Exploring Conceptualisations of the Definite Integral in Mathematics Education: A Systematic Literature Analysis

Background/purpose. The teaching of integral calculus has become increasingly important in higher education due to its role in the development of advanced mathematical thinking. In this context, the definite integral is recognised as a complex mathematical object with multiple interpretations. The present article aims to systematically review the literature on its conceptualisations in mathematics education research, focusing on identifying the predominant approaches, uncovering theoretical gaps, and identifying opportunities to improve teaching and learning practices for this mathematical object.

Materials/methods. A systematic review of the literature was conducted between 2010 and 2024, following PRISMA guidelines. The search was conducted across databases including Scopus, ERIC, ScienceDirect, Taylor & Francis, and Google Scholar. In total, 64 articles were selected for analysis. Artificial intelligence tools and VOSviewer-based bibliometric network analysis were applied to identify conceptual patterns.

Results. Eight main conceptualisations of the definite integral were identified: area under the curve, antiderivative, accumulation, accumulation function, average value, numerical approximation, application to real situations, and solids of revolution. The results reveal a fragmentation between formal, technological, and curricular approaches. Bibliometric networks show poorly connected clusters, which indicates a weak link between theoretical frameworks and their implementation in teaching.

Conclusion. This study demonstrates that fostering a deep understanding of definite integrals requires integrated teaching, explicit attention to infinity, and thoughtful use of technology. Although this review provides an updated theoretical basis, it has limitations: it excludes studies prior to 2010 and focuses mainly on publications in English, thereby limiting the diversity of perspectives. It is suggested that future research expand the analysis to other languages and different educational levels.

Keywords: Definite integral, conceptualisations, educational mathematics, systematic review literature, bibliometric analysis

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