Exploring Students’ Mindset in Learning Real Analysis: Challenges, Responses, and Learning Experiences

Abstract

Students’ beliefs about mathematical ability may shape how they interpret difficulty and respond to unsuccessful attempts, particularly in proof-oriented courses such as Real Analysis. Previous studies have documented that learning Real Analysis can involve substantial affective and cognitive challenges, including frustration, anxiety, and difficulties in constructing formal mathematical proofs. This study explored mathematics education students’ mindsets in learning Real Analysis by examining their responses to a Likert-scale questionnaire and five open-ended questions. The participants were 16 fifth-semester students enrolled in the Real Analysis course in the Mathematics Education Program at IAIN Kerinci, Indonesia. Data were collected during the odd semester of the 2026/2027 academic year using a questionnaire consisting of 23 closed-ended items on a four-point Likert scale and five open-ended questions. The questionnaire used a four-point response scale and covered beliefs about mathematical ability, responses to challenges, effort and persistence, and feedback, learning, and improvement. Open-ended responses were examined thematically to identify students’ perceived challenges, beliefs about their abilities, coping strategies, interpretations of feedback, and reported changes in perspective. Descriptive questionnaire patterns suggested an overall growth-oriented tendency. The quantitative findings showed mean scores of 2.78 for beliefs about mathematical ability, 2.55 for responses to challenges, 2.98 for effort, failure, and persistence, and 2.88 for feedback, learning, and improvement. These scores indicate varying degrees of growth-oriented responses across the four dimensions rather than a uniformly strong growth mindset. The qualitative analysis identified five themes: perceived challenges in understanding formal definitions and mathematical proofs; beliefs about mathematical abilities; strategies for coping with learning difficulties; interpretations of feedback and assessment; and perceived changes in learning perspectives. Students reported using strategies such as reviewing concepts, practicing problems, seeking assistance, and adjusting learning approaches, although some also experienced self-doubt, frustration, and difficulty sustaining their efforts. The findings suggest that growth-oriented beliefs can coexist with uncertainty and avoidance in demanding mathematical situations. These findings highlight the importance of instructional practices that provide structured scaffolding for mathematical proof construction, opportunities to revise unsuccessful attempts, and formative feedback that emphasizes students' learning processes.