The construct “semiotic leap” emerged during collaboraitve microgenetic analysis of empirical data gathered in the Seeing Chance project. The construct attempts to characterize an aspect of student behavior during facilitated engagement with a mathematical activity, particulalrly an activity involving both a realistic problem situation and a formal model of that situation built as a means of establishing a solution. As the word “semiotic” implies in this context, the process is viewed from the perspective of the sign the student builds by virtue of assigning meaning to the model; and as the word “leap” implies here, the behavior is abrupt yet deliberate — a continuous action instantaneously connecting a presymbolic notion with an object in the learning environment.
Thus, a semiotic leap is a heuristic-based appropriation of a cultural form as a means of objectifying an intuitive inference regarding a situation that the form allegedly models. For example, a student may appropriate a sample space as meaning her intuitive inference regarding a situated probabilistic distribution. More specifically, the child first perceives in the situation that some Type A event will occur more often than Type B event. Later, the child views a sample space of the situation that contains more permuations on Type A as compared to Type B. The child claims that Type A event will occur more often that Type B event because there are more Type A elemental events than Type B elemental events. This, even though the child does not yet understand why we expanded the sample space into all the permutations on the events. In this case, the child comes to assign the sample space particular intuitive meanings, even before the logic of the analysis makes sense to her. In fact, it could be that the analysis procedure makes sense to the student — or, rather, that the student makes sense of the analysis procedure — as an entailment of having built personal meaning for the artifact [read more]