Eye gaze patterns reveal how we reason about fractions

ABSTRACT

Fractions are defined by numerical relationships, and comparing two fractions’ magnitudes requires within-fraction (holistic) and/or between-fraction (componential) relational comparisons. To better understand how individuals spontaneously reason about fractions, we collected eye-tracking data while they performed a fraction comparison task with conditions that promoted or obstructed different types of comparisons. We found evidence for both componential and holistic processing in this mixed-pairs task, consistent with the hybrid theory of fraction representation. Additionally, making within-fraction eye movements on trials that promoted a between-fraction comparison strategy was associated with slower responses. Finally, participants who performed better on a non-numerical test of reasoning took longer to respond to the most difficult fraction trials, which suggests that those who had greater facility with non-numerical reasoning attended more to numerical relationships. These findings extend prior research and support the continued investigation into the mechanistic links between numerical and non-numerical reasoning.     

Collective Reasoning and the Discursive Dilemma

Abstract

The paper begins with a discussion of Philip Pettit's distinction between individualistic and collectivistic reasoning strategies. I argue that many of his examples, when correctly analysed, do not give rise to what he calls the discursive dilemma. I argue for a collectivistic strategy, which is a holistic premise-driven strategy. I will concentrate on three aspects of collective reasoning, which I call the publicity aspect, the collective acceptance aspect, and the historical constraint aspect: First, the premises of collective reasoning, unlike the premises of a private individual, have to be public in some sense. Second, the group members collectively accept the public premises, and thereby commit themselves to following them in their collective practical reasoning.Third, a person need not be consistent with his earlier private judgements, he is free to change his mind, but prior collective judgements, if not collectively abandoned, constrain the member's future judgements and decisions. I conclude that collective practical reasoning can be accounted for without collectivist ontological commitments.     

A severe capacity limit in the consolidation of orientation information into visual short-term memory

Previous research has suggested that two color patches can be consolidated into visual short-term memory (VSTM) via an unlimited parallel process. Here we examined whether the same unlimited-capacity parallel process occurs for two oriented grating patches. Participants viewed two gratings that were presented briefly and masked. In blocks of trials, the gratings were presented either simultaneously or sequentially. In Experiments 1 and 2, the presentation of the stimuli was followed by a location cue that indicated the grating on which to base one’s response. In Experiment 1, participants responded whether the target grating was oriented clockwise or counterclockwise with respect to vertical. In Experiment 2, participants indicated whether the target grating was oriented along one of the cardinal directions (vertical or horizontal) or was obliquely oriented. Finally, in Experiment 3, the location cue was replaced with a third grating that appeared at fixation, and participants indicated whether either of the two test gratings matched this probe. Despite the fact that these responses required fairly coarse coding of the orientation information, across all methods of responding we found superior performance for sequential over simultaneous presentations. These findings suggest that the consolidation of oriented gratings into VSTM is severely limited in capacity and differs from the consolidation of color information.     

Confidence and accuracy of near-threshold discrimination responses.

This article reports four subliminal perception experiments using the relationship between confidence and accuracy to assess awareness. Subjects discriminated among stimuli and indicated their confidence in each discrimination response. Subjects were classified as being aware of the stimuli if their confidence judgments predicted accuracy and as being unaware if they did not. In the first experiment, confidence predicted accuracy even at stimulus durations so brief that subjects claimed to be performing at chance. This finding indicates that subjects's claims that they are "just guessing" should not be accepted as sufficient evidence that they are completely unaware of the stimuli. Experiments 2-4 tested directly for subliminal perception by comparing the minimum exposure duration needed for better than chance discrimination performance against the minimum needed for confidence to predict accuracy. The latter durations were slightly but significantly longer, suggesting that under certain circumstances people can make perceptual discriminations even though the information that was used to make those discriminations is not consciously available.     

A longitudinal examination of a three‐letter holland code

The author investigated the degree of change in a single client's 3‐letter Holland code (J. L. Holland, 1985) over a 10‐year period. Results seem to support Holland's theory that personality traits remain relatively stable over time.     

Relations Among and Between Career Values and Christian Religious Values

Empirical research and vocational theory indicate that values are important in career counseling and vocational choice. Development of these values is influenced by environmental factors, such as religion. However, there are few empirical investigations of the relation between religious values and career values. The purpose of this study was to investigate the relationship of career values to Christian religious values as they might be assessed in career counseling. Results indicate that there was some overlap between religious and career values, although only for specific extrinsic values.     

Chronic psychological stress and the regulation of pro-inflammatory cytokines: a glucocorticoid-resistance model.

This study examined whether chronic stress impairs the immune system's capacity to respond to hormonal signals that terminate inflammation. Fifty healthy adults were studied; half were parents of cancer patients, and half were parents of healthy children. Parents of cancer patients reported more psychological distress than parents of healthy children. They also had flatter diurnal slopes of cortisol secretion, primarily because of reduced output during the morning hours. There was also evidence that chronic stress impaired the immune system's response to anti-inflammatory signals: The capacity of a synthetic glucocorticoid hormone to suppress in vitro production of the pro-inflammatory cytokine interleukin-6 was diminished among parents of cancer patients. Findings suggest a novel pathway by which chronic stress might alter the course of inflammatory disease.     

Staff survey results and characteristics that predict assault and injury to personnel working in mental health facilities

The purpose of this study was to complete a mental health staff opinion survey to identify patient and staff characteristics associated with staff assault and injury in psychiatric treatment settings and to develop a model of prediction for staff assault and injury utilizing these survey variables. The data consisted of opinion surveys sent to staff of 15 child, adolescent, and adult psychiatry inpatient units in the United States. Multivariate logistic regression was used to determine the level of assault and staff‐reported injury prediction that could be obtained from the staff‐completed opinion survey. Responses indicated a high prevalence of reported aggression, with 62.3% of staff endorsing verbal and physical aggression, property destruction, and self‐injurious behavior as being prevalent at their site, whereas only 4.1% rated none of these as prevalent. Staff working with children and adolescents in settings with high rates of psychiatric diagnoses reported increased frequency of assault and injury compared with those working with adults. Younger, less experienced staff reported higher rates of assault and injury. Staff working with female patients reported similar rates of assault and injury to those working with males. A logistic regression analysis using staff‐reported survey results of both staff and patient characteristics predicted assault correctly 73.7% of the time and injury 66.1% of the time. Resources for violence prevention and staff training programs in violence prevention are needed in child and adolescent psychiatry wards. Results are consistent with theories emphasizing the importance of negative emotions and affects, impulsivity, and frustration in goal‐directed activities in human aggression. Aggr. Behav. 29:31–40, 2003. © 2003 Wiley‐Liss, Inc.