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Isomorphism between Endomorphism Rings of Modules over A Semisimple Ring Susanto, Hery; Irawati, Santi; Hidayah, Indriati Nurul; -, Irawati
Journal of the Indonesian Mathematical Society Volume 26 Number 2 (July 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.2.824.170-174

Our question is what ring R which all modules over R are determined, up to isomorphism, by their endomorphism rings? Examples of this ring are division ring and simple Artinian ring. Any semi simple ring does not satisfy this property. We construct a semi simple ring R but R is not a simple Artinian ring which all modules over R are determined, up to isomorphism, by their endomorphism rings.

CHARACTERISTICS OF STUDENTSâ€™ ABDUCTIVE REASONING IN SOLVING ALGEBRA PROBLEMS Hidayah, Indriati Nurul; Sa'dijah, Cholis; Subanji, Subanji; Sudirman, Sudirman
Journal on Mathematics Education Vol 11, No 3 (2020)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.11.3.11869.347-362

When students solve an algebra problem, students try to deduce the facts in the problem. This step is imperative, students can draw conclusions from the facts and devise a plan to solve the problem. Drawing conclusions from facts is called reasoning. Some kinds of reasoning are deductive, inductive, and abductive. This article explores the characteristics of some types of abductive reasoning used by mathematics education students in problem-solving related to using facts on the problems. Fifty-eight students were asked to solve an algebra problem. It was found that the studentâ€™s solutions could be grouped into four types of abductive reasoning. From each group, one student was interviewed to have more details on the types. First, the creative conjectures type, the students can solve the problems and develop new ideas related to the problems; second, fact optimization type,Â the students make conjecture of the answer, then confirm it by deductive reasoning; third, factual error type, students use facts outside of the problems to solve it, but the facts are wrong; and fourth,Â Â mistaken fact type, the students assume the questionable thing as a given fact. Therefore, teachers should encourage the students to use creative conjectures and fact optimization when learning mathematics.

PELATIHAN PENYUSUNAN SOAL MENGGUNAKAN KAHOOT DAN VALIDITAS SOAL MENGGUNAKAN MODEL RASCH UNTUK GURU MATEMATIKA SMK KOTA BATU Hidayah, Indriati Nurul; Oktoviana, Lucky Tri
PEDULI: Jurnal Ilmiah Pengabdian Pada Masyarakat Vol 5 No 2 (2021)
Publisher : Lembaga Penelitian dan Pengabdian Kepada Masyarakat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37303/peduli.v5i2.376

Asesmen merupakan upaya untuk mendapatkan informasi dari proses dan hasil pembelajaran. Proses assesmen yang baik didukung oleh kualitas soal yang baik dan bisa memberikan informasi yang lengkap dari abilitas siswa. Metode yang dapat digunakan adalah pengukuran pemodelan Rasch (Rasch model measurement) pada data hasil ujian. Pemanfaatan teknologi dalam asesmen salah satunya adalah penyusunan soal online yang interaktif. Salah satu aplikasi yang dapat digunakan dalam penyusunan soal online adalah aplikasi Kahoot yang berbasis platform pembelajaran gratis. Sasaran dari kegiatan pengabdian ini adalah guru matematika SMK di Kota Batu yang tergabung dalam MGMP Matematika SMK Kota Batu.Pengabdian kepada masyarakat ini bertujuan untuk meningkatkan motivasi guru-guru SMK dalam pemanfaatan teknologi untuk meningkatkan kualitas pembelajaran daring baik dari segi penyusunan soal, media soal online maupun validitas dari soal tes yang dibuat. Mekanisme pelaksanaan kegiatan ini dilakukan dengan mengadopsi langkah-langkah action research yang terdiri dari 4 (empat) tahapan, yaitu: perencanaan, tindakan, observasi dan evaluasi, serta refleksi. Pada tahap tindakan, pelaksanaan pengabdian dilakukan menjadi dua kegiatan workshop yang dilakukan secara daring. Workshop pertama memberikan materi Pembuatan soal dan aplikasi Kahoot sedangkan workshop kedua diawali dengan review hasil tugas dari workshop pertama yang sudah diunggah dan pemberian materi pemodelan Rasch dengan alat bantu aplikasi ministep.

CHARACTERISTICS OF STUDENTS’ ABDUCTIVE REASONING IN SOLVING ALGEBRA PROBLEMS Indriati Nurul Hidayah; Cholis Sa'dijah; Subanji Subanji; Sudirman Sudirman
Journal on Mathematics Education Vol 11, No 3 (2020)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.11.3.11869.347-362

When students solve an algebra problem, students try to deduce the facts in the problem. This step is imperative, students can draw conclusions from the facts and devise a plan to solve the problem. Drawing conclusions from facts is called reasoning. Some kinds of reasoning are deductive, inductive, and abductive. This article explores the characteristics of some types of abductive reasoning used by mathematics education students in problem-solving related to using facts on the problems. Fifty-eight students were asked to solve an algebra problem. It was found that the student’s solutions could be grouped into four types of abductive reasoning. From each group, one student was interviewed to have more details on the types. First, the creative conjectures type, the students can solve the problems and develop new ideas related to the problems; second, fact optimization type, the students make conjecture of the answer, then confirm it by deductive reasoning; third, factual error type, students use facts outside of the problems to solve it, but the facts are wrong; and fourth, mistaken fact type, the students assume the questionable thing as a given fact. Therefore, teachers should encourage the students to use creative conjectures and fact optimization when learning mathematics.

Isomorphism between Endomorphism Rings of Modules over A Semisimple Ring Hery Susanto; Santi Irawati; Indriati Nurul Hidayah; Irawati -
Journal of the Indonesian Mathematical Society Volume 26 Number 2 (July 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.2.824.170-174

Our question is what ring R which all modules over R are determined, up to isomorphism, by their endomorphism rings? Examples of this ring are division ring and simple Artinian ring. Any semi simple ring does not satisfy this property. We construct a semi simple ring R but R is not a simple Artinian ring which all modules over R are determined, up to isomorphism, by their endomorphism rings.

BENTUK CAYLEY COLOR DIGRAPH GRUP SIKLIK G DENGAN ORDER n M. Ariq Zainurrifqi; Mohammad Agung; Indriati Nurul Hidayah
Jurnal Kajian Matematika dan Aplikasinya (JKMA) Vol 3, No 2 (2022): July
Publisher : UNIVERSITAS NEGERI MALANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um055v3i22022p1-14

Let G be a cyclic group with set of generators . Let G with color xi is a digraph with vertices elements of and there is an arrow from to if . In this artcle, we find the Cayley color digraph of a cylic group of order . We also proved the existence of Hamiltonian cycle of the graph

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