Twenty students who earned A or B course-grades in the proof unit(s) of a secondary course that addressed proof in geometry were asked to work on two proof tasks while sharing their thinking aloud and using smartpens. Students were classified into two categories: those who were successful with both proofs and those who were unsuccessful with both…

Navigational and reaching spaces are known to involve different cognitive strategies and brain networks, whose development in humans is still debated. In fact, high-level spatial processing, including allocentric location encoding, is already available to very young children, but navigational strategies are not mature until late childhood. The…