| Anna Muzsnay , Csilla Zámbó , Janka Szeibert , Csaba Szabó - Vol. 46 Num. 1 (2026) | ||
| Where to find the fifth floor | 54-59 | |
| ABSTRACT: The framework of van Hiele's theory and the corresponding test developed by Usiskin have been widely used in studies investigating students' understanding of geometry across the world. This paper focuses on examining the geometric understanding on higher levels, among mathematics majors and pre-service mathematics teachers, through the application of Usiskin's Van Hiele Geometry Test and follow-up interviews. Our findings, in line with concerns known from the literature, suggest that the fifth van Hiele level requires reconceptualization and an extension of the theoretical framework. In this context, we propose potential continuations of level 4, addressing key questions such as: What constitutes a higher geometric level, and how progression occurs in one's thinking at level 4 and beyond? | ||