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All Journal Al-Jabar : Jurnal Pendidikan Matematika Journal on Mathematics Education
Sosa-Moguel, Landy
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Education Mathematics Social Sciences Other

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Secondary school mathematics teachers’ perceptions about inductive reasoning and their interpretation in teaching Sosa-Moguel, Landy; Aparicio-Landa, Eddie
Journal on Mathematics Education Vol. 12 No. 2 (2021): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

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Abstract

Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers’ perceptions of inductive reasoning and interprets this mathematical reasoning type in teaching the quadratic equation. The data were collected from a questionnaire administered to 22 teachers and an interview conducted to expand their answers. Through the thematic analysis method, it was found that more than half the teachers perceived inductive reasoning as a process for moving from the particular to the general and as a way to acquire mathematical knowledge through questioning. Because teachers have little clarity about inductive phases and processes, they expressed confusion about teaching the quadratic equation inductively. Results indicate that secondary school teachers need professional learning experiences geared towards using inductive reasoning processes and tasks to form concepts and generalizations in mathematics.
Tracing students understanding and misconceptions of continuity and differentiability through multi representations of mathematical problem Arsyad, Nurdin; Ikram, Muhammad; Alimuddin, Fauziyyah; Nisa, Khaerun; Sosa-Moguel, Landy; Garcia-Garcia, Javier
Al-Jabar: Jurnal Pendidikan Matematika Vol 17 No 1 (2026): Al-Jabar : Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v17i1.29062

Abstract

Purpose: This study investigates undergraduate students’ understanding and misconceptions concerning continuity and differentiability across multiple mathematical representations. It specifically examines whether misconceptions remain stable or shift when concepts are presented in symbolic, graphical, and contextual forms. Method: A qualitative exploratory case study was conducted involving 83 undergraduate mathematics education students at a leading public university in Indonesia. Data were collected using 11 validated and reliable multiple-choice items designed to elicit reasoning across different representations. Students’ written responses were analyzed to identify patterns of understanding and error. In-depth interviews with selected participants were conducted to clarify underlying reasoning processes. A collective case study framework was employed, treating each representation as a micro case to enable systematic cross-representation comparison. Findings: The results indicate that misconceptions were widespread and often consistent across representations. Common errors included interpreting graphical smoothness as proof of differentiability, assuming differentiability without verifying continuity, and conflating the existence of a limit with the function’s value. Many students relied on procedural manipulation, visual intuition, or contextual familiarity rather than formal limit-based reasoning, revealing fragmented conceptual understanding. Significance: The findings highlight the need for instructional approaches that explicitly integrate multiple representations and strengthen connections between intuitive reasoning and formal definitions. By addressing persistent misconceptions across representations, calculus instruction can better support the development of coherent and conceptually grounded mathematical understanding.
Co-Authors Alimuddin, Fauziyyah Aparicio-Landa, Eddie García-García, Javier Ikram, Muhammad Nisa, Khaerun Nurdin Arsyad, Nurdin