Mental representations in fraction comparison

In this study, we investigated the mental representations used in a fraction comparison task. Adults were asked to quickly and accurately pick the larger of two fractions presented on a computer screen and provide trial-by-trial reports of the types of strategies they used. We found that adults used a variety of strategies to compare fractions, ranging among just knowing the answer, using holistic knowledge of fractions to determine the answer, and using component-based procedures such as cross multiplication. Across all strategy types, regression analyses identified that reaction times were significantly predicted by numerical distance between fractions, indicating that the participants used a magnitude-based representation to compare the fraction magnitudes. In addition, a variant of the problem-size effect (e.g., Ashcraft, 1992) appeared, whereby reaction times were significantly predicted by the average cross product of the two fractions. This effect was primarily found for component-based strategies, indicating a role for strategy choice in the formation of mental representations of fractions.     

Movement Control in a Reciprocal Tapping Task

A cross-sectional approach was used to replicate and examine developmental flexibility in eye-hand relationships during alternate tapping performance. A group of 68 male subjects, 34 younger (mean 75.6 months) and 34 older (mean 128.9 months) practiced 12 5-sec trials of alternate tapping in one of three accuracy conditions. Trials 2 and 11 were filmed to determine the eye movement index (EMI), a fraction relating eye movements (numerator) to alternate taps (denominator). Fractional EMI values close to 1 were labelled discontinuity and values closer to 0 (1/N) continuity. Accuracy variation tested the flexibility of EMI. for developmental change, revealing that EMIs for older subjects were more continuous than for younger subjects at trial 11, but not at trial 2. Level of EMI was related to age and condition, while change in EMI due to practice was related to age. The data showed EMI strategy flexibility increased with age, and that faster tapping was afforded by less direct visual monitoring of the hand.     

Movement control in a reciprocal tapping task: a developmental study

A cross-sectional approach was used to replicate and examine developmental flexibility in eye-hand relationships during alternate tapping performance. A group of 68 male subjects, 34 younger (mean 75.6 months) and 34 older (mean 128.9 months) practiced 12 5-sec trials of alternate tapping in one of three accuracy conditions. Trials 2 and 11 were filmed to determine the eye movement index (EMI), a fraction relating eye movements (numerator) to alternate taps (denominator). Fractional EMI values close to 1 were labelled discontinuity and values closer to 0 (1/N) continuity. Accuracy variation tested the flexibility of EMI for developmental change, revealing that EMIs for older subjects were more continuous than for younger subjects at trial 11, but not at trial 2. Level of EMI was related to age and condition, while change in EMI due to practice was related to age. The data showed EMI strategy flexibility increased with age, and that faster tapping was afforded by less direct visual monitoring of the hand.     

小学生分数比较中的加工模式:基于反应时和口语报告的研究

选取北京和四川两地53名小学六年级学生分别完成同分子、同分母与异分子异分母三类分数比较任务,收集被试口语报告的策略作为直接证据,并以分数大小和分数距离对反应时的回归分析结果作为间接证据,共同探究被试在分数比较任务中的加工模式,结果发现,（1）在三类分数比较中,被试均采用成分加工模式而非整体加工模式;（2）口语报告的策略与反应时回归分析的结果并不完全吻合,从侧面证明了原有研究方法的不稳定性。     

Independent allocation of attention to eye and hand targets in coordinated eye-hand movements

When reaching for objects, people frequently look where they reach. This raises the question of whether the targets for the eye and hand in concurrent eye and hand movements are selected by a unitary attentional system or by independent mechanisms. We used the deployment of visual attention as an index of the selection of movement targets and asked observers to reach and look to either the same location or separate locations. Results show that during the preparation of coordinated movements, attention is allocated in parallel to the targets of a saccade and a reaching movement. Attentional allocations for the two movements interact synergistically when both are directed to a common goal. Delaying the eye movement delays the attentional shift to the saccade target while leaving attentional deployment to the reach target unaffected. Our findings demonstrate that attentional resources are allocated independently to the targets of eye and hand movements and suggest that the goals for these effectors are selected by separate attentional mechanisms.     

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.     

