PRESERVICE MATHEMATICS TEACHERS’ CONCEPTUAL UNDERSTANDING OF LIMITS: A SYSTEMATIC REVIEW OF MATHEMATICAL AND PEDAGOGICAL KNOWLEDGE

Akbar Nasrum(1*), Sufri Mashuri(2),

(1) Universitas Sembilanbelas November Kolaka
(2) Universitas Sembilanbelas November Kolaka
(*) Corresponding Author

Abstract


The concept of limits is a fundamental foundation of calculus; however, it remains one of the concepts that preservice mathematics teachers find difficult to understand conceptually. These difficulties are not limited to procedural problem-solving skills but also involve understanding the meaning of limits, coordinating multiple representations, constructing formal proofs, and developing the pedagogical ability to explain the concept effectively to students. This study aims to synthesize research on preservice mathematics teachers’ conceptual understanding of the concept of limits by examining the dimensions of mathematical knowledge and pedagogical knowledge. A systematic literature review was conducted following the PRISMA 2020 guidelines. Data were collected from the Scopus and Dimensions databases through RIS files exported in June 2026. From an initial set of 127 records, 23 core articles were selected after the processes of deduplication and screening based on inclusion and exclusion criteria. The selected studies were analyzed using thematic synthesis. The review findings indicate that previous studies have predominantly focused on the mathematical knowledge dimension, particularly difficulties related to understanding the meaning of limits, transforming representations, graph visualization, formal definitions, mathematical proof, sequence limits, trigonometric limits, and asymptotic behavior. In contrast, the pedagogical knowledge dimension has received relatively less attention, although it has been explored through studies on anticipating students’ responses, teacher noticing, representation selection, the use of GeoGebra, and technology-based didactical design. This review highlights that preservice mathematics teachers’ conceptual understanding of limits should be viewed as an integration of mathematical knowledge and pedagogical knowledge. The findings imply the need for calculus instruction in teacher education programs that emphasizes multiple representations, mathematical proof, pedagogical reflection, analysis of students’ thinking, and the conceptual integration of technology.

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References


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DOI: https://doi.org/10.31327/jme.v11i1.2797

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