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Students’ Combinatorial Thinking Processes in Solving Mathematics Problem Uripno, Gusti; Rosyidi, Abdul Haris
Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM) Vol 2, No 2 (2019): JRPIPM April 2019 Volume 2 Nomor 2
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jrpipm.v2n2.p80-92

Abstract

Combinatorial thinking is a way of thinking in solving combinatory problems. Combinatory problems are one of the difficult problems for students to solve. This study aims to analyses students? combinatorial thinking processes in solving problems. Given two combinatory problems that consist of problems with multiplication rule and combination. The Problems were given to two 11th grade senior-high school students. The results obtained were that there was a tendency for male Participants to do the two different ways which are direct counting and using diagram. The female participants did the work with one way which is direct counting. On more complex issues, namely about combination, students' thinking models go through stages of set of outcomes. From this research, it is expected that combinatory material learning is emphasized on the discovery of formulas by students themselves inductively, especially deductively. So that in this case the students interpret the combinatory formula more.
Students Combinatorial Thinking Processes in Solving Mathematics Problem Gusti Uripno; Abdul Haris Rosyidi
Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM) Vol. 2 No. 2 (2019): JRPIPM April 2019 Volume 2 Nomor 2
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jrpipm.v2n2.p80-92

Abstract

Combinatorial thinking is a way of thinking in solving combinatory problems. Combinatory problems are one of the difficult problems for students to solve. This study aims to analyses students combinatorial thinking processes in solving problems. Given two combinatory problems that consist of problems with multiplication rule and combination. The Problems were given to two 11th grade senior-high school students. The results obtained were that there was a tendency for male Participants to do the two different ways which are direct counting and using diagram. The female participants did the work with one way which is direct counting. On more complex issues, namely about combination, students' thinking models go through stages of set of outcomes. From this research, it is expected that combinatory material learning is emphasized on the discovery of formulas by students themselves inductively, especially deductively. So that in this case the students interpret the combinatory formula more.
Students’ Combinatorial Thinking Error in Solving Combinatorial Problem Gusti Uripno; Tatag Yuli Eko Siswono; Endah Budi Rahaju; Arief Budi Wicaksono
Indonesian Journal of Mathematics Education Vol. 6 No. 1 (2023): Indonesian Journal of Mathematics Education
Publisher : Universitas Tidar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31002/ijome.v6i1.589

Abstract

Combinatorial thinking errors describe students’ difficulties and obstacles in solving combinatorial problems. This study aims to describe the errors experienced by students in solving combinatorial problems in terms of combinatorial thinking processes. This research involved two subjects who were 12th grade high school students at a school in Gresik, Indonesia. The students have already taken a combinatorics course. Data collection was conducted using the think-aloud observation method and task-based interviews. Both methods of data collection were conducted to validate the data using the triangulation method. The two subjects experienced similar errors. The research shows that the filling slots method is a simple and easy way for students to understand, but problems arise when students cannot understand the meaning of the questions and input the correct numbers for the problem. The combinatorial thinking error includes the general counting process and vertical upward formulas or expressions. The general counting process error is generating a number that represents the given aspects of the problem and the vertical upward formula/expression is identifying the concept that fits the problem. This research suggests enhancing students understanding of number representation when teaching the filling slot method. The teacher should illustrate some of the multiplication rule and addition rule examples to help students distinguish between these two fundamental rules. Further research is needed to provide solutions to the constraints experienced by students in solving combinatorial problems.
Berpikir Kombinatorik: Relevansi AI dengan Model Pembelajaran Matematika Uripno, Gusti; Yuliastuti, Rita; Nurfalah, Edy; Islami, Irma Fauztina
Jurnal Teladan: Jurnal Ilmu Pendidikan dan Pembelajaran Vol 9 No 2 (2024): Jurnal Teladan Vol.9. No.2 November 2024
Publisher : FKIP Unirow Tuban

