involved during the research. The four designed learning goals were determining the quotient of division of integer by proper fraction, proper fraction by integer, two proper fractions, and two fractions. Students succeeded in demonstrating their understanding and stated that 16:1/2 = 32; 25/36:5 = 5/36; 24/64:1/2 = 6/8; and 15/2:3/4 = 10 respectively at the end of each designed activity. The interesting results of this study are not a proof, so that a much larger study is needed to determine if the results are due to this approach or due to the teachers’ enthusiasm or what is known as the Hawthorne Effect.

scholarly journals The Hypothetical Learning Trajectory on Research in Mathematics Education Using Research-Based Learning

Pedagogika ◽  
2016 ◽  
Vol 123 (3) ◽  
pp. 42-54 ◽  
Author(s):  
Rully Charitas Indra Prahmana ◽  
Yaya S. Kusumah
Keyword(s):  
Mathematics Education ◽  
Mathematics Teachers ◽  
Academic Writing ◽  
Design Research ◽  
Writing Skills ◽  
Education Institution ◽  
Learning Trajectory ◽  
National Congress ◽  
Design Research Methodology ◽  
Research In Mathematics Education

This study aims to create a learning trajectory on research in mathematics education using design research methodology to enhance research and academic writing skills for pre-service mathematics teachers. The fourteen pre-service mathematics teachers during 5 months period from one higher education institution in Tangerang – Indonesia was collected. The design research method was carried out in three phases: preliminary design phase, teaching experiments phase, and retrospective analysis phase. Initial data analysis of 14 pre-service teachers’ research and academic writing skills was conducted in six stages and the learning trajectories on this topic was identified. The fourteen pre-service teachers were divided into 7 groups and research independently to produce seven scientific articles. The six articles were published in the proceedings of Konferensi Nasional Matematika (National Congress of Mathematics) XVII 2014 and one article was published in the Elemen Journal Vol. 1 No. 1.

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

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

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 HYPOTHETICAL LEARNING TRAJECTORY PADA PEMBELAJARAN BILANGAN NEGATIF BERDASARKAN TEORI SITUASI DIDAKTIS DI SEKOLAH MENENGAH

2018 ◽  
Vol 6 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Nyiayu Fahriza Fuadiah
Keyword(s):  
Learning Process ◽  
Teaching And Learning ◽  
Design Research ◽  
Lesson Plan ◽  
Mathematics Learning ◽  
Learning Goals ◽  
Learning Trajectory ◽  
Mathematical Activity ◽  
Negative Numbers ◽  
Hypothetical Learning Trajectory

Penelitian ini bertujuan untuk mendesain Hypothetical Learning Trajectory (HLT) pada pembelajaran bilangan negatif sebagai hasil dari tahap pertama Didactical Design Research yaitu Analisis Prospektif. HLT ini merupakan tindak lanjut dari hasil identifikasi Learning Obstacle yang yang dilakukan peneliti dalam pembelajaran bilangan negatif yang terintegrasi dalam materi Bilangan Bulat di kelas 7 sekolah menengah pertama. Observasi mendalam terhadap proses belajar mengajar di kelas yang diamati peneliti memperlihatkan kesulitan guru dalam menanamkan konsep bilangan negatif dan operasi bilangan yang melibatkan bilangan negatif serta beberapa kesalahan konstruksi konsep yang dialami oleh siswa. Istilah HLT merujuk pada rencana pembelajaran berdasarkan antisipasi belajar siswa yang mungkin dicapai dalam proses pembelajaran yang didasari pada tujuan pembelajaran matematika yang diharapkan pada siswa, pengetahuan, dan perkiraan tingkat pemahaman siswa, serta pilihan aktivitas matematika secara berurut. HLT ini disusun berdasarkan analisis terhadap Learning Obstacle, tahap berpikir siswa, dan analisis terhadap kurikulum dengan tetap berpijak pada konsep materi yang harus dipahami siswa.This research aims to design Hypothetical Learning Trajectory (HLT) on learning of negative numbers as a result of the first stage on Didactical Design Research specifically in Prospective Analysis. This HLT is a follow up of the results of the identification of the Learning Obstacle conducted by researcher in learning negative numbers that integrated in the material Integer in the 7th grade secondary school. From the observations conducted by researcher on the teaching and learning process in the classroom showed the difficulties of teachers in embedding the concept of negative numbers and arithmetic operations involving negative numbers and several construction errors of concepts that experienced by the students. Term of HLT refers to a lesson plan based on the anticipation of student learning possibly achievable in the learning process which is based on mathematics learning goals expected on students, knowledge, estimates of the level of students understanding, and the selection of mathematical activity sequentially. This HLT is compiled based on an analysis of the Learning Obstacle, level of students thinking, and analysis of the curriculum that standing on the concept that must be understood by the students.

scholarly journals Desain Pembelajaran Luas Segi Banyak Menggunakan Tangram Berpetak di Kelas IV

