Sources of difficulty in deductive reasoning: The THOG task

The THOG task presents four designs constructed from two shapes and two colours. Subjects are told that the experimenter has written down one of the shapes and one of the colours and are provided the rule that if, and only if, any design has either the shape or the colour, but not both, written down, then it is a THOG. Finally, they are given an exemplar and are asked to classify the remaining designs. Successful solution requires construction of hypotheses, reasoning under each hypothesis, and comparison of the results under each to reach a final conclusion. Few subjects are able to provide adequate responses on the standard version of the task. We present the results of four experiments, with 160 undergraduates each presented with one of eight versions of the task. Experiments 1 and 2 indicate that (1) some subjects think that the properties that are written down are identical to those of the exemplar, although these are not the same subjects who exhibit the modal error pattern, (2) many subjects correctly understand the disjunction of the rule but fail to consider the hypotheses, and (3) poor initial encoding of the problem is not easily corrected. Experiment 3 investigates the sufficiency of the claim of Griggs and Newstead (1982) that appropriate problem solution follows from explicit presentation of all problem information (including use of positive labels for properties that are not written down), and Experiment 4 investigates the necessity of the claim. The results of Experiments 3 and 4 show that presenting positive category labels does increase the frequency of correct solution; however, positive category labels are not necessary for such improvement. Separation of the labels of the THOG rule from those of the exemplar, or informing subjects that only one other design is a THOG, also increases the frequency of successful solution. The results suggest that many people have some fairly sophisticated reasoning skills. but application of these skills is easily discouraged when the features of the task lead to poor initial encoding.     

Grasping a better understanding of the intrinsic dynamics of rhythmical and discrete prehension

In this study, the authors examined the influence of the intrinsic dynamics of discrete and rhythmical prehension. Six adults underwent a scaling procedure in which the movement time was systematically increased so that it corresponded with 6 frequencies: 0.5, 0.75, 1.0, 1.25, 1.5, and 1.75 Hz. In posttests, participants moved at their own preferred pace. No differences were found in the relative time to final hand closure (T[rfc]) between the rhythmical and discrete conditions. The variability of T[rfc] was shown to be less at the preferred step of scaling than during the posttest. With the scaling technique, one can guide participants into more stable movement patterns than they can achieve when the metronome is not present, because, when the metronome is present, their movements become anchored to the external pacing cue. Those findings provide support for the use of a scaling technique to identify the influence of the intrinsic dynamics during rhythmical and discrete movements.     

Differences in judgments of learning difficulty

Academically successful and less successful fifth graders were asked to make judgments about the ease of understanding and remembering various sentences and were given the opportunity to attempt to remember some of them before being asked to judge new sets of sentences. The results of the first experiment indicate that, at the beginning of the experiment, the successful students were much more likely than their less successful peers to realize that sentences expressing arbitrary relationships were more difficult to remember. These differences became even greater after students were given the opportunity to attempt to remember some of the sentences they had judged initially. The memory performance of the successful students also improved as they became more familiar with the experimental task, but the performance of the less successful students did not. The results of the second experiment showed that less successful students who had received appropriate training were able to use information about the arbitrariness of relationships as the basis for their judgments of learning difficulty. The training also facilitated their ability to remember. Implications of these findings are discussed.     

Motivation and flow: toward an understanding of the dynamics of the relation in architecture students

The authors investigated the relation between motivation and flow in a sample of 327 architecture students. Specifically, they investigated the relation between flow and several levels of intrinsic and extrinsic motivation, as well as amotivation. They also assessed the need for autonomy in moderating the relation between intrinsic motivation and engagement. Results indicated a significant relation between flow experiences in academic activities and the more self-determined forms of intrinsic motivation, but not for extrinsic motivation. The need for autonomy moderated the relation between flow and intrinsic motivation. These results are discussed in the context of understanding flow as an intrinsically motivating state and a viable construct for understanding engagement.     

