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Cascade Explains and Informs the Utility of Fading Examples to Problems

Cascade Explains and Informs the Utility of Fading Examples to Problems Randolph M. Jones (rjones@colby.edu) Eric S. Fleischman (esfleisc@colby.edu) Computer Science, Colby College 5847 Mayflower Hill Drive Waterville, ME 04901-8858 USA Abstract Recent research demonstrates that people learn to solve problems more effectively when presented with a series of faded examples and problems, than when presented with completely worked out examples and completely unsolved problems alone. We propose an explanation for this effect, based on the Cascade model. Cascade was originally built to model the self-explanation effect, but it also accounts for other aspects of human learning and problem solving strategies. A relatively straightforward application of Cascade, without alteration, also explains why fading might be beneficial. This explanation provides further support for Cascade as an accurate model of human learning and problem solving, and it also augments the results on fading with specific insight into how, and when, example fading should be effective. Introduction There are a variety of research results characterizing factors that facilitate the human ability to learn how to solve problems. Among recent results, Renkl, Atkinson, and Maier (2000) report that people learn more effectively when presented with a set of “faded” examples and study problems than they do when presented with study examples alone (followed by completely unworked problems). Given this result, our interest is in identifying the cognitive mechanisms that explain why the effect exists. Additionally, if we understand the underlying mechanisms, they may provide extra insight into precisely how to create effective sets of study examples and problems. We have identified a potential set of explanatory mechanisms, which are precisely the mechanisms that define Cascade, an existing model of human learning in problem solving (VanLehn, Jones, & Chi, 1991; VanLehn & Jones, 1993a). The Cascade model suggests which study and learning mechanisms contribute to the fading effect, and provides a tool for pinpointing precisely which types of faded examples will be most effective. Fading Examples A common curriculum for teaching students to solve problems in a particular domain involves having the students first read some domain material, then study some completely worked out example problems, and finally solve problems that have not been worked out. Various studies explore why it is beneficial for students to study completely worked out examples (e.g., Chi et al., 1989; Pirolli & Anderson, 1985; Renkl, 1997, VanLehn, 1996). The technique of fading examples constitutes a particular variation on such a course of study. When fading, the teacher first presents a completely worked example and then follows this with a series of nearly completely worked examples. Each subsequent problem removes an explanatory step, forcing the students to solve that portion of the problem themselves. This gives more guidance than a regular problem, because the student still has the guidance of the rest of the worked out example, but it gives less guidance than a completely worked example. Renkl et al. (2000) demonstrated that different particular methods of presentation can yield different levels of learning. Specifically, they showed that fading sometimes improves learning over other orders of presentation. In their initial study, they presented subjects with a completely worked example, followed by an example that omits the last step in the solution. This was then followed by an example that omits the second to last and last steps and finally one presentation of a completely unworked problem. They compared this situation to one in which students first studied a completely worked example, and then solved a completely unworked problem. The results of this study confirmed that the group of subjects exposed to faded examples learned more effectively than the other group, even though both groups had similar pre-test performances. A more thorough, but similar, experiment produced comparable results. Renkl et al.’s study provides us with valuable information about potential ways to design study curricula. However, the research also leaves a few unanswered questions. Among these are why fading works as well as it does. In addition, it would be useful to know exactly what forms of fading will be effective. Is it always the case that examples should be faded from back to front? Or are there more formal methods we can use to design faded examples? Such questions can, and should, be answered in part by further