Introduction: The study presented here investigated the ways in which students who read braille were able to complete geometric tasks and how they constructed mental representations of the shapes of objects. Methods: Data were collected in an educational experiment conducted as a geometry course for students who read braille. A case study approach was used to study two students, aged 10 and 11, who were competent in mathematics. Results: The two students complemented their multiple manual explorations with body movements and postures that corresponded to characteristic features of the shapes of objects. They typically rotated small three-dimensional objects and experimented with the objects' point of balance. Another important result is that they continually measured geometric properties, such as length, area, and volume, as part of their way of "seeing" the shapes of objects. Discussion: The two students "played with" the physical characteristics of environments. Each used his whole body as an explorative instrument. Thus, the study makes a powerful claim for the idea of embodied mathematics. Implications for practitioners: What seems to be important for students aged 10-11 who read braille is to offer a diversity of objects and geometric figures, not only prototypes. Teachers should challenge students to talk about the dimensions of objects in everyday language and in natural situations as a prerequisite to the transition to studying standard units in numerical measurements. (Contains 5 figures and 1 table.)