Eric S. Fleischman
Senior Scholars Abstract
Last updated: February 24, 2002

A Cognitive Model of New Data on Human Problem Solving

During the educational process there are a multitude of strategies that educators may employ in order to maximize learning among their pupils. For symbolic problem-solving skills (such as mathematics), a particularly effective technique is to have students study worked-out example problems and unworked practice problems. Research shows that students who explain parts of worked examples to themselves learn more effectively than students who do not. This is called the self-explanation effect (Chi et al., 1989; Fergusson-Hessler & de Jong, 1990; Pirolli & Bielaczyc, 1989). In summary, this research proved that students learn most effectively by studying examples when they are careful to explain to themselves as many steps of the example as they can. This theory further states that students who do not carefully explain worked out example steps do not perform as well on subsequent problems. To explain this result, VanLehn and Jones (VenLehn, Jones & Chi, 1991) developed Cascade, a cognitive model that posits particular memory, problem-solving, and learning mechanisms to account for the self-explanation effect.

Subsequent psychological research has concluded that fading completely worked examples can further improve learning (Renkl, Atkinson & Maier, 2000). Fading consists of removing some of the solution steps in an example, forcing students to solve those portions themselves. To explain this new result, Jones and Fleischman (2001) used Cascade to model the basic cognitive processes of subjects given faded examples. This explanation relied on a small set of assumptions, to be verified by future experiments on human subjects.

My primary work this year has been in collaboration with psychologists who have run further detailed experiments, in part to test the predictions we made last year. The new data provide detailed behavior traces of students studying a variety of different sets of example problems, in order to learn some basic principles of mathematical probabilities. The detailed nature of the data allows me to use Cascade to do a very precise analysis of the errors the subjects generate, the learning episodes they experience, and the knowledge they acquire. Part of my task has been to engineer Cascade’s knowledge base from classical physics to the probability principles in the current experiments. The rest of my work involves coding the subject behavior traces and tuning Cascade’s parameters to fit them. The upshot of this work is that the new data are consistent with the predictions we made last year, providing further evidence that Cascade is a useful model of human learning and problem solving, and further insight into effective teaching procedures for problem-solving skills.

Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science, 13, 145-182.
Ferguson-Hessler, M. G. M., & de Jong, T. (1990). Studying physics texts: Differences in study processes between good and poor solvers. Cognition and Instruction, 7, 41-54.
Jones, R. M., & Fleischman, E. S. (2001). Cascade explains and informs the utility of fading examples to problems. Proceedings of the Twenty-Third Annual Conference of the Cognitive Science Society, 459-464. Mahwah, NJ: Lawrence Erlbaum.
Pirolli, P., & Bielaczyc, K. (1989). Empirical analyses of self-explanation and transfer in learning to program. In G. M. Olson & E. E. Smith (Eds.), Proceedings of the Eleventh Annual Conference of the Cognitive Science Society (pp. 450-457). Hillsdale, NJ: Lawrence Erlbaum.
Renkl, A., Atkinson, R. K., & Maier, U. H. (2000). From studying examples to solving problems: Fading worked-out solution steps helps learning. In L. R. Gleitman & A. K. Joshi (Eds.), Proceedings of the Twenty-Second Annual Conference of the Cognitive Science Society (pp. 393-398). Mahwah, NJ: Lawrence Erlbaum.
VanLehn, K., Jones, R. M., & Chi, M. T. H. (1991). A model of the self-explanation effect. Journal of the Learning Sciences, 2, 1-59.