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55719/jt.v9i2.1510

Abstract

This development study uses a qualitative approach and Didactic Engineering (DE) research methods. The aim of this research is to develop an AI-based learning model by combining discovery and problem based learning models involving mathematics students at PGRI Ronggolawe University, Tuban. AI or artificial intelligence is a tool that needs to be optimized in various fields, especially in the field of mathematics education. Meanwhile, mathematics education has issues related to problem solving on discrete mathematics topics. Starting from this issue, this research tries to offer a solution, the result of which is an AI-assisted blended learning model to improve combinatorial thinking. Through the combination of these models, a combination of syntax is obtained, namely: (1) Orientation; (2) Organization; (3) Exploration; (4) Execution; (5) Evaluation; (6) Generalization. This combination also considers the methods used, namely online and offline. Stages (1) and (2) are carried out offline via the LMS and quiz provider application. Meanwhile, Stages (3) and (4) were carried out involving Question AI. Stage (3) is carried out with the Geogebra alternative auxiliary application. Then stages (4) and (5) are carried out using technology-assisted presentations.
Artificial Intelligence Integration: Error Self-Reflection in Solving Integral Problems Uripno, Gusti; Suprihatiningsih, Siti; Rangkuti, Rizki Kurniawan
AlphaMath : Journal of Mathematics Education Alphamath: Vol. 10, No. 2, November 2024
Publisher : Department of Mathematics Education, Universitas Muhammadiyah Purwokerto, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30595/alphamath.v10i2.23133

Abstract

Integrity has had plenty of impact on human civilization development, especially in the development of human technology. The primary role of an integral is not well supported by students’ skill in solving integral problems. Due to this fact, mathematics educators need solutions. Artificial Intelligence (AI) integration is one of the solutions that mathematics educators can choose. This qualitative descriptive research aims to explore students' mistakes in solving integral problems with the help of  Photomath. This research will describe student mistakes and explain how students realize mistakes during rework assisted by Photomath. This research involved ten mathematics students who joined an integral course at a university in Indonesia. The errors were analyzed based on Newman error analysis. Errors found based on research results include (1) Comprehension and transformation, (2) Process skills, and (3) Encoding. This research found that comprehension errors have implications for transformation. Students who make comprehension errors will cause transformation errors. Meanwhile, the subject's errors in the previous stage affect the encoding stage. Apart from the errors already mentioned, errors were also found due to carelessness, which was not a significant part of Newman's error analysis.
Bibliometrics Analysis of AI Integration in Mathematics Teaching Tupulu, Nasri; Konstansia Hermiati; Gusti Uripno; Siti Suprihatiningsih; Rangkuti, Rizki Kurniawan
Mosharafa: Jurnal Pendidikan Matematika Vol. 13 No. 2 (2024): April
Publisher : Department of Mathematics Education Program IPI Garut

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31980/mosharafa.v13i2.1699

Abstract

Studi literatur ini bertujuan untuk menganalisis tren penelitian dengan menggunakan analisis bibliometrik yang terkait dengan Kecerdasan Buatan (AI) dalam pengajaran matematika. Pentingnya AI dalam pengajaran matematika tidak sesuai dengan banyaknya penelitian tentang hal tersebut. Sehingga penelitian ini disusun dengan tujuan untuk mengidentifikasi penelitian berkaitan dengan integrasi AI dalam pengajaran matematika selama 10 tahun terakhir.  Kata kunci yang digunakan untuk mengumpulkan artikel adalah “artificial intelligence” dan “mathematics teaching” dan diperoleh 460 dokumen di database scopus. Penelitian ini dilakukan dengan membatasi jumlah dokumen tergantung pada tahun, bahasa, dan jenis artikel. Batas tahun pada tahun 2014 hingga 2024, bahasa dibatasi hanya bahasa Inggris, dan dokumen dibatasi hanya pada jenis artikel. Jumlah dokumen dalam dekade terakhir meningkat dari 6 dokumen menjadi 26 dokumen. Zhongda Sun, yang berkecimpung dalam kecerdasan komputer, adalah penulis yang paling banyak dikutip. Negara paling produktif adalah Tiongkok yang menyalip jumlah publikasi Australia pada tahun 2021. Kecerdasan buatan dalam pengajaran matematika populer dalam ilmu sosial dan ilmu komputer dengan topik yang paling populer adalah siswa, kecerdasan buatan, dan guru. This literature study aims to analyze research trends by using bibliometrics analysis that related to Artificial Intelligence (AI) in mathematics teaching. The impact of AI in mathematics teaching did not match to the number of mathematics teaching research. So, this bibliometric study conducted in order to identify AI integration in mathematics teaching in last decade. Article gathered by two keywords, which are “artificial intelligence” and “mathematics teaching”and found 460 documents in scopus database. This study conducted by limiting the number of documents depend on years, language, and article type. The years limit in 2014 to 2024, languages limit to english only, and the documents limit to article type only. The number of documents in the last decade is increasing from 6 documents into 26 documents. Zhongda Sun, that concern in computer intelligence, is the most cited author. The most productive country was China that overtake Australia’s number of publications in 2021. Artificial intelligence in mathematics teaching was popular in social science and computer science and the most popular topics are students, artificial intelligence, and teacher.
AI-Enhanced Electronic Modules Bridge Mathematical Induction Learning Gap Sari, Mayang; Lestari, Isnawati Lujeng; Uripno, Gusti; Suprihatiningsih, Siti; Hariyanti, Firda
Indonesian Journal of Mathematics Education Vol. 8 No. 2 (2025): Indonesian Journal of Mathematics Education (In Press)
Publisher : Universitas Tidar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31002/ijome.v8i2.2988