Reasoning strategies with rational numbers revealed by eye tracking

Recent research has begun to investigate the impact of different formats for rational numbers on the processes by which people make relational judgments about quantitative relations. DeWolf, Bassok, and Holyoak (Journal of Experimental Psychology: General, 144(1), 127–150, 2015) found that accuracy on a relation identification task was highest when fractions were presented with countable sets, whereas accuracy was relatively low for all conditions where decimals were presented. However, it is unclear what processing strategies underlie these disparities in accuracy. We report an experiment that used eye-tracking methods to externalize the strategies that are evoked by different types of rational numbers for different types of quantities (discrete vs. continuous). Results showed that eye-movement behavior during the task was jointly determined by image and number format. Discrete images elicited a counting strategy for both fractions and decimals, but this strategy led to higher accuracy only for fractions. Continuous images encouraged magnitude estimation and comparison, but to a greater degree for decimals than fractions. This strategy led to decreased accuracy for both number formats. By analyzing participants’ eye movements when they viewed a relational context and made decisions, we were able to obtain an externalized representation of the strategic choices evoked by different ontological types of entities and different types of rational numbers. Our findings using eye-tracking measures enable us to go beyond previous studies based on accuracy data alone, demonstrating that quantitative properties of images and the different formats for rational numbers jointly influence strategies that generate eye-movement behavior.     

Older and younger adults' strategies in approximate quantification

In two experiments, participants were asked to provide a quick and rough estimate of the number of items in collections of 4-79 items. In Experiment 1 verbal strategy reports and performance on each item were collected, and in Experiment 2 performance and eye movements were collected, while young and older participants were tested in strategy-instructed conditions. Results showed that: (a) participants used six different estimation strategies, (b) overall, young and older participants used the same set of strategies, but varied in how often they used each strategy, (c) older adults' strategy repertoire was smaller than young adults' (i.e., inter-individual differences in strategy repertoire), (d) strategy use, participants' performance, and eye movements varied as a function of numerosities and configurations of items, (e) in both the age groups, each strategy was associated with distinctive performance measures and eye movement patterns. These findings show that different processes are available for approximate quantification in both young and older adults and that aging is associated with strategic variations.     

On the Eye Movement Control of Changing Reading Direction for a Single Word: The Case of Reading Numerals in Urdu

Typically orthographies are consistent in terms of reading direction, i.e. from left-to-right or right-to-left. However, some are bidirectional, i.e., certain parts of the text, (such as numerals in Urdu), are read against the default reading direction. Such sudden changes in reading direction may challenge the reader in many ways, at the level of planning of saccadic eye movements, changing the direction of attention, word recognition processes and cognitive reading strategies. The present study attempts to understand how readers achieve such sudden changes in reading direction at the level of eye movements and conscious cognitive reading strategies. Urdu readers reported employing a two-stage strategy for reading numerals by first counting the number of digits during right-to-left fixations, and only then forming numeric representation during left-to-right fixations. Eye movement findings were aligned with this strategy usage, as long numerals were often read with deliberate forward-and-backward fixation sequences. In these sequences fixations preceding saccades to default reading direction were shorter than against it, suggesting that different cognitive processes such as counting and formation of numeric representation were involved in fixations preceding left- and right-directed saccades. Finally, the change against the default reading direction was preceded by highly inflated fixation duration, pinpointing the oculomotor, attentional and cognitive demands in executing sudden changes in reading direction.     

Eye movements of monkey observers viewing vocalizing conspecifics

Primates, including humans, communicate using facial expressions, vocalizations and often a combination of the two modalities. For humans, such bimodal integration is best exemplified by speech-reading - humans readily use facial cues to enhance speech comprehension, particularly in noisy environments. Studies of the eye movement patterns of human speech-readers have revealed, unexpectedly, that they predominantly fixate on the eye region of the face as opposed to the mouth. Here, we tested the evolutionary basis for such a behavioral strategy by examining the eye movements of rhesus monkeys observers as they viewed vocalizing conspecifics. Under a variety of listening conditions, we found that rhesus monkeys predominantly focused on the eye region versus the mouth and that fixations on the mouth were tightly correlated with the onset of mouth movements. These eye movement patterns of rhesus monkeys are strikingly similar to those reported for humans observing the visual components of speech. The data therefore suggest that the sensorimotor strategies underlying bimodal speech perception may have a homologous counterpart in a closely related primate ancestor.     

An eye fixation analysis of multialternative choice

Eye fixations were recorded while subjects chose their most preferred of six used cars. Fixation sequences of the form X-Y-X-... were used to identify pair comparisons. This assumption was validated by verbal protocols and by a comparison between X-Y-X and X-Y-X-Y-... patterns. The results of three experiments showed: (1) that the multialternative choice process was composed primarily of pair comparisons; (2) that evaluative processing took placeonly during these comparisons; (3) that strategies for selecting the pairs were based primarily on information processing convenience; (4) that the sequence of pair comparisons was not used by the subjects as a sequential elimination process; and (5)that subjects changed their strategies to adapt to different task environments. These results have implications for current choice models and for the use of eye fixations in other complex tasks.     

