Thinking by Doing? Epistemic Actions in the Tower of Hanoi

Abstract

Thinking by Doing? Epistemic Actions in the Tower of Hanoi Hansj¨org Neth (NethH@Cardiff.ac.uk) Stephen J. Payne (PayneS@Cardiff.ac.uk) School of Psychology, Cardiff University Cardiff CF10 3YG, Wales, United Kingdom Abstract This article explores the concept of epistemic actions in the Tower of Hanoi (ToH) problem. Epistemic actions (Kirsh & Maglio, 1994) are actions that do not traverse the problem space toward the goal but facilitate subse- quent problem solving by changing the actor’s cogni- tive state. We report an experiment in which people re- peatedly solve ToH tasks. An instructional manipulation asked participants to minimize moves either trial by trial or only on the last three of six trials. This manipulation did not have the predicted effect on the trial-by-trial move counts. A second, device manipulation provided some participants with an “exploratory mode” in which move sequences could be tried then undone without affecting the criterion move count. Participants effectively used this mode to reduce moves on each trial, but there was no clear evidence that they used it to learn about the problem across trials. We conclude that there is strong evidence for one sub-type of epistemic action (acting-to-plan) but no evidence for a second sub-type (acting-to-learn). Introduction How do we learn to solve a problem? The most popu- lar view within the Cognitive Science community is that we do so by solving the problem. Anzai and Simon’s (1979) theory of ‘learning by doing’ marks a major breakthrough in research on learning through problem solving. They proposed an adaptive production system which mirrored the strategy transformations of a human participant as she solved the Tower of Hanoi (ToH) prob- lem, and in so doing provided the impetus for many sub- sequent theories of the mechanisms by which problem solving leads to learning (e.g. Klahr, Langley & Neches, All learning-by-doing accounts share the assumption that learning about a particular problem occurs as an au- tomatic by-product of problem solving activity. How- ever, in many problem solving situations learning may be more deliberate than the learning-by-doing account im- plies. We suggest that problem solvers may sometimes orient themselves to learning goals rather than solution goals (O’Hara & Payne, 1998; Trudel & Payne, 1995). In relation to the ToH task, this position is encouraged by VanLehn’s (1991) re-analysis of the original Anzai & Simon (1979) protocol, in which he notes that the partic- ipant was “acting like a scientist” (p. 16) and repeatedly suspended her problem solving activity to acquire new strategic knowledge. Further general support for a deliberate learning mode nested within problem solving activity can be derived from the work of Kirsh and colleagues (1995, Kirsh & Maglio, 1994), who have explored a distinction be- tween goal-directed pragmatic actions and epistemic ac- tions whose primary purpose is to improve cognition by changing an agent’s computational state. Although epis- temic actions are not immediately goal-directed, they may improve subsequent performance through their cog- nitive effects. The primary goal of this article is to seek experimen- tal evidence for the use of epistemic actions in problem solving with the ToH puzzle. Identifying epistemic ac- tions in ordinary problem solving activity is difficult, be- cause they are only distinguished by their cognitive moti- vations and consequences rather than directly observable characteristics (and not all actions that do not success- fully move toward the goal are epistemic!). We use two manipulations that may allow participants to utilise epis- temic actions, and at the same time facilitate their detec- tion. The first manipulation is instructional: participants were asked either to optimize their performance on every problem solving trial, or on trials 4, 5 and 6 of a series of six repeated problems. We hypothesize that delaying the enforcement of the performance criterion will encour- age a learning orientation, and the use of epistemic ac- tions, during the early first trials. The second manipula- tion is to provide device support that enables participants to separate pragmatic from epistemic actions. Thus, our computer-based version of ToH allowed participants to switch into an “exploratory mode” in which they could make move sequences that were later undone and were not counted towards the performance criterion. These twin manipulations allow us to refine Kirsh’s formulation of pragmatic and epistemic actions by dis- tinguishing between two kinds of epistemic action: those that have only immediate within-problem effects (acting- to-plan) and those that have longer-term cognitive con- sequences (acting-to-learn). If the exploratory mode is used merely as an external support for look-ahead or planning, motivated by questions such as ‘Is this a good sequence of moves?’, we would regard such usage as acting-to-plan. On the other hand, if additional actions on earlier trials are shown to lead to better problem solv- ing on later trials we would have evidence for acting-to- learn.