and varying degrees of access to that knowledge. Although persons, environment, and knowledge are defined in terms of one another, successful application of this approach makes it possible to separate the parameters associated with the person from those associated with the environment.
In specifying their model, dubbed M2RCML, Pirolli and Wilson assume that access to knowledge within a particular knowledge state varies continuously, but perhaps multidimensionally. That is, within a particular knowledge-content state (latent class), a student may be represented by a vector of student constructs. For instance, a group of people who know a particular problem-solving strategy or a specific set of instructions may be arrayed along a continuous scale to represent their proficiency in accessing and using that knowledge. Pirolli and Wilson also assume that people can belong to different knowledge-content states, and that each state can be characterized by the probability of people being in it. Also, they suppose that the environment in which these variables operate can be represented by a vector of environment parameters (traditionally termed “item parameters”). This approach makes an important distinction between knowledge-level and symbol-level learning (Dennett, 1988; Newell, 1982): the knowledge level is seen as being modeled by the knowledge states, and the symbol level by the IRM involving the proficiency continuum and the environment parameters. Pirolli and Wilson have illustrated their approach for data related to both learning on a LISP tutor and a rule assessment analysis of reasoning involving the balance scale as described in Chapter 2.
The generalized approaches of both the unified model and M2RCML have emerged from somewhat different branches of the psychometric tradition. Together they can be regarded as addressing almost all of the calls by Wolf and colleagues (1991, pp. 63–64) as cited earlier. The last call, however, poses a somewhat more demanding challenge: “…we have to consider different units of analysis…because so much of learning occurs either in social situations or in conjunction with tools or resources, we need to consider what performance looks like in those more complex units.” This call raises issues that are effectively outside the range of both general approaches discussed thus far: there are issues of the basic unit of analysis (individual or group), and of the interconnection between the different levels of analysis and the observations (whether the observations are at the individual or group level). For complications of this order (and this is certainly not the only such issue), greater flexibility is needed, and that is one of the possibilities offered by the approach described in the next section.
A more general modeling approach that has proven useful in a wide range of applications is Bayesian inference networks, also called Bayes nets