External Didactic Transposition of the Definite Integral Concept - Francis Yunito Rumlawang; Tanwey Gerson Ratumanan; Christina M Laamena (JURNAL PENDIDIKAN MATEMATIKA, 2026)
Calculus is a course included in the undergraduate curriculum of most science and engineering departments, including mathematics education. The definite integral is a fundamental concept in calculus, formally defined as the limit of a Riemann sum. However, in teaching practice, this concept is often reduced to a computational procedure using the fundamental theorem of calculus without emphasizing the meaning of the limit and the approximation process. This study aims to analyze the external didactic transposition of the concept of the definite integral as the limit of a Riemann sum, specifically, and to examine the alignment of Scholarly Knowledge and  Knowledge to be Taught based on textbooks and curriculum documents. The research method used is a qualitative descriptive approach. This type of research is descriptive. The results of the study indicate that there is consistency between Scholarly Knowledge and Knowledge to be Taught, as reflected in textbooks and semester learning plan (RPS) documents in the curriculum, regarding the concept of definite integrals. However, given the time allotted for the learning process, simplifications may occur, potentially reducing students’ learning experiences. Keywords: external didactic transposition, definite integral, Riemann sum