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An Analysis of Errors on Mathematical Symbol as a Metaphor in Linear Programming Saniyatul Wardah; Dwi Priyo Utomo; Octavina Rizky Utami Putri
Didaktik Matematika Vol 8, No 1 (2021): Jurnal Didaktik Matematika
Publisher : Universitas Syiah Kuala

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/jdm.v8i1.18304

Abstract

Symbol sense is crucial in the understanding of mathematical problems comprising various symbols. The misuses of symbols happen due to misinterpretation, which is considered the constraint to learn algebra more comprehensively, including in linear programming. The term metaphor is defined as a means to carry over symbol sense, and is used to improve mathematical understanding. This present research was aimed at analyzing errors on mathematical symbol as a metaphor in linear programming. This research was conducted by means of descriptive qualitative design, with a test and interview as the instruments. The test was made essay, and its results were analyzed qualitatively. The test, further, was administered to five eleventh graders selected according to highest rates of errors committed. This research has shown that the students committed a number of errors in some cases, such as representing symbols as variables, representing numbers, and interpreting symbols as relational operators. In addition, errors which the students committed in constructing mathematical models covered defining the final value, representing numbers, applying inequality system, and interpreting symbols as operation counts. This present research has provided some ways for symbol sense, and thus the errors on mathematical symbol as a metaphor could be lessened. Next, this research can be further followed up by reviewing the effectiveness of remedial instruction according to the committed errors on mathematical symbols.
Mathematical Creative Problem-Solving: Students’ Cognitive Flexibility in Idea Generation and Evaluation Putri, Octavina Rizky Utami; Zukhrufurrohmah, Zukhrufurrohmah; Syaifuddin, Mohammad; Lanya, Harfin
Mathematics Education Journal Vol. 20 No. 1 (2026): Mathematics Education Journal
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/mej.v20i1.pp145-164

Abstract

Learning experiences that rely on procedural memorization are insufficient to support students’ cognitive development in solving non-routine mathematical problems, as such contexts require cognitive flexibility to generate, evaluate, and adapt multiple solution strategies. This study aims to explore students’ cognitive flexibility activities in the phases of idea generation and idea evaluation through mathematical creative problem-solving. Using a multiple case study design, eight junior high school students from two different school contexts (public and private) participated in individual problem-solving and discussion activities. The research was conducted through three stages, namely: define and design, prepare–collect–analyze, and analyze–conclude. Data collected from written problem-solving tasks, video-recorded sessions, and follow-up discussions. Data were analyzed using NVivo 15 software through data condensation, data display, and cross-case conclusion drawing. The findings show that strategic and representational cognitive flexibility occurred in both idea generation and evaluation, with the latter occurring more frequently. These results highlight the importance of emphasizing idea evaluation in mathematics instruction to enhance students’ adaptive thinking and deepen their understanding when facing non-routine problems.
Pengembangan Rencana Pembelajaran Inovative dan Evaluasi Pembelajaran di Sekolah Kejuruan Bidang Matematika Zukhrufurrohmah, Zukhrufurrohmah; Octavina Rizky Utami Putri; Syaifuddin, Mohammad; Lanya, Harfin; Putri Jhahrotul Fitriana
PaKMas: Jurnal Pengabdian Kepada Masyarakat Vol 6 No 1 (2026): Mei 2026
Publisher : Yayasan Pendidikan Penelitian Pengabdian Algero

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.54259/pakmas.v6i1.4099

Abstract

This community engagement program was conducted at SMK Muhammadiyah 1 Probolinggo to develop innovative instructional designs and assessment instruments. The method employed was qualitative-descriptive, utilizing observation note sheets, reflective note sheets, and questionnaire sheets as instruments. The program comprised three main stages: workshops, mentoring, and evaluation. The first stage involved a workshop that covered presentations on innovative learning and the development of assessment instruments. The second stage consisted of mentoring sessions for the development of innovative teaching materials and assessment instruments, conducted through one online and one offline meeting. Evaluation was carried out during the workshop using observation note sheets, mentoring sessions through reflective discussion sheets and questionnaires, and an overall assessment of the community engagement activities through questionnaires. The evaluation results indicated a 92% increase in teachers' understanding of the Merdeka Curriculum, a 77% improvement in their confidence in designing teaching modules, and a 62% increase in their comprehension of assessment types. Additionally, 77% of teachers felt capable of developing teaching modules and assessments, although challenges remained in designing appropriate evaluation instruments. Meanwhile, the use of technology in teaching increased by 54%, yet it remains an area that requires further enhancement. These findings suggest that the mentoring provided had a positive impact on teachers' competency development, particularly in designing innovative instructional strategies. Therefore, further mentoring sessions are needed with a greater focus on strengthening teachers' skills in designing assessments and integrating technology into teaching to support the optimal implementation of the Merdeka Curriculum.