Articles

BI-MULTIPLIER SIMETRIK PADA ALJABAR INCLINE LOKA DEWI, FITA; LUKITO, AGUNG
Mathunesa : Jurnal Ilmiah Matematika Vol 7, No 2 (2019)
Publisher : Unesa

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Abstract

Aljabarjincline merupakanjgeneralisasi semiring dan latis. Aljabarjincline adalah himpunanjtak-kosong dengan operasi biner ? ? dan ? ? yang memenuhi aksioma-aksioma tertentu. Konsep multiplier juga diterapkan pada aljabar incline dengan sifat reguler dan kanselatif kanan. Setiap bi-multiplier -simetrik adalah reguler. Bi-multiplier -simetrik pada aljabar incline bersifat kanselatif kanan. Kata kunci: Aljabarjincline, bi-multiplier simetrik, jlatis.
PELATIHAN PEMBELAJARAN MATEMATIKA REALISTIK (PMR) DENGAN MEDIA BERBAHAN BEKAS DI SEKOLAH DASAR Palupi, Evangelista Lus Windyana; Lukito, Agung; Khabibah, Siti; Amin, Siti Maghfirotun
Jurnal ABDI: Media Pengabdian Kepada Masyarakat Vol 5, No 2 (2020)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/ja.v5n2.p97-105

Abstract

Pembelajaran Matematika Realistik (PMR) merupakan salah satu alternatif pendekatan pembelajaran yang memberikan kesempatan kepada siswa untuk belajar matematika secara bermakna dan realistik bagi siswa. Prinsip emergent modeling dalam PMR menuntut ketersediaan media pembelajaran agar siswa dapat membayangkan situasi masalah yang diberikan. Namun permasalahan yang muncul adalah keterbatasan media murah yang dapat digunakan guru dan keterbatasan pengetahuan guru dalam merancang pembelajaran matematika realistik berbantuan media. Di lain pihak, sejumlah besar barang bekas dibiarkan menumpuk, kurang dimanfaatkan. Padahal barang bekas dapat didaur ulang menjadi barang dengan nilai guna, salah satunya dengan memanfaatkannya untuk kepentingan belajar dan mengajar matematika. Pelatihan pembelajaran matematika realistik dengan bantuan media berbahan bekas di sekolah dasar dapat menjadi solusi praktis untuk membantu guru menyelenggarakan proses pembelajaran matematika yang bermakna, menarik, interaktif, mudah diikuti dan murah. Meskipun rancangan pembelajaran yang dihasilkan belum memenuhi prinsip dan karakteristik pembelajaran matematika realistik, kegiatan ini dinilai bermanfaat dan berhasil dalam membantu guru untuk memilih bahan bekas sebagai media dan merancang pembelajaran matematika dengan media tersebut. Dari kegiatan ini, dihasilkan 27 desain pembelajaran matematika dengan media berbahan bekas yang berbeda dari 36 desain yang dibuat. Rancangan pembelajaran yang dibuat meliputi beberapa topik matematika untuk kelas 3 dan 4 sekolah dasar.
Learning The Concept of Area and Perimeter by Exploring Their Relation Winarti, Destina Wahyu; Amin, Siti Maghfirotun; Lukito, Agung; Gallen, Frans Van
Journal on Mathematics Education Vol 3, No 1 (2012)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.3.1.616.41 - 44

