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All Journal Jurnal Sains Matematika dan Statistika SJME (Supremum Journal of Mathematics Education) JUMLAHKU: Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan Journal of Didactic Mathematics JUPIKA: JURNAL PENDIDIKAN MATEMATIKA Griya Journal of Mathematics Education and Application Plusminus: Jurnal Pendidikan Matematika Jurnal Didactical Mathematics JME (Journal of Mathematics Education) Jurnal Matematika Ilmiah Universitas Muhammadiyah Kuningan
Nur Azizah
Universitas Singaperbangsa Karawang
Humanities Computer Science & IT Education Mathematics Social Sciences Other

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THE REVIEW OF WAYS OF UNDERSTANDING IN PROVING CONGRUENCE OF TWO TRIANGLES Aditya Prihandhika; Nur Azizah
JUMLAHKU: Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan Vol 10 No 2 (2024): JUMLAHKU VOL.10 NO.2 2024
Publisher : Program Studi Pendidikan Matematika Universitas Muhammadiyah Kuningan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33222/jumlahku.v10i2.4259

Abstract

This study aims to reviewing ways of understanding of prospective mathematics teacher students in the process of proving the triangle congruence theorem deductively. Deductive proof is a process that is quite difficult to do if students do not know the postulates, theorems, definitions, and properties that can be used as references in the proof process. The mathematical critical thinking process needs to be reviewed to determine the relevance of students' considerations in choosing the various references needed. The study used a case study to investigate the phenomenon specifically. The participants involved in the study were five students from a university in West Java. Theory of ways of understanding is needed to examine students' understanding of postulates, theorems, definitions, and other properties that have been studied previously so that it can be known to what extent students can validate the proof process carried out. The results of the study showed that based on the ways of understanding they have, students can prove the congruence theorem of two triangles by formulating the main problems, expressing facts, choosing logical arguments, detecting information bias with different points of view, and being able to draw conclusions. Thus, in the deductive proof process, a good way of understanding is required regarding postulates, theorems, definitions, and other relevant properties to reach systematic conclusions.
Application of the Mamdani Fuzzy Inference System in Evaluating Traffic Accident Risk for Four-Wheeled Vehicles Purnama, Fahrul; Budiman, Indra; Azizah, Nur
Jurnal Sains Matematika dan Statistika Vol 12, No 1 (2026): JSMS Januari 2026
Publisher : Universitas Islam Negeri Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24014/jsms.v12i1.38351

Abstract

Traffic accidents involving four-wheeled vehicles constitute a complex problem influenced by multiple factors, including vehicle speed and traffic density. Accurate accident-risk assessment is essential to support preventive and control efforts on road networks. This study aims to design and implement an accident-risk evaluation model based on a Mamdani-type Fuzzy Inference System (FIS) to accommodate uncertainty in decision-making. The research procedure includes identifying input and output variables, constructing membership functions, fuzzification, formulating fuzzy rules, and performing inference and defuzzification. Testing results indicate that, for a combination of 80 km/h speed and 70 vehicles/km density, the centroid defuzzification method yields a risk value of 25.31%. This value falls within the low-to-moderate risk category. These findings suggest that the developed Mamdani FIS model is effective as a methodological approach for accident-risk evaluation.
Analisis Kemampuan Pemecahan Masalah pada Soal Cerita Aljabar Ditinjau dari Kepercayaan Diri Siswa SMP. Thifal, Nadiah; Putra, Mulia; Azizah, Nur
Griya Journal of Mathematics Education and Application Vol. 6 No. 1 (2026): Maret 2026
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v6i1.1046

Abstract

Abstract Mathematical problem-solving skills are essential for junior high school students, especially in solving algebra story problems that require contextual understanding, problem modeling, and logical reasoning. This study aims to analyze the impact of self-confidence on junior high school students' ability to solve algebra story problems. This research uses a qualitative descriptive approach with three seventh-grade students from SMP Negeri 25 Kota Bekasi, selected based on their self-confidence levels: high, medium, and low. Data were collected through a self-confidence questionnaire, algebra story problem tests, and semi-structured interviews. Data analysis was done using source triangulation. The results show that students with high self-confidence are more consistent in understanding and solving problems, while students with low self-confidence struggle at the initial stage of problem understanding. These findings highlight the important role of self-confidence in mathematical problem-solving. The study provides new insights into the relationship between self-confidence and error patterns in solving algebra story problems. Keywords: Problem Solving; Story Problems; Algebra Material for Junior High School Abstrak Kemampuan memecahkan masalah matematis sangat penting bagi siswa SMP, terutama dalam soal cerita aljabar yang memerlukan pemahaman konteks, pemodelan masalah, dan penalaran logis. Penelitian ini bertujuan menganalisis pengaruh kepercayaan diri terhadap kemampuan siswa SMP dalam menyelesaikan soal cerita aljabar. Pendekatan yang digunakan adalah deskriptif kualitatif dengan subjek tiga siswa kelas VII SMP Negeri 25 Kota Bekasi, yang dipilih berdasarkan tingkat kepercayaan diri: tinggi, sedang, dan rendah. Data dikumpulkan melalui angket kepercayaan diri, tes soal cerita aljabar, dan wawancara semi terstruktur. Analisis data dilakukan dengan triangulasi sumber. Hasil penelitian menunjukkan bahwa siswa dengan kepercayaan diri tinggi lebih konsisten dalam memahami dan memecahkan masalah, sementara siswa dengan kepercayaan diri rendah kesulitan pada tahap awal pemahaman masalah. Temuan ini menunjukkan bahwa kepercayaan diri berperan penting dalam pemecahan masalah matematis. Penelitian ini memberikan wawasan baru tentang hubungan kepercayaan diri dengan pola kesalahan dalam pemecahan soal cerita aljabar. Kata Kunci: Pemecahan Masalah; Soal Cerita; Materi Aljabar SMP
GOAL-FREE PROBLEMS IN MATHEMATICS EDUCATION: A SYSTEMATIC REVIEW OF COGNITIVE LOAD AND PROBLEM-SOLVING RESEARCH Syakira Zalfani Asla; Indra Budiman; Nur Azizah
JME (Journal of Mathematics Education) Vol 11, No 1 (2026): JME (Jan - Jun)
Publisher : Universitas Sembilanbelas November Kolaka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31327/jme.v11i1.2822

