Goal Specificity and the Generality of Schema Acquisition

Goal Specificity and the Generality of Schema Acquisition David L. Trumpower (dtrumpow@unm.edu) Timothy E. Goldsmith (gold@unm.edu) Maureen Below (mollybe37@msn.com) University of New Mexico Department of Psychology, Logan Hall Albuquerque, NM 87131 USA Abstract Fourteen statistics novices were asked to solve three statistics word problems under standard (SGS) or reduced (RGS) goal specificity. Later, they were asked to solve both structurally identical and structurally different transfer problems, and their structural knowledge of the domain was assessed. Results indicate that participants in the RGS condition performed better on the structurally different transfer problems and had acquired structural knowledge more similar to that of a domain expert. These results extend previous work in showing that the schematic knowledge acquired under reduced goal specificity training is more general than previously realized. The goal specificity effect is discussed in terms of the attentional focus required to solve RGS and SGS problems. Introduction Most theorists agree that schemas form the basis for problem solving expertise. Schemas are typically described as knowledge structures that represent generalized concepts, and are comprised of facts and procedures as well as the interrelationships among those facts and procedures. With respect to problem solving, it is generally accepted that schemas allow: (1) problems to be classified according to the general principles required for their solution (Chi, Feltovich, & Glaser, 1981), (2) solution planning (Priest, & Lindsay, 1992), and (3) use of forward-chained solutions (Koedinger, & Anderson, 1990), all of which are hallmarks of expertise. Thus, an important issue for cognitive scientists and educators alike is to understand how schemas are learned. Cognitive Load Theory (CLT) has been advanced to describe the relationship between problem solving and learning (Sweller, & Levine, 1982; Sweller, 1988). CLT posits that acquisition of schematic knowledge during problem solving is not automatic; rather, it requires a certain amount of cognitive resources. Therefore, if a problem solving task or strategy demands a great deal of cognitive resources then learning will be impaired relative to a task or strategy that carries a low cognitive load. CLT has been used to explain the finding that reducing the specificity of goals enhances problem solving performance, otherwise know as the goal specificity effect. The goal specificity effect has been shown in maze learning (Sweller, & Levine, 1982), kinematics (Sweller, Mawer, & Ward, 1983), geometry (Ayres, 1993; Sweller, Mawer, & Ward, 1983), trigonometry (Owen, & Sweller, 1985; Sweller, 1988), and several more complex, dynamic tasks (Miller, Lehman, & Koedinger, 1999; Vollmeyer, Burns, & Holyoak, 1996). According to CLT, problems with standard goal specificity (SGS), in which problem solvers are given values for several variables and asked to solve for the value of a specific unknown variable, encourages use of a means-ends strategy. Under a means-ends strategy, problem solvers' attention is focused on reducing the difference between the current problem state and the goal. Moves are guided by the goal state, which requires solvers to keep in memory the goal, any subgoals, and the current problem state. Because this task is cognitively demanding, it detracts from the learning of relations that are relevant for schema acquisition. Reduced goal specificity (RGS) problems, in which problem solvers are asked to solve for the value of as many unknown variables as possible rather than the value of a specific unknown variable, eliminate the possibility of a means-ends strategy. Instead, they require a forward-working strategy where moves are generated solely by the current problem state. Because this strategy is less cognitively demanding (see Sweller, 1988), resources are available for learning the relations relevant to schema acquisition, namely, relations between the appropriate operators and problem states. According to CLT, training with RGS problems is more likely to lead to schema acquisition than training with SGS problems, where schemas are defined as knowledge of problem states and their associated operators. However, this definition of a schema is limited in that it is only applicable to problems with similar structure as those encountered during training (i.e., problems that share, at least some of, the same problem states as the training problems). We will call this the limited schema view. Actually, it is difficult to distinguish this view from one that simply postulates the storage of exemplar solutions. If one remembers previous problem solutions, they then have knowledge of problem states and their associated moves/operatorsOthe same information contained in limited schemas. Under this exemplar view, the goal specificity effect can be explained by the notion that RGS solutions are easier to remember than SGS solutions (since they require less cognitive load to perform, more resources are available to store them), and they are forward-working. A third alternative is that schemas are acquired under RGS training and that they are