We call those gestures “instrumental” that can enhance certain thinking processes of an agent by offering him representational models of his actions in a virtual space of imaginary performative possibilities. We argue that pointing is an instrumental gesture in that it represents geometrical information on one’s own gaze direction (i.e., a spatial model for attentional/ocular fixation/orientation), and provides a ritualized template for initiating gaze coordination and joint attention. We counter two possible objections, asserting respectively that the representational content of pointing is not constitutive, but derived from language, and that pointing directly solicits gaze coordination, without representing it. We consider two studies suggesting that attention and spatial perception are actively modified by one’s own pointing activity: the first study shows that pointing gestures help children link sets of objects to their corresponding number words; the second, that adults are faster and more accurate in counting when they point.