Abstract

This study develops and validates AI-integrated electronic modules (e-modules) for instruction in mathematical induction. Mathematical induction requires sophisticated logical reasoning, yet students often struggle to master this proof technique. The research employed a systematic three-phase approach: analysis of learning challenges, design of e-module architecture with AI integration, and development using the Canva platform with integrated AI tools including Wolfram Alpha, Interactive Theorem Provers, and ChatGPT. Validation used a 4-point Likert scale across four primary dimensions, including material aspect, media aspect, language aspect, and learning aspect. Unlike traditional materials, these AI-integrated e-modules provide personalized feedback, adaptive learning pathways, and real-time diagnostic support tailored to individual student needs. Results demonstrate the potential of AI-enhanced educational technology in bridging the gap between complex mathematical reasoning and student comprehension.
Menguatkan literasi numerasi siswa SD melalui perkalian kontekstual berbasis RME Rahayu, Puji; Warli, Warli; Uripno, Gusti
SELAPARANG: Jurnal Pengabdian Masyarakat Berkemajuan Vol 10, No 1 (2026): February
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jpmb.v10i1.37823

Abstract

Abstrak Literasi numerasi merupakan kompetensi dasar yang esensial bagi siswa untuk memecahkan masalah dalam kehidupan sehari-hari. Namun, fenomena di lapangan menunjukkan bahwa banyak siswa sekolah dasar masih kesulitan memahami konsep matematika secara bermakna, terutama pada materi perkalian. Siswa cenderung menghafal fakta angka tanpa memahami logika di baliknya, sehingga gagap saat dihadapkan pada soal berbasis cerita. Artikel ini mendeskripsikan implementasi program pengabdian masyarakat yang bertujuan untuk meningkatkan literasi numerasi siswa kelas III UPT SD Negeri Sugiharjo 1 Tuban melalui pelatihan metode perkalian kontekstual berbasis Realistic Mathematics Education (RME). Kegiatan melibatkan kolaborasi tiga dosen dan 14 mahasiswa sebagai fasilitator pendamping. Metode yang digunakan meliputi tahapan observasi, persiapan media konkret berbasis kearifan lokal, pelatihan dengan pendekatan hands-on, serta evaluasi melalui pre-test dan post-test. Hasil kegiatan menunjukkan bahwa pemanfaatan media konkret dan Lembar Kerja Siswa (LKS) kontekstual mampu mengubah pola belajar siswa dari hafalan mekanistik menjadi pemahaman konseptual. Selain itu, pendampingan intensif dalam kelompok kecil terbukti efektif mengatasi heterogenitas kemampuan siswa. Program ini memberikan kontribusi signifikan dalam menciptakan pembelajaran matematika yang menyenangkan dan bermakna, serta menjadi inspirasi bagi guru kelas untuk mengembangkan strategi pembelajaran inovatif berbasis kurikulum merdeka. Kata kunci: literasi numerasi; perkalian kontekstual; RME; media konkret. Abstract Numeracy literacy is an essential foundational competency for students to solve problems in everyday life. However, field observations indicate that many elementary school students still struggle to understand mathematical concepts meaningfully, particularly in the subject of multiplication. Students tend to memorize numerical facts without understanding the underlying logic, leading to difficulties when encountering word-based problems. This article describes the implementation of a community service program aimed at enhancing the numeracy literacy of third-grade students at UPT SD Negeri Sugiharjo 1 Tuban through training in contextual multiplication methods based on Realistic Mathematics Education (RME). The activity involved a collaboration between three lecturers and 14 students serving as accompanying facilitators. The methods employed included observation stages, the preparation of concrete media based on local wisdom, training with a hands-on approach, and evaluation through pre-tests and post-tests. The results of the activity indicate that the use of concrete media and contextual Student Worksheets (LKS) successfully shifted student learning patterns from mechanistic memorization to conceptual understanding. Furthermore, intensive mentoring in small groups proved effective in addressing the heterogeneity of students' abilities. This program provides a significant contribution to creating enjoyable and meaningful mathematics learning and serves as an inspiration for classroom teachers to develop innovative learning strategies based on the Kurikulum Merdeka. Keywords: numeracy literacy; contextual multiplication; RME; concrete media
Transformasi Literasi Digital Guru SMP melalui Pelatihan AI Generatif dalam Penyusunan Bahan Ajar Puji Rahayu; Warli Warli; Gusti Uripno; Mario Fahmi Syahrial; Andy Haryoko; Riska Andriani; Kartika Widya Putri; Choiroz Zadit Taqwa
Jurnal Inovasi Penelitian dan Pengabdian Masyarakat Vol. 6 No. 1 (2026): Juni
Publisher : Indonesia Emerging Literacy Education