Abstract

Goal-Free Problems (GFP), based on Cognitive Load Theory (CLT), is an instructional strategy that reduces extraneous cognitive load by eliminating specific end goals from mathematical tasks. Although widely implemented in mathematics education, empirical findings remain fragmented and lack systematic synthesis. This study systematically reviews research on Goal-Free Problems with a focus on cognitive load and mathematical problem-solving. Literature was identified through Scopus, ERIC, and Google Scholar using Publish or Perish, covering publications from 2016–2026. Following the PRISMA 2020 guidelines, ten eligible studies were analyzed using narrative synthesis. The results indicate that Goal-Free Problems consistently reduce cognitive load and support learning outcomes such as transfer, retention, reasoning, flexible thinking, and higher-order thinking skills. However, their effectiveness is influenced by task complexity, prior knowledge, and instructional design. The review also reveals that direct evidence regarding mathematical problem-solving ability remains limited, as most studies emphasize cognitive load and related cognitive variables. These findings highlight the need for further experimental research examining mathematical problem-solving as the primary outcome.Goal-Free Problems (GFP), based on Cognitive Load Theory (CLT), is an instructional strategy that reduces extraneous cognitive load by eliminating specific end goals from mathematical tasks. Although widely implemented in mathematics education, empirical findings remain fragmented and lack systematic synthesis. This study systematically reviews research on Goal-Free Problems with a focus on cognitive load and mathematical problem-solving. Literature was identified through Scopus, ERIC, and Google Scholar using Publish or Perish, covering publications from 2016–2026. Following the PRISMA 2020 guidelines, ten eligible studies were analyzed using narrative synthesis. The results indicate that Goal-Free Problems consistently reduce cognitive load and support learning outcomes such as transfer, retention, reasoning, flexible thinking, and higher-order thinking skills. However, their effectiveness is influenced by task complexity, prior knowledge, and instructional design. The review also reveals that direct evidence regarding mathematical problem-solving ability remains limited, as most studies emphasize cognitive load and related cognitive variables. These findings highlight the need for further experimental research examining mathematical problem-solving as the primary outcome.
Extraneous Cognitive Load as a Moderator of the Relationship Between Mathematical Literacy and Mathematical Reasoning in Indonesian Junior High School Mathematics Putri Nur Aeni; Hanifah Nurus Sopiany; Nur Azizah
Jurnal Didactical Mathematics Vol. 8 No. 2 (2026): Oktober 2026
Publisher : Program Studi Pendidikan Matematika, Universitas Majalengka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31949/dm.v8i2.18674

Abstract

Mathematical literacy and mathematical reasoning are widely recognized as essential competencies for meaningful engagement with mathematics; however, the cognitive conditions shaping their relationship remain insufficiently understood. Drawing on Cognitive Load Theory, this study examined the association between mathematical literacy and mathematical reasoning and investigated whether Extraneous Cognitive Load (ECL) significantly moderates this association among Indonesian junior high school students. A quantitative ex post facto correlational design was employed involving 275 eighth-grade students selected through proportionate stratified random sampling. Data were collected using a mathematical literacy test, a mathematical reasoning test, and an ECL questionnaire adapted from the Cognitive Load Component Questionnaire. The data were analyzed using descriptive statistics, simple linear regression, and Moderated Regression Analysis (MRA). The findings revealed a significant positive association between mathematical literacy and mathematical reasoning, with mathematical literacy explaining 18.2% of the variance in mathematical reasoning (R² = .182). After the inclusion of Extraneous Cognitive Load and the interaction term, the explained variance increased to 19.4% (R² = .194), representing a modest increase in explanatory power (ΔR² = .012). Although ECL did not show a significant direct association with mathematical reasoning, the interaction between mathematical literacy and ECL was statistically significant and negative (β = −0.371, p = .048), indicating that higher levels of ECL were associated with a weaker positive association between mathematical literacy and mathematical reasoning. These findings provide empirical evidence that the association between mathematical literacy and mathematical reasoning varies according to students' perceived levels of Extraneous Cognitive Load and highlight the importance of fostering mathematical literacy while minimizing unnecessary extraneous cognitive demands to better support students' mathematical reasoning
Co-Authors Abdul Rosyid Hanifah Nurus Sopiany Indra Budiman Indra Budiman Intan Noorfitriani Mulia Putra Pratama, David Prihandhika, Aditya Purnama, Fahrul Putri Nur Aeni Ressy Rustanuarsi, Ressy RR. Ella Evrita Hestiandari Syakira Zalfani Asla Thifal, Nadiah Uba Umbara Umbara, Uba Yudi Yudianto