Reasoning Through Instructional Analogies

Abstract

This article aims to account for students’ assessments of the plausibility and applicability of analogical explanations, and individual differences in these assessments, by analyzing properties of students’ underlying knowledge systems. We developed a model of explanation and change in explanation focusing on knowledge elements that provide a sense of satisfaction to those judging the explanation. We call these elements “explanatory primitives.” In this model, explanations are accepted or rejected on the basis of (a) the individual's convictions concerning particular explanatory primitives and (b) the fit of these primitives to current circumstances. Data are drawn from clinical interviews with three high school students who worked through a bridging analogies tutoring sequence on the existence of the normal force in mechanics. Methodologically, our work involves fine-grain analysis of process data and explicit principles of empirical accountability; we believe it marks a methodological advance over most previously reported empirical studies of analogical reasoning.

ACKNOWLEDGMENTS

We thank John Clement, David Brown, and two anonymous reviewers for their thoughtful comments on earlier versions of this article. We also thank the members of the Patterns and Knowledge Analysis research groups at UC Berkeley for the helpful discussions. This research was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Program. The second author acknowledges and thanks the Spencer Foundation for continuing support for the study of intuitive knowledge and its development (Grant #201100101).

Notes

DiSessa (1993) makes an abbreviated argument that a related idea unsupported things fall is indeed a p-prim.

The e-prim's features should be among those attended to or derivable from what is attended to.

One can imagine the suspension of belief in the force requires agency e-prim in this context to be a step in a process of either generally reducing the priority of that e-prim or changing the meaning of “agency.” We discuss these considerations later in light of the other students’ reasoning. Note, also, that Jacob's state here is interestingly complex. One could gloss it as “gradually increasing the confidence he has in dynamic balance.” However, in this case, this potential increase in confidence is entangled specifically with the current state and future trajectory of another e-prim, force requires agency. In general, we believe our model provides important and empirically tractible refinements over more global assessments and descriptions, such as “becoming comfortable with an idea,” or “gaining more skill in using it.”

Self-motion is an early index to “alive” in Piagetian studies (Piaget & Garcia, 1974), and we interpret Sara's reference to it to be a common consideration for the more sophisticated notion of agency.

In a later discussion, we substantiate via the existing literature the fact that size or weight can convey strength or capacity.

Adam heard the term kinetic energy in chemistry class.

Methodological note: This is a case where intrinsic and contextual priorities seem definitively distinct. In cases where Adam thinks that springiness applies, he uses it fluently. In the case of rigid objects, he doubts it applies. The contextual range of the rigidity p-prim explains the boundary.

Adam's belief that a deformation is a requisite condition for energy transfer is correct according to Newtonian physics.

This is a particularly clear case methodologically where the properties of a knowledge element important to the acceptance of a model can be seen in contexts other than the model, before the model has been presented.

^*Editor in chief and co-author Andrea diSessa had no role in the review and decision process, neither as participant nor as observer, that led to the acceptance of this article.