From Studying Examples to Solving Problem: Fading Worked-Out Solution Steps Helps Learning

From Studying Examples to Solving Problems: Fading Worked-Out Solution Steps Helps Learning Alexander Renkl ( renkl@psychologie.uni-freiburg.de ) University of Freiburg; Department of Educational Psychology; Belfortstr. 16 D-79085 Freiburg; Germany Robert K. Atkinson ( atkinson@ra.msstate.edu ) Department Counselor Education and Educational Psychology; Box 9727 Mississippi State, MS 39762; USA Uwe H. Maier ( uwe.harald.maier@t-online.de ) Educational University of Schwabisch Gmund; Oberbettringer Str. 200 D-73525 Schwabisch Gmund; Germany Abstract Research has shown that it is effective to combine example study and problem solving in the initial acquisition of cognitive skills. Present methods for combining these learning modes are, however, static and do not support a transition from example study in early stages of skill ac- quisition to later problem solving. Against this back- ground, we propose a successive integration of problem- solving elements into example study until the learners solve problems on their own (i.e., complete example e increasingly more incomplete examples e problem to-be- solved). We tested the effectiveness of such a fading proce- dure against the traditional method of employing example- problem pairs. In a field experiment and in a more con- trolled lab experiment, we found that the fading procedure fosters learning, at least when near transfer performance i s considered. Moreover, this effect is mediated by a lower number of errors under the fading condition as compared t o the example-problem condition. Introduction Worked-out examples consist of a problem formulation, solution steps, and the final solution itself. Research has shown that learning from such examples is of major impor- tance for the initial acquisition of cognitive skills in well- structured domains such as mathematics, physics, and pro- gramming (for an overview see VanLehn, 1996). In addition, novices prefer this learning mode, and they are right: It is quite an effective way of learning. Studies performed by Sweller and his colleagues (e.g., Sweller & Cooper, 1985; for an overview see Sweller, van Merrienboer, & Paas, 1998) showed that learning from worked-out examples can be more effective than learning by problem solving. Although worked-out examples have significant advan- tages, their employment as a learning methodology does not, of course, guarantee effective learning. First, the extent to which learners profit from the study of examples depends on how well they explain the solutions of the examples to themselves (Chi, Bassok, Lewis, Reimann, & Glaser, 1989; Renkl, 1997). Second, it is important how the learning ma- terials (examples and problems) are structured (cf. Atkinson, Derry, Renkl, & Wortham, in press). The second aspect is the focus of this study. More specifically, this study inves- tigates one possible approach to integrating elements of problem solving into example study. We propose that these learning modes can be combined by successively introducing more and more elements of problem solving in example study until learners are solving the problems on their own. This rationale can also be used as a way to structure the transition from studying examples in initial skill acquisition to problem solving in later phases of the learning process. In the next section, the literature with respect to the issue of combining example study and problem solving is dis- cussed. Then we outline open questions and give preliminary answers that were tested in two studies, first in a field ex- periment and then in a more controlled lab experiment. How to Combine Example Study and Problem Solving? – State of the Art Empirical evidence has shown that pure example study (i.e., examples alone) is not as effective as learning from exam- ples in which elements of problem solving are integrated. There are two traditional ways to combine example study and problem solving: (1) Making the solutions of examples incomplete and (2) employing example-problem pairs. Incomplete Examples Some researchers argue that incomplete examples, which the learners have to complete, effectively support the acquisition of cognitive skills (van Merrienboer, 1990; van Merrienboer & de Crook, 1992; Paas, 1992; Stark, 1999). Stark (1999) conducted a controlled experiment designed to examine the extent to which the insertion of “blanks” into the solution of examples—which, in a certain sense, forced the learners to determine the next solution step on their own—fostered learning. In his study, half of the participants studied in- complete examples (experimental group), while the other half learned from complete examples (control group). In the experimental group, portions of the example solutions pre- sented to the participants were replaced by “question marks. ” The learners were then asked to identify what solution step