Supporting Students’ Reasoning About Multiplication of Fractions by Constructing an Array Model

The aim of the research is to support students in constructing an array model as a bridge from their informal knowledge to the formal one in understanding the part-whole relation concept. The part-whole relation concept is important for students to reason about multiplication of fractions. Realistic Mathematics Education which is in Indonesia adapted as Pendidikan Matematika Realistik Indonesia (PMRI) is used as an approach in designing a series of lessons. For this purpose, hypothetical learning trajectory (HLT) became the base for conducting a teaching experiment and designing its learning materials. The research was conducted in the fifth grade of SD Al Hikmah Surabaya, an elementary school in Indonesia, with five students as the participants. The collected data were qualitative data in the form of students’ written works and the transcript of video recording during the lesson. The data were analyzed retrospectively by confronting the conjecture of students’ thinking in the HLT with the fact in the teaching experiment. The result of the research shows that most students could use the contextual problem in promoting their ability on constructing their own array model to reason about part-whole relation.

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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 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 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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Application Of Realistic Mathematics Education Approach With Concrete Materials To Improve Mathematics Learning Outcomes About Solid Figures For The Fifth Grade Students Of SDN Bangkal 01 In The Academic Year Of 2019/2020

Kalam Cendekia: Jurnal Ilmiah Kependidikan ◽

10.20961/jkc.v8i1.39765 ◽

2020 ◽

Vol 8 (1) ◽

Author(s):

Rizky Indah Tri Wahyuni ◽

Ngatman Ngatman ◽

Wahyudi Wahyudi

Keyword(s):

Mathematics Education ◽

Learning Outcomes ◽

Qualitative Data ◽

Mathematics Learning ◽

Fifth Grade ◽

Realistic Mathematics Education ◽

Fifth Grade Students ◽

Realistic Mathematics ◽

Concrete Materials ◽

Academic Year

The purposes of this study are: (1) describing the steps of applying the Realistic Mathematics Education approach with concrete materials, (2) improving mathematics learning outcomes about solid figures, and (3) describing the obstacles and solutions to the application of the Realistic Mathematics Education approach. This collaborative classroom action research was conducted in three cycles and six meetings. The research data are quantitative and qualitative data. Data collection techniques include observation, interviews and tests. The results of the study are: (1) the steps in the application of the Realistic Mathematics Education approach to improve Mathematics learning outcomes about solid figures are: a. understanding contextual problems through concrete materials, b. explaining contextual problems with concrete materials, c. resolving contextual problems with concrete materials, d. comparing, discussing, and answering question with concrete materials, and e. drawing conclusion; (2) the application of the Realistic Matematics Education approach can improve Mathematics learning outcomes about solid figures; (3) the obstacle in this study is students lack understanding to do worksheets, The solution is that the teacher asks the students concern to the instruction in worksheets.

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PEMAHAMAN MAHASISWA TERHADAP INTEGRAL SEBAGAI ANTI TURUNAN, SUATU DESAIN RISET PADA KALKULUS INTEGRAL

JURNAL EKSAKTA PENDIDIKAN (JEP) ◽

10.24036/jep/vol1-iss1/28 ◽

2017 ◽

Vol 1 (1) ◽

pp. 9 ◽

Cited By ~ 2

Author(s):

Fridgo Tasman ◽

Defri Ahmad

Keyword(s):

Learning Outcomes ◽

Teaching Experiment ◽

Learning Trajectory ◽

First Year ◽

Realistic Mathematics Education ◽

Classroom Discussions ◽

First Year Students ◽

Realistic Mathematics ◽

Instructional Activities ◽

Class Room

The low learning outcomes and student’s difficulties in understanding calculus courses, espe-cially integral topic, encourage us as researcher to design a calculus lesson for first year students by using realistic mathematical approach (Realistic Mathematics Education). For that we try to design a series of instructional activities starting from understanding integral as an anti derivative. The in-structional activity is designed and developed based on the learning process that occurs in the class-room by involving 30 first year students in FMIPA UNP. The classroom learning compared with our Hypothetical Learning Trajectory (HLT). The results of teaching experiment show that students' un-derstanding of derivative plays important role in understanding the integrals, in general students have difficulty in communicating their ideas in determining the anti-derivative of a function. Through class-room discussions students can get ideas and discuss it in determining the anti-derivative of a function. Based on these results it is recommended to conduct classroom discussions to build students' under-standing in studying calculus especially integral as an anti derived.