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.53621/jippmas.v6i1.812

Abstract

Perkembangan teknologi kecerdasan buatan (Artificial Intelligence/AI) membuka peluang baru dalam dunia pendidikan, khususnya dalam penyusunan bahan ajar. Namun, banyak guru SMP masih memiliki keterbatasan literasi digital dan belum memanfaatkan AI secara optimal. Kegiatan pengabdian kepada masyarakat ini bertujuan memberikan pelatihan dan pendampingan kepada guru-guru UPT SMP Negeri 4 Tuban dalam menggunakan platform AI Z.ai untuk menyusun bahan ajar berbentuk buku. Kegiatan menggunakan desain evaluatif campuran (mixed-methods pre-post) dengan 23 peserta yang terdiri dari guru dan mahasiswa PLP. Pelatihan dilaksanakan pada 10 Desember 2025 selama satu hari sinkronus dan tujuh hari asinkronus (total 64 jam), mencakup modul: persiapan sumber draf, pembuatan ide dan outline dengan Z.ai, penyusunan isi buku, serta finalisasi naskah. Data dikumpulkan melalui kuesioner, observasi kinerja, dan penilaian produk. Hasil menunjukkan bahwa 88% peserta mampu mengoperasikan Z.ai secara mandiri, melampaui target 80%. Sebanyak 80% peserta berhasil menyelesaikan minimal satu draft bab buku ajar. Rata-rata skor posttest meningkat signifikan dibandingkan pretest pada semua konstruk yang diukur (skor total: pretest M=2,49; posttest M=3,93; Δ=1,44). Secara kualitatif, terjadi peningkatan motivasi, kepercayaan diri, dan terbentuknya komunitas belajar. Kegiatan ini membuktikan bahwa pelatihan berbasis AI dapat menjadi strategi efektif untuk meningkatkan kapasitas guru dalam pengembangan bahan ajar di era digital.
Mathematical Critical Thinking Skills of Students in Solving Set Theory Problems Intan Rimawati; Siti Suprihatiningsih; Gusti Uripno; Milagros R. Baldemor
AlphaMath : Journal of Mathematics Education Alphamath: Vol. 12, No. 1, May 2026
Publisher : Department of Mathematics Education, Universitas Muhammadiyah Purwokerto, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30595/alphamath.v12i1.30338

Abstract

Mathematical critical thinking is a fundamental competency that students must develop to solve complex problems effectively; however, empirical evidence consistently indicates that this ability remains underdeveloped among junior high school students in Indonesia, particularly in the domain of set theory. This study aims to describe and analyze the mathematical critical thinking skills of seventh-grade students at a public junior high school located in a rural district of West Kalimantan, Indonesia, in solving set theory problems, based on four Facione indicators: interpretation, analysis, evaluation, and inference. A descriptive qualitative design was employed, involving six students selected through purposive sampling from a class of 29 students in the 2025/2026 academic year, categorized into high, medium, and low ability groups. Data were collected through a written essay test and semi-structured interviews, then analyzed using an interactive model comprising data reduction, data display, and conclusion drawing. Results show that high-ability students fulfilled all four critical thinking indicators optimally but demonstrated a consistent limitation in verbal mathematical justification. Medium-ability students performed adequately on interpretation and analysis but encountered difficulties in evaluation and systematic inference. Low-ability students failed to meet most indicators, with the most pronounced deficits in evaluation and inference. This study contributes to the field by investigating the distribution of critical thinking profiles within a unified classroom environment. Crucially, it highlights that verbal mathematical justification represents a fundamental developmental barrier that transcends procedural competence, offering specific implications for the refinement of mathematics instruction.