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.     

The link between logic,mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain‐specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain‐general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief‐laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief‐neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real‐life referents) develops later than the ability to reason about belief‐inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8     

Saccadic eye movements as indicators of cognitive function in older adults

Older adults appear to have greater difficulty ignoring distractions during day-to-day activities than younger adults. To assess these effects of age, the ability of adults aged between 50 and 80 years to ignore distracting stimuli was measured using the antisaccade and oculomotor capture tasks. In the antisaccade task, observers are instructed to look away from a visual cue, whereas in the oculomotor capture task, observers are instructed to look toward a colored singleton in the presence of a concurrent onset distractor. Index scores of the Repeatable Battery for the Assessment of Neuropsychological Status (RBANS) were compared with capture errors, and with prosaccade errors on the antisaccade task. A higher percentage of capture errors were made on the oculomotor capture tasks by the older members of the cohort compared to the younger members. There was a weak relationship between the attention index and capture errors, but the visuospatial/constructional index was the strongest predictor of prosaccade error rate in the antisaccade task. The saccade reaction times (SRTs) of correct initial saccades in the oculomotor capture task were poorly correlated with age, and with the neurospsychological tests, but prosaccade SRTs in both tasks moderately correlated with antisaccade error rate. These results were interpreted in terms of a competitive integration (or race) model. Any variable that reduces the strength of the top-down neural signal to produce a voluntary saccade, or that increases saccade speed, will enhance the likelihood that a reflexive saccade to a stimulus with an abrupt onset will occur.     

Mechanisms of theory formation in young children

Research suggests that by the age of five, children have extensive causal knowledge, in the form of intuitive theories. The crucial question for developmental cognitive science is how young children are able to learn causal structure from evidence. Recently, researchers in computer science and statistics have developed representations (causal Bayes nets) and learning algorithms to infer causal structure from evidence. Here we explore evidence suggesting that infants and children have the prerequisites for making causal inferences consistent with causal Bayes net learning algorithms. Specifically, we look at infants and children's ability to learn from evidence in the form of conditional probabilities, interventions and combinations of the two.     

Children's understanding of the pretence–reality distinction: a review of current theory and evidence

This paper provides an update on the current status of theory and evidence relating to children's understanding of the pretence–reality distinction. The paper starts by highlighting the striking paradox between children's early competence in pretence and their experiences of pretence–reality confusions as late as middle childhood. This is followed by a detailed review of various theories that have been offered to explain this phenomenon. Specifically, theories attributing the paradoxical findings to methodological differences between studies are reviewed and dismissed before considering the transmigration and availability hypotheses ( Harris, Brown, Marriott, Whittall & Harmer, 1991 ; Johnson & Harris, 1994 ), the role of context and the child's emotional involvement in the pretence, and the pretence continuation account ( Golomb & Galasso, 1995 ). It is argued that none of these theories alone can explain pretence–reality confusions and that these are best explained in terms of the combined influences of cognitive availability, empirical evidence of reality, context, affect and individual differences. Further research is necessary to fully explore the nature, cause and developmental trajectory of individual differences in this domain.     

The Genetic Counseling Workplace—An Australasian Perspective. A National Study of Workplace Issues for Genetic Counselors and Associate Genetic Counselors

Genetic counseling in Australasia (Australia and New Zealand) has been recognized as a profession since the 1980s and has steadily expanded over the past 20 years. The demography of major cities with metropolitan sprawl and sparsely populated rural areas has led to the establishment of 3 types of genetics units: main units in cities, metropolitan outreach, and rural outreach units. A questionnaire was developed to obtain information about the needs, resources, and day-to-day operation of the genetic counselors. The questionnaire addressed the areas of resource availability, professional development, responsibility of genetic counselors in the clinical setting, and their involvement in promotion of the service and public education. Differences observed between the 3 settings in all of these areas included large clinical loads for metropolitan outreach counselors, varying responsibilities in the clinical setting, and a lack of support and resources for rural outreach counselors. Australasian Genetic counselors were found to have a significant interest in developing mechanisms for supervision and were keenly interested in maintaining credentials and professional role development. The results of this study allows genetic counselors themselves to have a better understanding of the roles of their colleagues in the different units; they can also be used by service providers in establishing and supporting genetic counselors, and identifying inequalities and deficiencies in the different practice areas.     

Habituation in high‐risk infants: reliability and patterns of responding

We examined both the reliability of infant‐controlled habituation and patterns of responding in a group of high‐risk infants (mean age 16 mos). Good test–retest reliability was found for mean, total, and baseline looking time for one of the stimuli. Classification of infants' pattern of performance yielded two groups: linear (57%) and non‐linear (29%) responders; 14% of cases could not be classified because of cross‐session inconsistencies in performance. Linear responders had shorter total looking times, fewer trials to criterion, and showed more habituation than non‐linear responders, thus validating the linear/non‐linear distinction. Our findings indicate that the infant‐controlled habituation task can be used reliably with infants who are at high risk for developmental disorders. Indeed, we provide evidence that this task is not only reliable, but may also provide meaningful distinctions between infants within the high‐risk population. Discussion focuses on the role of attention in distinguishing between short (linear) and long (non‐linear) lookers. Copyright © 2003 John Wiley & Sons, Ltd.