A Didactical Analysis of Altitude in Geometric Figures

This study aims to analyze how the concept of altitude is defined and presented in Korean mathematics textbooks in order to strengthen coherence across units and grade levels. To this end, the study examined elementary school textbooks for grades 5-6 and middle school textbooks for grade 7, focusing on instances where the concept of altitude is introduced. The analysis revealed that textbooks tend to treat altitude as a quantity rather than a geometric object, and that its definition varies depending on the type of figure. For example, in plane figures, the definitions of altitude for triangles and quadrilaterals differ, and even in solid figures such as prisms and cylinders, despite their similar geometric structures, altitude is defined inconsistently. In addition, elementary textbooks often define altitude using the term “distance,” which implies the shortest path, whereas middle school textbooks tend to adopt a more intuitive expression, defining altitude as the “length of a line segment.” Based on these findings, this study proposes pedagogical implications for enhancing the coherence of altitude-related concepts within and across grade levels in mathematics textbooks.