Improving spatial ability of blind and visually impaired people is the main target of orientation and mobility (O&M) programs. In this study, we use a minimalistic mouse-shaped haptic device to show a new approach aimed at evaluating devices providing tactile representations of virtual objects. We consider psychophysical, behavioral, and subjective parameters to clarify under which circumstances mental representations of spaces (cognitive maps) can be efficiently constructed with touch by blindfolded sighted subjects. We study two complementary processes that determine map construction: low-level perception (in a passive stimulation task) and high-level information integration (in an active exploration task). We show that jointly considering a behavioral measure of information acquisition and a subjective measure of cognitive load can give an accurate prediction and a practical interpretation of mapping performance. Our simple TActile MOuse (TAMO) uses haptics to assess spatial ability: this may help individuals who are blind or visually impaired to be better evaluated by O&M practitioners or to evaluate their own performance.