Abstract

Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a  given area, there are many possibilities of perimeter and vice versa. When student are not aware of this relation they might confuse about the concept in their continuation of learning process. This research was conducted to study if it would support students’ understanding of the concept of perimeter and area if we let them explore the relation between perimeter and area in the very first phase of the learning process. Design research was chosen as the method to study this issue and the three basic principles in The Realistic Mathematics approach were applied in this study to support the learning process of perimeter and area. Real life context such as picture frames was choosen in developing a sequence of learning line to reach the learning goal of perimeter and area. The partipants of this research were students and mathematics teacher of grade 3 in one of the elementary school in Surabaya. Two classes were taken to involve in the first cycle and second cycle respectively.  The teaching experiment shows that the class activities such as making photo frame, measuring photo paper with sticky paper and arranging shapes with wooden matches are activities which can be used to reveal the relation of perimeter and area. From those activities students build their own understanding that in fact area and perimeter are not in one to one correspondence, they found that for the given area they might find different perimeter or vice versa. They also found the reason why they multiply length and width to count the area of rectangular or square shape from sticky paper activity. Somehow some students were found still struggle with their understanding of area and perimeter. They often simply count the area and perimeter but when it comes into comparing the area or perimeter  they still struggle to differentiate between area and perimeter. Keywords: Perimeter, Area, Relation between perimeter and area, Understanding DOI: http://dx.doi.org/10.22342/jme.3.1.616.41-54
Students Modelling in Learning The Concept of Speed Khikmiyah, Fatimatul; Lukito, Agung; Patahudin, Sitti Maesuri
Journal on Mathematics Education Vol 3, No 1 (2012)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (143.714 KB) | DOI: 10.22342/jme.3.1.618.87-98

Abstract

Previous researchs shows that speed is one of the most difficult in the upper grades of primary school. It is because students must take into consideration of two variables; distance and time. Nevertheless, Indonesian students usually learn this concept as a transmission subject and teacher more emphasizes on formal mathematics in which the concept of speed given as distance by time rigorously. A sequence of learning activities with toy cars context was designed based on students development and Realistic Mathematics Education (RME) principles which are guided reinvention, didactical phenomenology and emergent modelling. Using their own models, students are able to explain a proportion among distance and time in speed as well the relationship of it. Keywords: The concept of speed, design research, Toy cars, context, ratio tables model
Learning The Concept of Area and Perimeter by Exploring Their Relation Winarti, Destina Wahyu; Amin, Siti Maghfirotun; Lukito, Agung; Gallen, Frans Van
Journal on Mathematics Education (JME) Vol 3, No 01 (2012): Journal on Mathematics Education (JME)
Publisher : IndoMS Pusat

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Abstract

Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a  given area, there are many possibilities of perimeter and vice versa. When student are not aware of this relation they might confuse about the concept in their continuation of learning process. This research was conducted to study if it would support students’ understanding of the concept of perimeter and area if we let them explore the relation between perimeter and area in the very first phase of the learning process.  Design research was chosen as the method to study this issue and the three basic principles in The Realistic Mathematics approach were applied in this study to support the learning process of perimeter and area. Real life context such as picture frames was choosen in developing a sequence of learning line to reach the learning goal of perimeter and area. The partipants of this research were students and mathematics teacher of grade 3 in one of the elementary school in Surabaya. Two classes were taken to involve in the first cycle and second cycle respectively.  The teaching experiment shows that the class activities such as making photo frame, measuring photo paper with sticky paper and arranging shapes with wooden matches are activities which can be used to reveal the relation of perimeter and area. From those activities students build their own understanding that in fact area and perimeter are not in one to one correspondence, they found that for the given area they might find different perimeter or vice versa. They also found the reason why they multiply length and width to count the area of rectangular or square shape from sticky paper activity. Somehow some students were found still struggle with their understanding of area and perimeter. They often simply count the area and perimeter but when it comes into comparing the area or perimeter  they still struggle to differentiate between area and perimeter.  Keywords: Perimeter, Area, Relation between perimeter and area, Understanding
Students’ Modelling in Learning The Concept of Speed Khikmiyah, Fatimatul; Lukito, Agung; Patahudin, Sitti Maesuri
Journal on Mathematics Education (JME) Vol 3, No 01 (2012): Journal on Mathematics Education (JME)
Publisher : IndoMS Pusat

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Abstract

Previous researchs shows that speed is one of the most difficult in the upper grades of primary school. It is because students must  take into consideration of two variables; distance and time. Nevertheless, Indonesian students usually learn this concept as a transmission subject and teacher more emphasizes on formal mathematics in which the concept of speed given as “distance by time”rigorously. A sequence of learning activities with toy cars context was designed based on students’ development and Realistic Mathematics Education (RME) principles which are guided reinvention, didactical phenomenology and emergent modelling. Using their own models, students are able to explain a proportion among distance and time in speed as well the relationship of it.  Key words: The concept of speed, design research, Toy cars, context, ‘ratio table’ model
Student's Understanding of Graph Based on Information-Processing Mampouw, Helti Lygia; Lukito, Agung; Suwarsono, St.
International Journal of Active Learning Vol 1, No 1 (2016): April 2016
Publisher : International Journal of Active Learning

