The added value of eye-tracking in diagnosing dyscalculia: a case study

Twenty-four or four-and-twenty: Language modulates cross-modal matching for multidigit numbers in children and adults

Does number-word structure have a long-lasting impact on transcoding? Contrary to English, German number words comprise decade-unit inversion (e.g., vierundzwanzig is literally translated as four-and-twenty). To investigate the mental representation of numbers, we tested the effect of visual and linguistic-morphological characteristics on the development of verbal-visual transcoding. In a longitudinal cross-linguistic design, response times (RTs) in a number-matching experiment were analyzed in Grade 2 (119 German-speaking and 179 English-speaking children) and in Grade 3 (131 German-speaking and 160 English-speaking children). To test for long-term effects, the same experiment was given to 38 German-speaking and 42 English-speaking adults. Participants needed to decide whether a spoken number matched a subsequent visual Arabic number. Systematic variation of digits in the nonmatching distractors allowed comparison of three different transcoding accounts (lexicalization, visual, and linguistic-morphological). German speakers were generally slower in rejecting inverted number distractors than English speakers. Across age groups, German speakers were more distracted by Arabic numbers that included the correct unit digit, whereas English speakers showed stronger distraction when the correct decade digit was included. These RT patterns reflect differences in number-word morphology. The individual cost of rejecting an inverted distractor (inversion effect) predicted arithmetic skills in German-speaking second-graders only. The moderate relationship between the efficiency to identify a matching number and arithmetic performance could be observed cross-linguistically in all age groups but was not significant in German-speaking adults. Thus, findings provide consistent evidence of a persistent impact of number-word structure on number processing, whereas the relationship with arithmetic performance was particularly pronounced in young children.

Numerical Estimation and Mathematical Learning Methodology in Preschoolers

One of the means for representing quantities/magnitudes is the mental number line. It is still a nonsolved question as to whether the method of learning mathematics in the early years could improve this type of estimating. A total of 233 students, aged four and five years, who learned mathematics with a new method called Open Algorithm Based on Number or the more traditional Closed Based on Ciphers approach, were evaluated with a reliable estimation on the number line test. Results revealed significant differences in participants' estimation functions based on the learning method used. Students who learned mathematics through the Open Algorithm Based on Number method used a linear representation more efficiently than those who were taught with the Closed Based on Ciphers methodology. This group exhibited a logarithmic function in their approach. We discussed whether these differences can be attributed to a recurrent practice in estimation tasks at school, characterized by the Open Algorithm Based on Number methodology.

Specific learning disability in mathematics: a comprehensive review

Math skills are necessary for success in the childhood educational and future adult work environment. This article reviews the changing terminology for specific learning disabilities (SLD) in math and describes the emerging genetics and neuroimaging studies that relate to individuals with math disability (MD). It is important to maintain a developmental perspective on MD, as presentation changes with age, instruction, and the different models (educational and medical) of identification. Intervention requires a systematic approach to screening and remediation that has evolved with more evidence-based literature. Newer directions in behavioral, educational and novel interventions are described.

Benchmark-based strategies in whole number line estimation

In this study, we used verbal protocols to identify whether adults spontaneously apply quartile-based strategies or whether they need additional external support to use these strategies when solving a 0-1,000 number line estimation (NLE) task. Participants were assigned to one of three conditions based on the number of external benchmarks provided on the number line. In the bounded condition only the origin and endpoint were indicated, the mid-point condition included an additional external benchmark at 50%, and in the quartile condition three additional external benchmarks at 25%, 50%, and 75% were specified. Firstly, participants in the bounded condition reported to spontaneously apply quartile-based strategies to calibrate their estimates. Moreover, participants frequently relied on the external benchmarks for creating internal benchmarks at the mid-point, quartiles, and even octiles of the number line. Secondly, overall estimation accuracy improved as the number of external benchmarks increased, and target numbers close to external benchmarks were estimated more accurately and with less variability. Thirdly, the use of a larger variety in benchmark-based strategies was positively related to NLE accuracy. In summary, this study provides evidence that the NLE task induces more sophisticated strategy use in participants than initially anticipated.

The visual number world: A dynamic approach to study the mathematical mind

In the domain of language research, the simultaneous presentation of a visual scene and its auditory description (i.e., the visual world paradigm) has been used to reveal the timing of mental mechanisms. Here we apply this rationale to the domain of numerical cognition in order to explore the differences between fast and slow arithmetic performance, and to further study the role of spatial-numerical associations during mental arithmetic. We presented 30 healthy adults simultaneously with visual displays containing four numbers and with auditory addition and subtraction problems. Analysis of eye movements revealed that participants look spontaneously at the numbers they currently process (operands, solution). Faster performance was characterized by shorter latencies prior to fixating the relevant numbers and fewer revisits to the first operand while computing the solution. These signatures of superior task performance were more pronounced for addition and visual numbers arranged in ascending order, and for subtraction and numbers arranged in descending order (compared to the opposite pairings). Our results show that the "visual number world"-paradigm provides on-line access to the mind during mental arithmetic, is able to capture variability in arithmetic performance, and is sensitive to visual layout manipulations that are otherwise not reflected in response time measurements.

Numerical abilities of school-age children with Developmental Coordination Disorder (DCD): A behavioral and eye-tracking study

Developmental Coordination Disorder (DCD) is a disorder of motor coordination which interferes with academic achievement. Difficulties in mathematics have been reported. Performance in the number line task is very sensitive to atypical development of numerical cognition. We used a position-to-number task in which twenty 7-to-10years old children with DCD and 20 age-matched typically developing (TD) children had to estimate the number that corresponded to a hatch mark placed on a 0-100 number line. Eye movements were recorded. Children with DCD were less accurate and slower to respond than their peers. However, they were able to map numbers onto space linearly and used anchoring strategies as control. We suggest that the shift to a linear trend reflects the ability of DCD children to use efficient strategies to solve the task despite a possibly more imprecise underlying numerical acuity.

