Maxwell J. Roberts

Strategy Selection and Metacognition.

The concept of metacognition is one of the most important developments in the contemporary study of cognition, especially with regard to problem solving and the transfer of cognitive skills. Its study has followed the experimental paradigm with researchers looking for universal principles; metacognition has only a small role to play in looking for explanations of individual differences in cognition. In this paper we are attempting a theoretical analysis of a number of interrelated issues with regard to their importance for metacognition in the light of some current empirical work. It considers mainly the role of these processes in strategy selection, especially in light of the impasse‐based theories of problem solving, and explores the relationship of individual differences to metacognition.

Inspection times, the change task, and the rapid-response selection task

Three experiments are reported, which are based upon the Wason four-card selection task inspection time paradigm, in which subjects solve computer-presented trials while using a mouse to indicate the card currently under consideration. Evans (1996) had shown that selected cards were inspected for longer than non-selected cards, and this was taken as support for the existence of pre-conscious heuristic processes that direct attention towards relevant aspects of a problem. However, Roberts (1998b) suggested that this inspection time effect is artefactual, due to task format induced biases. Experiment 1 utilized a “change” task: Cards were presented either as selected or not selected, and subjects changed these where necessary. This demonstrated an association between card selection and inspection time independently of one between the act of response and inspection time. Experiment 2 utilized a standard selection task, but subjects either responded within 2 s of each card presentation, or made selections with no time pressure. The curtailment of thinking time increased matching behaviour—more cards matching the terms in the rules were selected—and was replicated in Experiment 3 using a within-subjects design. Overall, the data support Evans’ heuristic-analytic framework albeit with some caveats.

Human Reasoning: Deduction Rules or Mental Models, or Both?

A good deal of energy is currently being expended into discovering the fundamental machinery underlying deductive reasoning. Is it based upon mental models (arrays) or deduction rules (propositions)? The appeal of finding a “grand unified theory” of reasoning is obvious, but the likelihood of achieving this must also be considered. This paper discusses the use of experimental psychology in attempts to discover the processes associated with the fundamental reasoning mechanism. One particular problem is that individuals can use different strategies to solve reasoning problems. The consequences of this are assessed in relation to: (1) the assumptions underlying the experiments, (2) the choice of tasks and task presentations intended to enable the fundamental reasoning processes to be viewed directly, and (3) the power status of the theories and the nature of the evidence required to show that either theory is superior. Under close scrutiny the debate appears to be unresolvable by using empirical techniques. However, although the main conclusions are negative, it is suggested that approaches that directly investigate individual differences are likely to be useful alternatives.

Task-switching costs, Stroop-costs, and executive control: A correlational study

Three correlational studies investigated the relationship between the time costs associated with Stroop stimuli (Stroop-costs) with the time costs associated with task-switching (switch-costs) obtained from colour-word stimuli and digit stimuli. In all studies, large and significant positive correlations were found between different measures of switch-costs. However, only small (and sometimes non-significant) correlations were obtained between the different measures of Stroop-costs and between measures of Stroop-costs and measures of switch-costs. The results are taken as evidence for the existence of some common or shared specialized mechanisms involved in taskswitching, which are different from those used to overcome Stroop interference.

Strategies in relational inference

Three experiments are reported in which the relationships between task format, item type, and strategy usage were investigated for a two-dimensional relational inference task. Contrary to past findings with linear syllogisms, it was found that parallel presentation (presenting problem statements simultaneously) did not result in any increased use of deduction rule processes compared with serial presentation (presenting problem statements individually). Instead, the results suggested that mental models were used by the majority of subjects, and that multiple models were more likely to be constructed with parallel presentation. It is proposed that, in general, multiple model construction will be more frequent for deduction tasks where the cognitive load is relatively low. Hence, contrary to suggestions by Polk and Newell (1995), reasoning in this way appears to be prevalent and highly robust—where supported by task format—even where the use of this strategy is disadvantageous.