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PERCENTAGE BAR: A MODEL FOR HELPING FIFTH GRADE STUDENTS UNDERSTAND PERCENTAGES

Mosharafa: Jurnal Pendidikan Matematika ◽

10.31980/mosharafa.v7i2.35 ◽

2018 ◽

Vol 7 (2) ◽

pp. 155-166

Author(s):

Yenny Anggreini Sarumaha ◽

Ratu Ilma Indra Putri ◽

Yusuf Hartono

Keyword(s):

Mathematics Education ◽

Teaching And Learning ◽

Design Research ◽

Classroom Teacher ◽

Fifth Grade ◽

Realistic Mathematics Education ◽

Fifth Grade Students ◽

Realistic Mathematics ◽

Grade 5 ◽

Support Students

AbstrakPenelitian ini bertujuan untuk mengembangkan teori instruksional lokal untuk mendukung pengembangan siswa pemahaman dasar tentang persentase. Penelitian desain dipilih sebagai sarana yang tepat untuk mencapai tujuan. Penelitian dilakukan di Pusri Sekolah Dasar Palembang, Kelas 5 yang melibatkan 42 siswa secara total dan satu guru kelas. Pendidikan Matematika Realistik Indonesia (PMRI) yang diadaptasi dari Realistic Mathematics Education (RME) sengaja dipilih sebagai pendekatan dalam proses belajar mengajar. Keakuratan ini mengungkapkan bahwa bar persentase yang disajikan sebagai model dalam pembelajaran membantu siswa untuk memahami persentase. Siswa menggunakannya sebagai alat untuk penalaran dan juga sebagai alat untuk menghitung. Itu juga membantu mereka untuk menyampaikan pemikiran mereka kepada orang lain. Untuk beberapa siswa yang biasanya menggunakan cara formal untuk menyelesaikan masalah persentase, temukan kotak persentase sebagai cara lain untuk membuktikan hasilnya. AbstractThis present study is aimed to develop a local instructional theory to support students development of basic understanding of percentages. Design research was chosen as an appropriate mean to achieve the goal. The study was conducted in Pusri Primary School Palembang, Grade 5 involving 42 students in total and one classroom teacher. Pendidikan Matematika Realistik Indonesia (PMRI) which was adapted from Realistic Mathematics Education (RME) was deliberately chosen as an approach in the teaching and learning process. This stuidy revealed that a percentage bar which is served as a model in learning helped students to understand percentages. Students used it as a tool for reasoning and also as a tool for calculating. It also helped them to represent the percents stated and to communicate their thoughts to others. For some students who usually utilized the formal way to solve percentage problems, found the bar as another way to prove the result.

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IMPROVEMENT OF LEARNING OUTCOMES IN RESULT USING REALISTIC MATHEMATIC EDUCATION APPROACH IN BASIC SCHOOL

Unes Journal of Education Scienties ◽

10.31933/ujes.2.2.157-165.2018 ◽

2018 ◽

Vol 2 (2) ◽

pp. 157

Author(s):

Mimik Fernandes ◽

Farida F ◽

Yanti Fitria ◽

Ahmad Fauzan ◽

Nelvyarni Nelvyarni

Keyword(s):

Mathematics Education ◽

Action Research ◽

Student Learning ◽

Learning Outcomes ◽

Student Learning Outcomes ◽

Class Action ◽

Realistic Mathematics Education ◽

Realistic Mathematics ◽

Multiplication Of Fractions ◽

Mathematic Education

Based on experience and reflection multiplication of fractions learning at fifth class SDN 33 VII Koto Padang Pariaman district. Student learning outcomes is still low and the learning undertaken by teachers arenot using realistic problem to beginning of learning. So the author through this research trying to improve student learning outcomes in subjects multiplication of fractions. The purpose of this study was to describe the planning, implementation and learning outcomes. This research is action research (class action research), this study used a qualitative and quantitative approach. Learning is used by using the realistic mathematics education approach. After doing research hence an increase in student learning outcomes in multiplication of fractions lesson using realistic mathematics education approach. It can be seen, both from the ability of teachers in designing learning from 83% up to 94%, implementation of learning increased 94% from 77%, and learning outcomes increased to 86,87 from 74,04.

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DESIGNING LEARNING ROTATION USING THE CONTEXT OF BAMBOO WOVEN MOTIF

Prima Jurnal Pendidikan Matematika ◽

10.31000/prima.v4i2.2600 ◽

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.

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