This study explores the coordination of several semiotic presentations in the process of the objectification of Cartesian coordinates by first grade children. By means of novel dual eye-tracking technology, I investigated the micro-dynamics of a child's and her parent's attentions as they were involved in the teaching-learning process. The analysis of the synchronized data that were retrieved from two eye-trackers and from an external video camera showed ambiguity, not only of verbal terms and visual inscriptions, but also of pointing gestures. It brought out the joint attention moments as crucial for acquiring the culturally adequate meaning of the Cartesian plane. The active disclosure of different presentations' complementarity determined the moment when the child acquired some meaning, yet not always the cultural one. The joint attention (or the absence of it) allowed the adult to keep track of the understanding that was emerging in the child's mind, to compare it with her own perception of the cultural representation, and to rectify the child's perception.