The role that the mental, or internal, representation plays when people are solving hard computational problems has largely been overlooked to date, despite the reality that this internal representation drives problem solving. In this work we investigate how performance on versions of two hard computational problems differs based on what internal representations can be generated. Our findings suggest that problem solving performance depends not only on the objective difficulty of the problem, and of course the particular problem instance at hand, but also on how feasible it is to encode the goal of the given problem. A further implication of these findings is that previous human performance studies using NP-hard problems may have, surprisingly, underestimated human performance on instances of problems of this class. We suggest ways to meaningfully frame human performance results on instances of computationally hard problems in terms of these problems' computational complexity, and present a novel framework for interpreting results on problems of this type. The framework takes into account the limitations of the human cognitive system, in particular as it applies to the generation of internal representations of problems of this class.

Abstract:Recent studies on a computationally hard visual optimization problem, the Traveling Salesperson Problem (TSP), indicate that humans are capable of finding close to optimal solutions in near-linear time. The current study is a preliminary step in investigating human performance on another hard problem, the Minimum Vertex Cover Problem, in which solvers attempt to find a smallest set of vertices that ensures that every edge in an undirected graph is incident with at least one of the selected vertices. We identify appropriate measures of performance, examine features of problem instances that impact performance, and describe strategies typically employed by participants to solve instances of the Vertex Cover problem.

THIS EMIC, QUALITATIVE STUDY EXAMINES HOW MASTER'S-LEVEL SPECIAL EDUCATION TEACHERS OPER-ATIONALIZED CONSTRUCTIVIST TEACHING. WE ANALYZED 21 VIDEOTAPED TEACHING DEMONSTRATIONS AND INFORMATION GLEANED FROM THE TEACHERS' ESSAYS, JOURNALS, AND UNIVERSITY CLASS DISCUSSIONS TO DESCRIBE THE TEACHERS' BELIEFS (TRADITIONAL), THE INSTRUCTIONAL TASKS THEY DEVISED (HANDS-ON AND TEXT-BASED), AND THE DYNAMIC INSTRUCTIONAL GOALS THEY PURSUED: (A) STRUCTURE AND ORDERLINESS, (B) SHARED TASK UNDERSTANDING, (C) OBJECTIFICATION OF KNOWLEDGE, (D) INDEPENDENT USE OF KNOWLEDGE, AND (E) POSITIVE MOTIVATION AND AFFECT. THEIR LESSONS VARIED CONSIDERABLY FROM WHAT WE HAD MODELED IN THEIR UNIVERSITY CLASS AND FROM THE LITERATURE DESCRIPTIONS OF CONSTRUCTIVIST TEACHING, WHICH EMPHASIZE STUDENT MEANING MAKING THROUGH SELF-REGULATION, SOCIAL INTERACTION, AND PROBLEM SOLVING. OUR PURPOSES WERE TO PROVIDE A RICH DESCRIPTION OF THE WAY PRACTITIONERS FRAME AND TRANSFORM THEIR FIRST EXPOSURE TO CONSTRUCTIVISM AND TO CONTRIBUTE TO A SCHOLARLY DISCOURSE IN WHICH PRACTICE INFORMS THE KNOWLEDGE BASE OF THE PROFESSION.

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Explicitly cued task switching slows performance relative to performing the same task on consecutive trials. This effect appears to be due partly to more efficient encoding of the task cue when the same cue is used on consecutive trials and partly to an additional task-switching process. These components were examined by comparing explicitly cued and voluntary task switching groups, with external cues presented to both groups. Cue-switch effects varied in predictable ways to dissociate explicitly cued and voluntary task switching, whereas task-switch effects had similar characteristics for both instructional groups. The data were well fitted by a mathematical model of task switching that included a cue-encoding mechanism (whereby cue repetition improves performance) and an additional process that was invoked on task-switch trials. Analyses of response-time distributions suggest that this additional process involves task-set reconfiguration that may or may not be engaged before the target stimulus is presented.Keywords: Cue encoding; Task switching; Voluntary task switching Cognitive control operations that govern the ability to shift from one task to another, particularly under conditions that afford multiple tasks simultaneously, can be separated into two kinds. One type of operation involves endogenously controlled shifts in processes that direct attention to the correct aspect of a stimulus display and retrieve and apply the appropriate stimulus-response mapping rules to generate the correct response (e.g., Mayr & Kliegl, 2003;Meiran, 2000;Rogers & Monsell, 1995). An additional class of processes is exogenous in nature and appears to operate without top-down control. These processes may include interference from residual activation of previous task sets, priming of performance when a task is repeated, and, when the task switches, negative priming of a previously ignored task (e.g., Allport, Styles, & Hsieh, 1994;Arrington & Logan, 2004a;Sohn & Carlson, 2000;Waszak, Hommel, & Allport, 2003). A question of central importance in developing an account of how efficient switching between tasks is accomplished concerns the relative contributions made by these two types of processing.From one theoretical perspective, proposed by Logan and colleagues (e.g., Logan & Bundesen, 2003;Schneider & Logan, 2005), task switching is orchestrated by purely exogenous processes. They proposed that the cost of switching tasks, when explicit cues are used to indicate which task Correspondence should be addressed to Michael Masson, Department of Psychology, University of Victoria, P.O. Box 1700 STN CSC, Victoria BC V8 W 2Y2, Canada. E-mail: mmasson@uvic.caWe thank Marnie Jedynak for assistance with data collection and analysis and Gordon Logan for helpful suggestions on model fitting.