We report on the case study of a student in a tutoring experiment using this approach in the study of electric circuits. We concentrate on the student's moments of surprise as motivators of conceptual change. Most of these come from discrepant events, but one of them appears to come from the student's own sensed lack of coherence in an intermediate model. In this case study, the teaching method appears to lead to the construction of an explanatory model that is fairly deeply understood by the student in the sense that it can generate predictions and coherent explanations of a complex system in a transfer problem.
Some of our conclusions and hypotheses generated with respect to learning processes are: (1) Discrepant events produced reactions of surprise and were eventually followed by model revisions, leading us to hypothesize a motivating and guiding role for these events. (2) The subject was able to map and apply an air pressure analogy used for electric potential and continued to exhibit traces of it through the posttest interview. (3) The subject's spontaneous use of similar depictive hand motions during the instruction and during the posttest provides initial evidence that the instruction fostered development of dynamic mental models, such as those of fluid-like flows caused by pressure differences, that can generate new mental simulations for understanding relatively difficult transfer problems. This leads us to describe the core of her new knowledge as explanatory models at an intermediate level of generality that allow her to run imagistic simulations and to hypothesize a "transfer of runnability" from the analog conception to the model in this case. (4) We hypothesize that: the process underlying model generations and revisions was one of scaffolded abductive knowledge construction rather than induction or deduction; that evaluation and revision cycles can make up for the conjectural nature of individual abductions; and that engagement and comprehension in the cycle was fostered by small step sizes for revisions from using multiple "small" discrepant events and analogies built into the lessons.
The theoretical model elaborated here is grounded in data drawn from a study of 10-11 year olds' construction of meanings for randomness in the context of a carefully designed computational microworld, whose central feature was the visibility of its mechanisms--how the random behavior of objects actually "worked". In this paper, we illustrate the theory by reference to a single case study chosen to illuminate the relationship between the situation (including, crucially, its tools and tasks) and the emergence of new knowledge. Our explanation will employ the notion of situated abstraction as an explanatory device that attempts to synthesize existing micro- and macro-level descriptions of knowledge construction. One implication will be that the apparent dichotomy between mathematical knowledge as de-contextualized or highly situated can be usefully resolved as affording different perspectives on a broadening of contextual neighborhood over which a network of knowledge elements applies.