The dynamics of search,impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem

The nine-dot problem is often used to demonstrate and explain mental impasse, creativity, and out of the box thinking. The present study investigated the interplay of a restricted initial search space, the likelihood of invoking a representational change, and the subsequent constraining of an unrestricted search space. In three experimental conditions, participants worked on different versions of the nine-dot problem that hinted at removing particular sources of difficulty from the standard problem. The hints were incremental such that the first suggested a possible route for a solution attempt; the second additionally indicated the dot at which lines meet on the solution path; and the final condition also provided non-dot locations that appear in the solution path. The results showed that in the experimental conditions, representational change is encountered more quickly and problems are solved more often than for the control group. We propose a cognitive model that focuses on general problem-solving heuristics and representational change to explain problem difficulty.     

Analysis of distractor difficulty in multiple-choice items

Two psychometric models are presented for evaluating the difficulty of the distractors in multiple-choice items. They are based on the criterion of rising distractor selection ratios, which facilitates interpretation of the subject and item parameters. Statistical inferential tools are developed in a Bayesian framework: modal a posteriori estimation by application of an EM algorithm and model evaluation by monitoring posterior predictive replications of the data matrix. An educational example with real data is included to exemplify the application of the models and compare them with the nominal categories model.This research was supported by the DGI grant BSO2002-01485.I would like to thank Eric Maris and Vicente Ponsoda for their advice, Juan Botella for providing the data for the empirical application, and three anonymous reviewers for their comments that were essential for improving the quality of the paper.     

Fragment difficulty in priming on word-completion tests

Word-fragment completion is a frequently used test in implicit memory research. In this test priming is the relevant variable. Priming is obtained by subtracting the proportion of nonstudied word fragments correctly completed (called "completion difficulty baseline") from the studied word fragments correctly completed. Since completion difficulty can spuriously vary greatly between experimental conditions, its effect on magnitude of priming is studied. Normative frequency of occurrence of target words was considered because their influence over performance is known. In an experiment using a word-fragment completion test, participants' completion of fragments at three levels of completion difficulty and two levels of frequency was tested. Analysis showed that completion difficulty had a significant effect on global priming. The priming magnitude was higher for Difficult and Moderately Difficult fragments than for Easy ones. An interaction between fragment difficulty and normative word frequency was observed. When the fragments were easy to complete, the expected effect of higher priming for low-frequency words than for high-frequency words was not observed.     

Intralingual and interlingual factors in language-learning difficulty

A distinction between behavioral and linguistic measures of difficulty in language learning is made explicit. It is argued that behavioral measures must be regarded as primary and linguistic measures as secondary, the latter being only a component of the former. An evaluation of the evidence leads to the following conclusions: (a) No unequivocal answer can be given to the question of whether some languages are intrinsically more difficult to learn than others; (b) second-language learning is more difficult than first-language learning, to the extent that native-speaker competence is a very difficult goal to achieve by adult second-language learners; and (c) interlingual distance is a determinant of difficulty but simple, linear relations between them or between linguistic and behavioral measures of difficulty can hardly be expected.Preparation for this article was supported by the Committee on Research and Conference Grants, University of Hong Kong.     

The psychophysics of mental test difficulty

By the use of the Seashore tests of Pitch Discrimination, Intensity Discrimination, Time Discrimination, and the test of Tonal Memory, it is shown that the easiness of an item, as determined by absolute scaling methods, is proportional to the logarithm of the magnitude of the stimulus. It is proposed that this is a case of Fechner's psychophysical law and that the unit of absolute scaling as applied to test items may become a satisfactory unit of allS-scales in the more traditional psychophysical problem.     

Agents necessitating effects in newtonian time and space: from power and opportunity to effectivity

Synthese - We extend stit logic by adding a spatial dimension. This enables us to distinguish between powers and opportunities of agents. Powers are agent-specific and do not depend on an...     

