M. Mahmudi Prasetiyo
Universitas Islam Malang

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INTEGRATION OF MEANINGFUL LEARNING THEORY IN EXPLORING GEOMETRIC REASONING BARRIERS THROUGH THINK ALOUD PROTOCOL ANALYSIS Ila Maya Suprapti; M. Mahmudi Prasetiyo; Surya Sari Faradiba
JME (Journal of Mathematics Education) Vol 11, No 1 (2026): JME (January - June)
Publisher : Universitas Sembilanbelas November Kolaka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31327/jme.v11i1.2718

Abstract

This study was motivated by the urgency of low geometric reasoning skills among students in Indonesia and the failure of traditional evaluation methods to capture students' mental dynamics in real time. The main objective of this study was to analyze in depth the reasoning process of students in order to obtain a complete cognitive picture of the mechanisms of meaningful learning and the manifestation of relational-instrumental understanding in solving geometric problems. This study uses a qualitative approach with a descriptive-exploratory design on a single subject, a vocational high school student in Probolinggo City with the initials MK, who was selected through purposive sampling. Data collection was conducted through the Think Aloud Protocol (TAP), supported by retrospective interviews to ensure data triangulation. Data analysis techniques involved verbatim transcription, segmentation, and hierarchical coding procedures to form a cognitive map of the subject. The specific findings show that the subject did not operate dichotomously but rather demonstrated an adaptive hybrid mechanism between instrumental and relational understanding. A crucial moment was identified at 03:26, where the subject performed self-correction that triggered the assimilation (subsumption) of new information into the cognitive structure, which manifested as a pause or visual latency. Contextually, the discussion reveals that the subject used instrumental understanding as a cognitive efficiency strategy after the problem structure was solved relationally. In addition, verbalization in TAP functions as external scaffolding that strengthens students' metacognitive awareness in detecting calculation anomalies. This study concludes that mastery of geometry requires time for visual assimilation before symbolic manipulation is performed.
Heuristic Strategies as Cognitive Bridges in Solving Arithmetic Sequence Word Problems: A Case Study Fuad Rifai; M. Mahmudi Prasetiyo; Irbah Tsabitah
JME (Journal of Mathematics Education) Vol 11, No 1 (2026): JME (January - June)
Publisher : Universitas Sembilanbelas November Kolaka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31327/jme.v11i1.2628

Abstract

This study explores the micro-process dynamics of students in applying heuristic strategies to arithmetic sequence word problems through a qualitative case study. Using Think Aloud with the subject YD, the results show a paradox between procedural fluency with formulas and cognitive failure when switching to manual strategies. This transition triggers cognitive overload and representational misconceptions, where the subject is distracted by visuals, resulting in inconsistent answers. This study concludes that without a solid conceptual foundation, heuristic instruction risks weakening students' confidence and triggering logical errors, leading to a loss of focus in their work.
The Role of Metacognitive Monitoring and Control in Overcoming Cognitive Overload during the Impasse Phase Rika Wahyu Saputri; Surya Sari Faradiba; M. Mahmudi Prasetiyo
JME (Journal of Mathematics Education) Vol 11, No 1 (2026): JME (January - June)
Publisher : Universitas Sembilanbelas November Kolaka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31327/jme.v11i1.2701

Abstract

This study was motivated by the urgency of the phenomenon of cognitive overload, which often triggers a phase of impasse or mental block in students when solving contextual mathematics problems. This condition causes students to often rush to apply irrelevant calculation procedures without analyzing the structure of the problem, resulting in strategic failure. This study aims to describe in depth the dynamics of students' metacognition, particularly the monitoring and control functions, and to analyze the effectiveness of visualization strategies in reducing this cognitive load. The research method used is a qualitative approach with a descriptive-exploratory design. The research subjects included junior high school students who were tested on their ability to solve PISA-type questions. Data collection was carried out using the Think Aloud Protocol (TAP) technique to record students' mental processes and verbalizations in real time when they encountered a deadlock. Data analysis techniques were carried out systematically through the stages of verbal data transcription, data reduction, visual presentation, and conclusion drawing, which were validated through interview triangulation. The results showed that the monitoring of metacognitive function plays a vital role as an early detection mechanism that helps students recognize anomalies between their tentative answers and the logic of the problem. Furthermore, the control strategy through image visualization proved effective in reducing extraneous cognitive load, enabling students to transform abstract representations into concrete ones and find the turning point for solving the problem. In addition to improving cognitive accuracy, successfully overcoming this impasse phase simultaneously increases students' self-efficacy or self-confidence. These findings recommend the importance of integrating metacognitive interventions in learning to build students' mathematical resilience.