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All Journal JMPM: Jurnal Matematika dan Pendidikan Matematika JTAM (Jurnal Teori dan Aplikasi Matematika) Journal of Advanced Sciences and Mathematics Education
Parameswari, Pradina
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Chemistry Education Mathematics Physics Social Sciences

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The Growth of Students' Function Limit Concepts Understanding in Solving Controversial Problems Based on Pirie Kieren's Theory Susiswo, Susiswo; Parameswari, Pradina; Putri, Octavina Rizky Utami; Lanya, Harfin; Utami, Anita Dewi; Murniasih, Tatik Retno
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16835

Abstract

Almost all students understand the limit of a function only up to an intuitive definition and have difficulty understanding the concept of a limit function formally. This study aims to describe the growth of student understanding of functions limit concept in solving controversial problems based on Pirie Kieren's theory. There were twelve Calculus class students in the short semester as participants.   The students selected were those who had taken calculus courses. Students are given the task of solving controversial problems to understand the concept of limit functions. There was only one student who showed a growing understanding of the concept of the limit of a function and was interviewed for further exploration. This research is a qualitative descriptive research. Therefore, the researchers analyzed the results of students' work through data reduction, data presentation, and conclusion drawing. The result shows that through controversial problems, students' understanding grows to an inventising level. However, students did ‘fold back’ at the observing level. At this level, students look at or re-read their notebooks to recall previously owned concepts.   For further research it is suggested that researchers can design a learning process that can help grow student understanding through controversial problems.
When Proportion Problems Confuse: Prospective Teachers’ Reasoning Difficulties Parameswari, Pradina; Fitria, Analisa; Labuem, Susana
JMPM: Jurnal Matematika dan Pendidikan Matematika Vol 10 No 2 (2025): September 2025 - February 2026
Publisher : Prodi Pendidikan Matematika Universitas Pesantren Tinggi Darul Ulum Jombang

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Abstract

Difficulties in completing school mathematics material are also experienced by prospective teacher students. Proportion is the foundational mathematical material for studying other mathematics. Commonly known proportion concepts are direct and inverse proportion. Most students still have difficulty distinguishing between direct and inverse proportion. To distinguish between two problems requires proportional reasoning. Therefore, this study aimed to describe the forms of proportional reasoning difficulties of prospective teacher students in distinguishing between direct and inverse proportion. This research was a case study which conducted at a private university in Malang City, attended by 10 third-semester students. Two subjects were selected based on mathematics tests, interviews, and student willingness. The results showed that students experienced intuitive, additive, and proportion attempt difficulties in the first problem. Meanwhile, students experienced difficulties with additive and proportion attempts difficulties in the second problem. This research can provide insight into how prospective teacher students effectively teach the concept of proportion.
Mindsponge framework: Tracing students’ proactive interference Parameswari, Pradina; Umah, Ulumul; Nasution, Nurul Rafiqah; Susana Labuem; Analisa Fitria; Putri, Jihan Hidayah
Journal of Advanced Sciences and Mathematics Education Vol. 6 No. 1 (2026): Journal of Advanced Sciences and Mathematics Education
Publisher : CV. FOUNDAE

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58524/jasme.v6i1.988

Abstract

Background: Many students have difficulty distinguishing between direct and inverse proportion problems. This difficulty can cause interference during problem solving. One form of interference is proactive interference, which occurs when previously learned information disrupts the understanding of new information. In proportion problems, students’ prior knowledge of direct proportion often influences how they approach inverse proportion tasks, leading them to apply incorrect strategies. Aim: This study aims to describe the process of proactive interference experienced by students when solving proportion problems using the Mindsponge framework. Method: This study used a qualitative descriptive approach. The participants were 32 eighth-grade students from Junior High School 3 Malang. The selected subjects were students who could correctly solve direct proportion problems but applied the direct proportion concept when solving inverse proportion problems. Data were collected through proportion problem tests and interviews. Students’ written work was analyzed using indicators from the Mindsponge framework, and the findings were triangulated by comparing students’ work with interview results. Results: The results show that proactive interference occurred at three stages of the Mindsponge framework: environmental, filtering, and mindset. At the environmental stage, students made errors in observing and understanding the problem. In the filtering stage, students incorrectly determined the quantitative relationship between variables. At the mindset stage, students relied on their prior knowledge of direct proportion and frequently used the cross-multiplication strategy. Conclusion: The study indicates that proactive interference occurs when previously learned concepts dominate students’ thinking processes. The Mindsponge framework helps explain how prior knowledge influences the way students interpret and apply new information when solving proportion problems. 
Co-Authors Analisa Fitria Anita Dewi Utami Harfin Lanya, Harfin Labuem, Susana Nasution, Nurul Rafiqah Putri, Jihan Hidayah Putri, Octavina Rizky Utami Susana Labuem Susiswo Tatik Retno Murniasih Umah, Ulumul