The intrinsic difficulty of recursive functions

This paper deals with a philosophical question that arises within the theory of computational complexity: how to understand the notion of INTRINSIC complexity or difficulty, as opposed to notions of difficulty that depend on the particular computational model used. The paper uses ideas from Blum's abstract approach to complexity theory to develop an extensional approach to this question. Among other things, it shows how such an approach gives detailed confirmation of the view that subrecursive hierarchies tend to rank functions in terms of their intrinsic, and not just their model-dependent, difficulty, and it shows how the approach allows us to model the idea that intrinsic difficulty is a fuzzy concept. Jan Zygmunt     

The factorial interpretation of test difficulty

This paper discusses the influence of test difficulty on the correlation between test items and between tests. The greater the difference in difficulty between two test items or between two tests the smaller the maximum correlation between them. In general, the greater the number of degrees of difficulty among the items in a test or among the tests in a battery, the higher the rank of the matrix of intercorrelations; that is, differences in difficulty are represented in the factorial configuration as additional factors. The suggestion is made that if all tests included in a battery are roughly homogeneous with respect to difficulty existing hierarchies will be more clearly defined and meaningful psychological interpretation of factors more readily attained.     

Qualitative and quantitative considerations in encoding difficulty effects

We hypothesized that the effects of encoding difficulty on the memorability of verbal material would depend on both the type of processing induced by the difficulty manipulation and the type of processing afforded by the material. We predicted that if the processing induced by encoding difficulty were complementary to the processing afforded by the material, then difficulty would enhance recall more so than if the processing induced by the two sources were redundant. These expectations were tested by requiring subjects to process either a structured or an unstructured word list with either a sorting task or a pleasantness rating task; the difficulty of each orienting task was also manipulated. We assumed that sorting and pleasantness rating required primarily relational and individual-item processing, respectively, and that the structured and unstructured word lists afforded relational and individual-item processing, respectively. These assumptions were supported by clustering in free recall and by recognition performance. The primary finding was that difficult sorting increased recall only for the unrelated list, whereas difficult pleasantness judgments increased recall most robustly for the related list. These results support the present framework and help illuminate the boundary conditions of the “difficulty effect.”     

Phonetic recoding and reading difficulty in beginning readers

The results of a recent study (Liberman, Shankweiler, Liberman, Fowler, & Fischer, 1977) suggest that good beginning readers are more affected than poor readers by the phonetic characteristics of visually presented items in a recall task. The good readers made significantly more recall errors on strings of letters with rhyming letter names than on nonrhyming sequences; in contrast, the poor readers made roughly equal numbers of errors on the rhyming and nonrhyming letter strings. The purpose of the present study was to determine whether the interaction between reading ability and phonetic similarity is solely determined by different rehearsal strategies of the two groups. Accordingly, good and poor readers were tested on rhyming and nonrhyming words using a recognition memory paradigm that minimized the opportunity for rehearsal. Performance of the good readers was more affected by phonetic similarity than that of the poor readers, in agreement with the earlier study. The present findings support the hypothesis that good and poor readers do differ in their ability to access a phonetic representation.     

Attention capacity and task difficulty in visual search

When a visual search task is very difficult (as when a small feature difference defines the target), even detection of a unique element may be substantially slowed by increases in display set size. This has been attributed to the influence of attentional capacity limits. We examined the influence of attentional capacity limits on three kinds of search task: difficult feature search (with a subtle featural difference), difficult conjunction search, and spatial-configuration search. In all 3 tasks, each trial contained sixteen items, divided into two eight-item sets. The two sets were presented either successively or simultaneously. Comparison of accuracy in successive versus simultaneous presentations revealed that attentional capacity limitations are present only in the case of spatial-configuration search. While the other two types of task were inefficient (as reflected in steep search slopes), no capacity limitations were evident. We conclude that the difficulty of a visual search task affects search efficiency but does not necessarily introduce attentional capacity limits.