In this paper, we investigate students' use of the generate-and-test strategy to solve algebra word problems. This strategy involves first choosing an estimate for the answer and then checking whether the estimate satisfies the constraints of the problem. Based on verbal protocol data, we developed a production system model to simulate students' behavior when they apply this informal strategy. The model predicts problem features that should affect the difficulty of the problems. A large-scale experiment tested the predictions of the model. Verbal protocol data provided additional insights into how students use the generate-and-test strategy.

In this paper, we review the literature on the relation between solving nonspecific goal problems and learning. Research has shown that reduced goal-specificity facilitates learning of rules and principles of the target domain. Researchers have accounted for this effect using a cognitive load theory (Sweller, 1988) and a dual space theory of problem solving (Vollmeyer, Bums, & Holyoak, 1996). Other researchers have shown that learning can be both facilitated by nonspecific as well as specific goals and account for their findings using goal appropriateness theory (Miller, Lehman. & Koedinger, 1997). W e judge each theoretical account by evaluating their consistencies with unified theories of cognition and other empirical data. We note the shortcomings of the each theory and incorporate elements of each to explain all the data.