Understanding strategy selection

This paper explores several issues associated with explanations of why different people use different strategies for learning and inference tasks. It is suggested that although the concept of cognitive style is a useful starting point, it is unable to account for many findings in the literature, and that any model of strategy usage that confines itself to mechanisms governing strategy selection is incomplete. In addition, it is necessary to take account of strategy availability: Which strategies do people possess, and how do people discover new strategies? Several findings in the literature indicate that strategy discovery is related to general abilities. Specifically, those who are best able to execute a current strategy are those who are the most likely to identify new, more effective methods. It is suggested that many findings that support the notion of cognitive style can be reinterpreted in this light.

Objective versus subjective measures of Paris Metro map usability: Investigating traditional octolinear versus all-curves schematics

Schematic maps are an important component of assistance for navigating transport networks worldwide. By showing routes as simple straight lines, they reduce the cognitive load of journey planning, and by revealing the underlying structure of networks, they make their key features easier to identify and learn. However, although there are many suggestions for optimizing schematic maps so as to maximize these benefits, to date these have not been directly supported by published usability studies or psychological theory. In this paper, we suggest that there are circumstances in which conventional schematic maps fail to yield benefits, and we compare journey planning using the current official RATP Paris Metro map with an all-curves design which replaces straight lines and corners with gentle curves. Three separate usability studies with slightly different methodologies showed that the journey planning time for the all-curves map was better than the RATP version, with effect sizes ranging from 0.48 to 1.12. Subjective usability ratings were derived from questionnaires, and user preferences, but neither were correlated with objective usability measures. We conclude that (1) in terms of designing schematics, there is no evidence to suggest that any rule-set can be claimed to be a gold-standard, and it is important to match the design rules to the properties of the network, (2) in some circumstances, radical departures from traditional ideas can yield usability benefits, and (3) map usability appears to be distinct from map engagement, although the latter is undoubtedly important in encouraging people fully to make use of navigation aides.

Quantifier interpretation and syllogistic reasoning

Many researchers have suggested that premise interpretation errors can account, at least in part, for errors on categorical syllogisms. However, although it is possible to show that people make such errors in simple inference tasks, the evidence for them is far less clear when actual syllogisms are administered. Part of the problem is due to the lack of clear predictions for the solutions that would be expected when using modified quantifiers, assuming that correct inferences are made from them. This paper presents the expected solutions for Gricean, reversible, and reversible Gricean interpretations, and evaluates these using three datasets (two currently available, and one new). The evidence supported the adoption of reversible and reversible Gricean interpretations, but not Gricean interpretations on their own. These results suggest that the categorical syllogism task tends to induce different quantifier interpretations from those identified in simple inference tasks.

Belief bias and relational reasoning

When people evaluate categorical syllogisms, they tend to reject unbelievable conclusions and accept believable ones irrespective of their validity. Typically, this effect is particularly marked for invalid conclusions that are possible, but do not necessarily follow, given the premises. However, smaller believability effects can also be detected for other types of conclusion. Three experiments are reported here, in which an attempt was made to determine whether belief bias effects can manifest themselves on the relational inference task. Subjects evaluated the validity of conclusions such as William the Conqueror was king after the Pyramids were built (temporal task) or Manchester is north of Bournemouth (spatial task) with respect to their premises. All of the major findings for equivalent categorical syllogism tasks were replicated. However, the overall size of the main effect of believability appears to be related to task presentation, a phenomenon not previously identified for categorical syllogisms and which current theories of belief bias have difficulty explaining.

Drawing metro maps using bézier curves

The automatic layout of metro maps has been investigated quite intensely over the last few years. Previous work has focused on the octilinear drawing style where edges are drawn horizontally, vertically, or diagonally at 45°. Inspired by manually created curvy metro maps, we advocate the use of the curvilinear drawing style; we draw edges as Bezier curves. Since we forbid metro lines to bend (even in stations), the user of such a map can trace the metro lines easily. In order to create such drawings, we use the force-directed framework. Our method is the first that directly represents and operates on edges as curves.