2015 ◽  
Vol 1 (2) ◽  
pp. 150
Author(s):  
Lia Puspasari ◽  
Zulkardi Zulkardi ◽  
Somakim Somakim
Keyword(s):  
Learning Process ◽  
Design Research ◽  
Fourth Grade ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Plane Figure ◽  
Square Grid ◽  
Polygon Area ◽  
Fourth Grade Students ◽  
Design Research Methodology

AbstractThis research is used for (1) knowing the understanding of fourth grade students of elementary school in finding polygon area concept through square-grid Tangram; (2) resulting the learning trajectory for the student in learning polygon area through square-grid Tangram by having approaching PMRI to the fourth grade students. This research involved 26 students of fourth grade at Az-Zahrah Palembang. It used design research methodology of learning polygon area through square-grid Tangram included preparing for experiment steps, teaching experiment, and retrsospective analysis. It’s resulted Learning Trajectory which is connected to the three learning process activities, hence: (1) determine kinds of plane figure and plane partitioned (using any kinds of employment context); (2) determine the area ofsquare unit (using square-grid Tangram); (3) founding algorithm of polygon area. The result shown by using PMRI approach, square-grid Tangram is useful as a model to support the students in finding polygon concepts. Keywords: Polygon area, Square-grid Tangram, design research, PMRI AbstrakPenelitian ini bertujuan (1) untuk mengetahui pemahaman siswa kelas IV Sekolah Dasar dalam menemukan konsep luas segi banyak menggunakan Tangram berpetak; (2) menghasilkan lintasan belajar bagi siswa melalui Tangram berpetak dalam pembelajaran luas segi banyak menggunakan pendekatan PMRI di kelas IV. Penelitian dilaksanakan di SD Islam Az-Zahrah Palembang yang melibatkan 26 orang siswa kelas IV. Metode yang digunakan adalah design research pembelajaran luas segi banyak menggunakan Tangram berpetak melalui tahap-tahap preparing for the experiment, teaching experiment, dan retrospective analysis. Penelitian ini menghasilkan Learning Trajectory yang memuat serangkaian proses pembelajaran dalam 3 aktivitas yaitu: (1) menentukan jenis bangun datar dan mempartisi bangun (menggunakan konteks berbagai pekerjaan); (2) menentukan luas dengan persegi satuan (menggunakan Tangram berpetak); (3) menemukan algoritma luas segi banyak. Hasil dari percobaan pembelajaran menunjukkan bahwa dengan pendekatan PMRI, Tangram berpetak berperan sebagai model yang mendorong siswa menemukan konsep luas segi banyak. Kata Kunci: Luas segi banyak, Tangram berpetak, design research, PMRI

scholarly journals Pengembangan Lintasan Belajar Pada Pokok Bahasan Segiempat degan Menggunakan Pendekatan Pendidikan Matematika Realistik kelas VII di SMP Negeri 6 Padangsidimpuan

2021 ◽  
Vol 1 ◽  
pp. 130-136
Author(s):  
Ananti Pratiwi ◽  
Haddad Alwi Siregar
Keyword(s):  
Design Research ◽  
Student Response ◽  
Learning Goals ◽  
Learning Trajectory ◽  
Trajectory Design ◽  
Mathematical Education ◽  
A Value ◽  
Lecture Method ◽  
The Subject ◽  
Student Discussion

This research is motivated by students lack understanding the concepts in the subject matter of a the rectangular for example, completing the area and circumference of the rectangular, because the material is presentad using the lecture method and only on certain materials using student discussion groups. The aim of the study was to determine validit, practicality and the trajectory design of the learning trajectory through a realistic mathematical education approach to the subject of rectangular at SMP N 6 Padangsidimpuan. This research is a design research with a type of validation study thet aims to develop local interaction theory (LIT) with collaboration between researches and educators to improve the quality of learning. This research was conducted at SMP N 6 Padangsidimpuan with trial subjects in class VII-2, totaling 31 students. The instrument of collecting data thet used is validation sheets, questionnaires, observations, and using validity and practical analysis techniques. The result of this study indicated thet the learning trajectory through a realistic mathematical education approach is said to be very valid and very practical. The vlidity of the learning trajectory is indicated by a value of 86,98% from analiyzing 3 validators. The practicality of the learning trajectory is shown by 82,71% of the student response questionnaire and observations. The learning trajectory produced in this study is in the form of activities carried out by students to achieve learning goals, where the purpose of the learning is to understanding of rectangular, types of rectangular, properties of rectangular, and circumference and area of rectangular.

scholarly journals LEARNING TRAJECTORY OF QUADRATIC INEQUALITY

2018 ◽  
Vol 2 (1) ◽  
pp. 12
Author(s):  
Kimura Patar Tamba ◽  
Melda Jaya Saragih ◽  
Tanti Listiani
Keyword(s):  
Learning Process ◽  
Design Research ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Learning Activities ◽  
Learning Goals ◽  
Learning Trajectory ◽  
Learning Trajectories ◽  
Quadratic Inequality ◽  
Trajectory Learning