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ijal.v1i1.7735

Abstract

This study is a preliminary research on how students understand patterns. Students' understanding of something is a cognitive phenomenon as, according to information processing perspective, an integral part of the stimulus, receiving, encoding, storing and retrieving information. This paper aims to describe the information processing by students when they interpret the graph as a task that was delivered using takjil context. There are 9 seven graders aged 11-12 years in various mathematics ability that three students in each its category high, mid and low. It was found that: (1) The graph given in the task attract students' attention with various reasons. (2) The level of abstraction and processing is in accordance with students' mathematical abilities. (3) The number of words related to the context activated at certain period was determined by reviews of their experiences with similar contexts. (4) Concepts of a new schemes were not solely determined by the students' mathematical abilities. Broadly, this study recommends students to have learning experiences through varying contexts and gain extensive experiences to develop appropriate and useful cognitive schemes for solving problems.How to CiteMampouw, H. L., Lukito, A., & Suwarsono, S. (2016). Student's Understanding of Graph Based on Information-Processing. International Journal of Active Learning, 1(1).
SIFAT-SIFAT Q-ALJABAR BADRIQUL MUDRIK, MOH; LUKITO, AGUNG
Mathunesa : Jurnal Ilmiah Matematika Vol 6, No 3 (2018)
Publisher : Unesa

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Abstract

Himpunan tak-kosong yang memuat konstanta 0 dengan suatu operasi biner disebut Q-aljabar jika memenuhi aksioma (Q1) , (Q2) , dan (Q3) , untuk setiap . Artikel ini membahas Q-aljabar yang merupakan perluasan dari BCK/BCI/BCH­-aljabar. Selain itu artikel ini juga membahas sifat-sifat dari Q-aljabar; yaitu, -bagian dan ideal pada Q-aljabar, serta Q-aljabar medial. Pada suatu Q-aljabar berorder 3, adalah ideal jika dan hanya jika berorder 1. adalah Q-aljabar medial jika dan hanya jika untuk setiap . Kata kunci: Q-aljabar, -bagian, ideal, Q-aljabar medial
KARAKTERISASI KONGRUENSI UNIMODULAR MATRIKS LAPLACIAN GRAF SEDERHANA NUFUS, ATIROTUN; LUKITO, AGUNG
Mathunesa : Jurnal Ilmiah Matematika Vol 6, No 3 (2018)
Publisher : Unesa

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Abstract

Misalkan graf sederhana. Matriks Laplacian graf adalah , dimana matriks diagonal dengan entri derajat titik dan matriks adjasensi graf . Skripsi ini mengkaji karakterisasi kongruensi unimodular matriks Laplacian graf sederhana. Hasil utamanya adalah bahwa matriks Laplacian yang terkait dengan graf adalah kongruen dengan matriks unimodular jika dan hanya jika dan adalah isomorfik sikel. Kata kunci : graf, matriks Laplacian, isomorfisme sikel, matriks unimodular, kongruensi unimodular.
IDEAL KOMUTATIF DALAM BE-ALJABAR INDRIANI, ENY; LUKITO, AGUNG
Mathunesa : Jurnal Ilmiah Matematika Vol 6, No 3 (2018)
Publisher : Unesa

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Abstract

Tripel dengan himpunan tak kosong operasi biner dan elemen khusus disebut BE-aljabar jika memenuhi , , dan , untuk semua . Subhimpunan dari disebut ideal komutatif pada jika memenuhi , dan mengakibatkan , untuk semua . Pada tulisan ini diturunkan sifat-sifat ideal komutatif dalam BE-aljabar. Kata Kunci: BE-aljabar, BE-aljabar Komutatif, Ideal Komutatif.