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All Journal SJME (Supremum Journal of Mathematics Education) JUMLAHKU: Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan Journal of Didactic Mathematics JUPIKA: JURNAL PENDIDIKAN MATEMATIKA Plusminus: Jurnal Pendidikan Matematika Jurnal Didactical Mathematics JME (Journal of Mathematics Education) Jurnal Matematika Ilmiah Universitas Muhammadiyah Kuningan Jurnal Didaktik Matematika
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.
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 Correlation 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
Integration of Preservice Teachers' Knowledge in Mathematical Problem Solving: A Perspective Based on Success Level Ramlah Ramlah; Tatag Yuli Eko Siswono; Iyan Rosita Dewi Nur; Nur Azizah; Aneu Pebrianti; Salsabila Az Zahra; Rita Diana
Jurnal Didaktik Matematika Vol. 13 No. 1 (2026): Jurnal Didaktik Matematika
Publisher : Universitas Syiah Kuala

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/jdm.v13i1.2038

Abstract

This study aims to describe the integration of preservice mathematics teachers’ declarative, procedural, and conditional knowledge in solving mathematical problems based on levels of problem-solving success. This study employed a descriptive qualitative approach. The participants were three preservice mathematics teachers selected from 40 undergraduate students in a Mathematics Education Study Program at a public university in West Java, Indonesia, based on problem-solving test results, the quality of solution processes, and representation of high, moderate, and low success levels. Data were collected through mathematical problem-solving tests and semi-structured interviews, and analyzed through data reduction, data display, and conclusion drawing. The findings show that the subject with high success had strong declarative knowledge coherently connected with procedural and conditional knowledge. The subject with moderate success demonstrated adequate conceptual understanding and initial strategy selection but was not consistent in controlling procedures and evaluating results. Meanwhile, the subject with low success showed fragmented conceptual understanding, inaccurate procedural application, and less-directed strategy selection. These findings confirm that mathematical problem-solving success is determined by the simultaneous integration of these three types of knowledge. Therefore, preservice teacher education needs to develop them in an integrated, systematic, and reflective manner.
Co-Authors Abdul Rosyid Aditya Prihandhika Aneu Pebrianti Hanifah Nurus Sopiany Indra Budiman Intan Noorfitriani Iyan Rosita Dewi Nur Pratama, David Putri Nur Aeni Ramlah Ressy Rustanuarsi, Ressy Rita Diana RR. Ella Evrita Hestiandari Salsabila Az Zahra Syakira Zalfani Asla Tatag Yuli Eko Siswono Uba Umbara Umbara, Uba Yudi Yudianto