儿童自我延迟满足的视觉认知

采用眼动研究方法,以儿童的延迟等待时间及眼动特征为指标,通过两个实验考察儿童在自我延迟满足情境中的注意分配策略及自我延迟满足能力发展的年龄特点。实验结果表明：偏爱策略能促进学前儿童的自我延迟满足;小学1、2年级儿童的自我延迟满足能力显著高于学前儿童;延迟奖励物的彩色照片比黑白照片更有利于儿童的延迟等待;眼动方法是延迟满足研究的有效方法     

Adaptive processing of fractions — Evidence from eye-tracking

Recent evidence indicated that fraction pair type determined whether a particular fraction is processed holistically, componentially or in a hybrid manner. Going beyond previous studies, we investigated how participants adapt their processing of fractions not only to fraction type, but also to experimental context. To examine adaptation in fraction processing, we recorded participants' eye-fixation behaviour in a fraction magnitude comparison task.     

Waldo reveals cultural differences in return fixations

ABSTRACT

Humans routinely perform visual search towards targets to adapt to the environment. These sequences of ballistic eye movements are shaped by a combination of top–down and bottom–up factors. Recent research documented that human observers display cultural-specific fixation patterns in a range of visual processing tasks. In particular, eye movement strategies extracting information from faces clearly differs between Western Caucasian (WC) and East Asian (EA) observers. However, whether such cultural differences are also present for visual scene processing remains debated. To this aim, we recorded the eye movements of WC and EA observers while they were solving visual search problems parametrically varying in difficulty: Where’s Waldo. Both groups had a comparable familiarity with the Waldo books reaching a comparable level of accuracy in target detection. Both cultural groups also showed a comparable temporal effect on inhibition of return, with longer fixation durations when saccades were performed to a return location compared to other locations. Westerners, however, located Waldo faster than Easterners. Interestingly, this modulation of speed was likely related to differences occurring on the low-level mechanisms of spatial inhibition of return, with EA observers returning more often to previously visited locations than the WC observers. This suboptimal eye movement strategy in the Easterners might be engendered by their cultural perceptual bias consisting in? a greater use of extra-foveal information. Overall, our data point towards the existence of a subtle, but significant difference in the processing of visual scenes across observers from different cultures during active visual search.     

Learning to like it: Aesthetic perception of bodies,movements and choreographic structure

Appreciating human movement can be a powerful aesthetic experience. We have used apparent biological motion to investigate the aesthetic effects of three levels of movement representation: body postures, movement transitions and choreographic structure. Symmetrical (ABCDCBA) and asymmetrical (ABCDBCA) sequences of apparent movement were created from static postures, and were presented in an artificial grammar learning paradigm. Additionally, “good” continuation of apparent movements was manipulated by changing the number of movement path reversals within a sequence. In an initial exposure phase, one group of participants saw only symmetrical sequences, while another group saw only asymmetrical sequences. In a subsequent test phase, both groups rated all sequences on an aesthetic evaluation scale. We found that posture, movement, and choreographic structure all influenced aesthetic ratings. Separate ratings for the static body postures presented individually showed that both groups preferred a posture that maximized spatial symmetry. Ratings for the experimental sequences showed that both groups gave higher ratings to symmetrical sequences with “good” continuation and lower ratings to sequences with many path reversals. Further, participants who had been initially familiarized with asymmetrical sequences showed increased liking for asymmetrical sequences, suggesting a structural mere exposure effect. Aesthetic preferences thus depend on body postures, apparent movement continuation and choreographic structure. We propose a hierarchical model of aesthetic perception of human movement with distinct processing levels for body postures, movements and choreographic structure.     

Saccades predict and synchronize to visual rhythms irrespective of musical beats

ABSTRACT

Music has been shown to entrain movement. One of the body’s most frequent movements, saccades, are arguably subject to a timer that may also be susceptible to musical entrainment. We developed a continuous and highly-controlled visual search task and varied the timing of the search target presentation, it was either gaze-contingent, tap-contingent, or visually-timed. We found: (1) explicit control of saccadic timing is limited to gross duration variations and imprecisely synchronized; (2) saccadic timing does not implicitly entrain to musical beats, even when closely aligned in phase; (3) eye movements predict visual onsets produced by motor-movements (finger-taps) and externally-timed sequences, beginning fixation prior to visual onset; (4) eye movement timing can be rhythmic, synchronizing to both motor-produced and externally timed visual sequences; each unaffected by musical beats. These results provide evidence that saccadic timing is sensitive to the temporal demands of visual tasks and impervious to influence from musical beats.     

