Acquiring powerful abstractions -- i.e., representations that enable one to reason about key aspects of a domain in an economical and generic form - should be a primary goal of learning. The most effective means for achieving this goal is not. we argue, the "topdown" approach of traditional curricula where students are first presented with an abstraction, such as F=ma. and then with examples of how it applies in a variety of contexts. Nor do we advocate the "bottom-up" approach proposed by situated cognition theorists. Instead, we argue for a "middle-out approach where students are introduced to new domains via intermediate abstractions in the form of mechanistic causal models. These models serve as "conceptual eyeglasses" that unpack causal mechanisms implicit in abstractions such as F=ma. Tney are readily mappable to a vanety of real-worid contexts since their objects and operators are generic and causal. Intermediate abstractions thus give meaning to higher-order abstractions as well as to real-world situations, provide a link between the two, and a route to understanding.

This paper presents a theory of how to enable people to understand how physical systems work Two key hypotheses have emerged from our research. The first is that in order to understand a physical system, students need to acquire causal mental models for how the system works. Further, it is not enough to have just a single mental model. Students need alternative mental models that represent the systems behavior from different, but coordinated, perspectives, such as at the macroscopic and microscopic levels.The second hypothesis is that in order to make causal understanding feasible in the initial stages of learning, students have to be introduced to simplified models. These models then get gradually refined into more sophisticated mental models. W e will present a theory outlining (1) the properties of an easily learnable, coherent set of initial models, and (2) the types of evolutions needed for students to acquire a more powerful set of models with broad utility.

Our objective has been to determine whether woii^ing with reductionistic models reduces students' mis- conceptions, and increases the coherence and flexibility of their expertise as they solve problems and generate expla- nations. W e conducted experimental trials of an interac- tive learning environment that provides models of circuit behavior. In these trials, w e examined students' perfor- mance on a variety of circuit problems before and after they worked with either (a) a "transport" model alone, or (b) the transport model augmented with explanations of its processes in terms of a "particle" model. T h e posttest re- sults reveal that, while both groups performed well o n a wide range of tasks, students w h o received the particle- model explanations achieved higher levels of performance on tasks that require an understanding of voltage and its distribution. W e conjecture that this is due to the particle model providing students with a mechanistic model for charge distribution that is consistent with the behavior of the transport model and that inhibits the construction and use of certain common misconceptions.