<p>A learning trajectory offers a description of key aspects in planning mathematics learning. It also helps teachers follow and interpret students’ mathematical thinking, so that learning can be developed in accordance with the characteristics of students, and even become a tool for teachers to develop curriculum. There are three main components of learning trajectory: learning goals, learning activities, and hypothetical learning processes. In this article, we constructed a learning trajectory of the quadratic inequality. This qualitative study used didactical design research with 105 grade 10 students as the participants. In the prospective analysis step, didactic design, learning obstacle, and quadratic inequality system were analyzed. Based on the results of this analysis, we constructed hypothetical learning trajectories in the form of didactical design. Then, hyphothetical learning trajectories were implemented in the learning process. Student’s responses were analyzed qualitatively. Results of this analysis were used to revise the learning trajectory in order to obtain alternative trajectory learning outcomes of theoretical and empirical analysis. Finally, this article offers an alternative learning trajectory of quadratic inequalities that are different from the existing learning trajectories presented in the current textbook. The learning trajectory that is offered is the learning quadratic inequality which starts from the function approach.</p><p> <strong>BAHASA INDONESIA ABSTRACT: </strong>Learning trajectory (LT) menawarkan sebuah deskripsi akan aspek kunci dalam perencanaan pembelajaran matematika. LT juga membantu guru belajar dalam mengikuti dan menginterpretasi cara berpikir matematisnya siswa, sehingga pembelajaran dapat dikembangkan sesuai dengan karateristik siswa, bahkan menjadi alat bagi guru untuk mengembangkan kurikulum.  Ada tiga komponen utama dari learning trajectory, yaitu: tujuan pembelajaran (learning goals), kegiatan pembelajaran (learning activities) dan hipotesis proses belajar siswa (hypothetical learning process). Dalam artikel ini akan dikonstruksi sebuah LT pertidaksamaan kuadrat. Penelitian ini menggunakan pendekatan kualitatif dengan didactical design research. Adapun partisipan sebanyak 105 siswa kelas X. Pada awal penelitian ini, dilakukan analisis propektif yaitu analisis atas materi pertidaksamaan kuadrat, hambatan belajar dan tingkat berpikir siswa. Kemudian dari hasil analisis ini disusunlah Hipotetical Learning Trajectories yang berupa desain didaktis. Desain didaktis berdasarkan Hypotetical Learning Trajectories ini diimplementasikan dalam pembelajaran. Respon siswa dianalisis secara kualitatif. Hasil analisis ini digunakan untuk merevisi Learning Trajectory, sehingga diperoleh Learning Trajectory alternatif hasil analisis teoritik dan empirik. Akhirnya, artikel ini menawarkan sebuah alternatif learning trajectory pertidaksamaan kuadrat yang berbeda dengan learning trajectories yang ada pada buku pelajaran sekarang. Learning trajectory yang ditawarkan adalah pembelajaran pertidaksamaan yang dimulai dengan pendekatan fungsi. </p>

A Proposed Instructional Theory for Integer Addition and Subtraction

2012 ◽  
Vol 43 (4) ◽  
pp. 428-464 ◽  
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.

What Can We Learn From Trustworthy Data? An Interview With John Wills Lloyd

2020 ◽  
pp. 105345122096310
Author(s):  
Kristin L. Sayeski
Keyword(s):  
Learning Disabilities ◽  
Best Practice ◽  
Design Research ◽  
Single Case ◽  
Professional Organizations ◽  
Professor Emeritus ◽  
University Of Virginia ◽  
Single Case Design ◽  
Design Research Methodology ◽  
The University

John Wills Lloyd is Professor Emeritus at the University of Virginia and co-editor of Exceptional Children. He earned his PhD from the University of Oregon and spent most of his career at the University of Virginia. Dr. Lloyd has been an integral part of many professional organizations, including the Council for Exceptional Children’s Division for Learning Disabilities, where he served as president and later as the executive director, and the Division for Research. Dr. Lloyd’s work has focused on the identification of effective instructional practices, best-practice in single-case design research methodology, and facilitating a deeper understanding of learning disabilities. He has produced numerous scholarly articles, foundational textbooks, and web-based materials that continue to inform readers about effective practice in special education.

scholarly journals Ten-Structure as Strategy of Addition 1-20 by Involving Spatial Structuring Ability for First Grade Students

2015 ◽  
Vol 8 (11) ◽  
pp. 16 ◽  
Author(s):  
Ummy Salmah ◽  
Ratu Ilma Indra Putri ◽  
Somakim Somakim
Keyword(s):  
Teaching And Learning ◽  
Design Research ◽  
First Grade ◽  
Learning Activities ◽  
Design Learning ◽  
Spatial Structuring ◽  
Support Students

<p class="apa">The aim of this study is to design learning activities that can support students to develop strategies for the addition of number 1 to 20 in the first grade by involving students’ spatial structuring ability. This study was conducted in Indonesia by involving 27 students. In this paper, one of three activities is discussed namely ten-box activity. This activity was aimed to introduce and develop ten-structure to be a students’ strategy in addition of number 1 to 20. The method was design research by designing learning activities involving spatial structuring ability. PMRI underlined the context and activity. The result of the study indicates that ten-box activities can help students to develop ten-structure as a strategy in addition of number 1 to 20. As a recommendation, PMRI can be implemented as an approach of teaching and learning addition 1 to 20.</p>

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