Eye Movement Patterns Characteristic of Cognitive Style

Various tools have been designed to classify the wholistic/analytic cognitive style, based mostly on behavioral data that reveals little about how these processes function. The main goal of this study is to characterize patterns of eye movements (EM) that are typical of learners with tendencies toward wholistic/analytic styles. Forty students completed the E-CSA-W/A test, while their EM were simultaneously monitored. The results revealed that the overall response time of the wholist group was lower in both tasks. The differences in response time between the groups are interpreted as being influenced by impulsive/reflective styles. While the behavioral data provide us with the end result and quantitative differences between the groups, EM provide us with the qualitative information about the process that led to the response. The study showed that the wholist group is characterized by less fixations and transitions than the analytic group, which is interpreted as reflecting use of whole/partial strategy.

Numbers in the eye of the beholder: What do eye movements reveal about numerical cognition?

The eyes, often called the window to our minds, reveal the focus of spatial attention and are therefore a powerful research tool for the study of spatial processing and spatially related higher cognitive functions. The aim of this paper is to highlight the potential of eye movement analysis in the domain of numerical cognition, to review several relevant findings, and to provide an outlook for future research.

Number line estimation strategies in children with mathematical learning difficulties measured by eye tracking

Introduction

Number line estimation is one of the skills related to mathematical performance. Previous research has shown that eye tracking can be used to identify differences in the estimation strategies children with dyscalculia and children with typical mathematical development use on number line estimation tasks. The current study extends these findings to a larger group of children with mathematical learning disabilities (MLD).

Method

A group of 9–11-year-old children with MLD (N = 14) was compared to a control group of children without math difficulties (N = 14). Number line estimation was measured using a 0–100 and a 0–1000 number-to-position task. A Tobii T60 eye tracker was used to measure the children’s eye movements during task performance.

Results

The behavioral data showed that the children with MLD had higher error scores on both number lines than the children in the control group. The eye tracking data showed that the groups also differed in their estimation strategies. The children with MLD showed less adaptation of their estimation strategies to the number to be estimated.

Conclusion

This study shows that children with MLD attend to different features of the number line than children without math difficulties. Children with math difficulties are less capable of adapting their estimation strategies to the numbers to be estimated and of effectively using reference points on the number line.

Electronic supplementary material

The online version of this article (doi:10.1007/s00426-015-0736-z) contains supplementary material, which is available to authorized users.

Blur, eye movements and performance on a driving visual recognition slide test

PURPOSE

Optical blur and ageing are known to affect driving performance but their effects on drivers' eye movements are poorly understood. This study examined the effects of optical blur and age on eye movement patterns and performance on the DriveSafe slide recognition test which is purported to predict fitness to drive.

METHODS

Twenty young (27.1 ± 4.6 years) and 20 older (73.3 ± 5.7 years) visually normal drivers performed the DriveSafe under two visual conditions: best-corrected vision and with +2.00 DS blur. The DriveSafe is a Visual Recognition Slide Test that consists of brief presentations of static, real-world driving scenes containing different road users (pedestrians, bicycles and vehicles). Participants reported the types, relative positions and direction of travel of the road users in each image; the score was the number of correctly reported items (maximum score of 128). Eye movements were recorded while participants performed the DriveSafe test using a Tobii TX300 eye tracking system.

RESULTS

There was a significant main effect of blur on DriveSafe scores (best-corrected: 114.9 vs blur: 93.2; p < 0.001). There was also a significant age and blur interaction on the DriveSafe scores (p < 0.001) such that the young drivers were more negatively affected by blur than the older drivers (reductions of 22% and 13% respectively; p < 0.001): with best-corrected vision, the young drivers performed better than the older drivers (DriveSafe scores: 118.4 vs 111.5; p = 0.001), while with blur, the young drivers performed worse than the older drivers (88.6 vs 95.9; p = 0.009). For the eye movement patterns, blur significantly reduced the number of fixations on road users (best-corrected: 5.1 vs blur: 4.5; p < 0.001), fixation duration on road users (2.0 s vs 1.8 s; p < 0.001) and saccade amplitudes (7.4° vs 6.7°; p < 0.001). A main effect of age on eye movements was also found where older drivers made smaller saccades than the young drivers (6.7° vs 7.4°; p < 0.001).

CONCLUSIONS

Blur reduced DriveSafe scores for both age groups and this effect was greater for the young drivers. The decrease in number of fixations and fixation duration on road users, as well as the reduction in saccade amplitudes under the blurred condition, highlight the difficulty experienced in performing the task in the presence of optical blur, which suggests that uncorrected refractive errors may have a detrimental impact on aspects of driving performance.

Pathways of Number Line Development in Children

Dyscalculia, or mathematics learning disability, has received growing attention in recent years. Working memory and number sense are hypothesized to form important determinants of dyscalculia, but longitudinal assessments of number sense in children with or at-risk for dyscalculia are scarce. The current study investigated number line development in first and second grade, in addition to kindergarten predictors and mathematical proficiency as an outcome. Children (n = 396) could be divided into three latent growth classes: at-risk, catch-up, and typical, based on their number line development. Growth was predicted by kindergarten number sense and verbal working memory. According to the class to which they were assigned, children differed in mathematical proficiency at the end of grade 2. The current study makes an important contribution to the understanding of risk for dyscalculia, showing that children at-risk can be distinguished based on their number line development, and that kindergarten variables are predictive of subsequent development.

Spatial biases during mental arithmetic: evidence from eye movements on a blank screen

While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the “mental number line”), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8–3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space.