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Examples and Non-examples as a Road to Understanding the Concept of Function Eka Resti Wulan; Yulia Izza El Milla
EduMa: Mathematics education learning and teaching Vol. 9 No. 2 (2020)
Publisher : Jurusan Tadris Matematika UIN Siber Syekh Nurjati Cirebon

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24235/eduma.v9i2.7368

Abstract

This qualitative study aims to describe the conceptual understanding of prospective mathematics teachers at STKIP PGRI Lumajang by determining examples and non-examples of functions. This research was conducted by giving tests and interviews with 12 subjects. Data were analyzed using Miles & Huberman model.  This study showed that the subjects investigated whether paired to determine a given statement is a function or not. Subjects focus on specific expressions, e.g., or others that they have previously recognized as a function. However, some subjects used the vertical line test to determine a given graph represents a function or not, although they were unable to explain why the vertical line test was the appropriate method. Their understanding is limited to procedural knowledge such as mental representations and incomplete concept images, then failing to be comprehensively linked to the definition of the concept of function 
CONTROVERSIAL REASONING LEVELS AMONG PROSPECTIVE MATHEMATICS TEACHERS IN REAL ANALYSIS PROOF CONSTRUCTION: A QUALITATIVE CASE STUDY Eka Resti Wulan; Nur Fadilatul Ilmiyah; Yulia Izza El Milla; Nurcan Yacan
MATEMATIKA DAN PEMBELAJARAN Vol. 14 No. 1 (2026): MATEMATIKA DAN PEMBELAJARAN
Publisher : IAIN Ambon

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33477/mp.v14i1.13775

Abstract

Constructing proofs in Real Analysis requires navigating complex cognitive conflicts, yet the mechanisms that bridge intuitive beliefs and formal logic remain underexplored. This study investigates the dynamics of controversial reasoning among prospective mathematics teachers as they construct proofs of the limits of real-valued sequences. Employing a qualitative case study at a university in Kediri, data were collected from 40 undergraduate students through controversial problem tasks and semi-structured interviews. Data analysis followed the Miles and Huberman framework, comprising data reduction, data display, and conclusion drawing, tracing cognitive trajectories across three levels: initial, exploration, and clarification. Results reveal that reasoning at the initial level is constrained by intuitive misconceptions, in which students recognise contradictions but offer conceptually irrelevant justifications. The exploration level emerges as a critical yet fragmented stage in which students initiate formal strategies, such as mathematical induction, but fail to integrate essential prerequisites for convergence, leading to biased conclusions. The clarification level is characterised by the ability to reconstruct logical consistency through the appropriate use of proof by contradiction. The distinct cognitive patterns observed across the three levels indicate that controversial reasoning constitutes a dynamic, evolving process rather than a static classification, as evidenced by qualitative differences in students' argumentation structures and proof strategies at each level.   Keywords: Cognitive Conflict; Contradiction; Controversial Reasoning; Mathematical Proof
Mathematical disposition as a predictor of students’ mathematical communication in solving HOTS-based contextual problems Hasna Nisa Arifinta; Eka Resti Wulan; Nurcan Yacan
Journal Focus Action of Research Mathematic (Factor M) Vol. 8 No. 2 (2025): December 2025
Publisher : Universitas Islam Negeri (UIN) Syekh Wasil Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30762/f_m.v8i2.6885

Abstract

This study examines the influence of mathematical disposition on students’ mathematical communication when solving contextual Higher Order Thinking Skills (HOTS)-based problems. Employing a quantitative ex-post facto design, data were collected from 101 eighth-grade students using a mathematical disposition questionnaire and a mathematical communication test that consisted of contextual HOTS tasks. The results indicate that while many students showed a positive mathematical disposition, their communication performance varied across problem-solving demands. Regression analysis revealed that mathematical disposition contributed to students’ communication, particularly at the analytical level, but its impact diminished as task complexity increased. Overall, disposition played only a modest role in predicting students’ communication in HOTS contexts. The findings suggest that although mathematical disposition enhances students’ willingness to engage with challenging tasks, effective communication at higher cognitive levels also requires stronger conceptual understanding and strategic problem-solving experience. This study highlights the need for instructional approaches that integrate affective and cognitive supports to strengthen students’ mathematical communication in complex, open-ended problem settings.