Intrinsic and extrinsic contributions to heavy tails in visual foraging

Eyes move over visual scenes to gather visual information. Studies have found heavy-tailed distributions in measures of eye movements during visual search, which raises questions about whether these distributions are pervasive to eye movements, and whether they arise from intrinsic or extrinsic factors. Three different measures of eye movement trajectories were examined during visual foraging of complex images, and all three were found to exhibit heavy tails: Spatial clustering of eye movements followed a power law distribution, saccade length distributions were lognormally distributed, and the speeds of slow, small amplitude movements occurring during fixations followed a 1/f spectral power law relation. Images were varied to test whether the spatial clustering of visual scene information is responsible for heavy tails in eye movements. Spatial clustering of eye movements and saccade length distributions were found to vary with image type and task demands, but no such effects were found for eye movement speeds during fixations. Results showed that heavy-tailed distributions are general and intrinsic to visual foraging, but some of them become aligned with visual stimuli when required by task demands. The potentially adaptive value of heavy-tailed distributions in visual foraging is discussed.     

Attention in risky choice

Previous research on the processes involved in risky decisions has rarely linked process data to choice directly. We used a simple measure based on the relative amount of attentional deployment to different components (gains/losses and their probabilities) of a risky gamble during the choice process, and we related this measure to the actual choice. In an experiment we recorded the decisions, decision times, and eye movements of 80 participants who made decisions on 11 choice problems. We used the number of eye fixations and fixation transitions to trace the deployment of attention during the choice process and obtained the following main results. First, different components of a gamble attracted different amounts of attention depending on participants' actual choice. This was reflected in both the number of fixations and the fixation transitions. Second, the last-fixated gamble but not the last-fixated reason predicted participants' choices. Third, a comparison of data obtained with eye tracking and data obtained with verbal protocols from a previous study showed a large degree of convergence regarding the process of risky choice. Together these findings tend to support dimensional decision strategies such as the priority heuristic.     

Memory representations guide targeting eye movements in a natural task

The change blindness phenomenon suggests that visual representations retained across saccades are very limited. In this paper we sought to specify the kind of information that is in fact retained. We investigated targeting performance for saccadic eye movements, since one need for visual representations across eye and body positions may be to guide coordinated movements. We examined saccades in the context of an ongoing sensory motor task in order to make stronger generalizations about natural visual functioning and deployment of attention. Human subjects copied random patterns of coloured blocks on a computer display. Their eye movement pattern was consistent from block to block, including a precise saccade to a previously-placed, neighbouring block during each additional block placement. This natural, consistent eye movement allowed the previously-placed, neighbouring block to serve as an implicit target without instructions to the subject. On random trials, we removed the target object from the display during a preceding saccade, so that observers were required to make the targeting saccade without a currently visible target. Targeting performance was excellent, and appeared to be influenced by spatial information that was not visible during the preceding fixation. Subjects were generally unaware of the disappearance and reappearance of the target. We conclude that spatial information about visual targets is retained across eye movements and used to guide subsequent movements.     

Influences of grasp selection in typically developing children

When reaching towards an object, adults favour grasps which, following the intended action, end in a comfortable position even when this requires them to start in an uncomfortable position (the end-state-comfort effect). However, this strategy is not consistently used by children who instead seem to favour a minimal pre-contact rotation of the hand, even when this results in an uncomfortable end position. In terms of multiple movements, the strategies used for grip selection are unclear; adults may still grasp for end-state-comfort given their propensity to plan to the end of a movement; however, children who are less able to concatenate movement may tend to start-state-comfort movements. The current study considered grip selection in children ranging from 4 to 12 years and in a group of adults. Participants were asked to rotate a disc so that an arrow pointed towards a specific target(s), the number of sequences in a movement was increased from one to three. Planning for end-state-comfort was seen in all participants and a clear developmental trajectory was identified whereby the relative comfort of an end position could be directly predicted by age in months. Adults and 10–12-year-olds favoured an end-state-comfort strategy whereas the younger children gave equal weighting to end-state-comfort, start-state-comfort and no initial rotation strategies. All groups were able to end a movement comfortably when it was composed of three steps; however, the proportion of movements relying on an end-state-comfort strategy decreased as sequence length increase whereas the proportion of start-state-comfort and no initial rotation strategies increased. The current data support the concept that a mechanism for planning grasps may be based on motor experience.