On the Difference Between Numerosity Processing and Number Processing

The ANS theory on the processing of non-symbolic numerosities and the ANS mapping account on the processing of symbolic numbers have been the most popular theories on numerosity and number processing, respectively, in the last 20 years. Recently, both the ANS theory and the ANS mapping account have been questioned. In the current study, we examined two main assumptions of both the ANS theory and the ANS mapping account. ERPs were measured in 21 participants during four same-different match-to-sample tasks, involving non-symbolic stimuli, symbolic stimuli, or a combination of symbolic and non-symbolic stimuli (i.e., mapping tasks). We strictly controlled the visual features in the non-symbolic stimuli. Based on the ANS theory, one would expect an early distance effect for numerosity in the non-symbolic task. However, the results show no distance effect for numerosity. When analyzing the stimuli based on visual properties, an early distance effect for area subtended by the convex hull was found. This finding is in line with recent claims that the processing of non-symbolic stimuli may be dependent on the processing of visual properties instead of on numerosity (only). With regards to the processing of symbolic numbers, the ANS mapping account states that symbolic numbers are first mapped onto their non-symbolic representations before further processing, since the non-symbolic representation is at the basis of processing the symbolic number. If the non-symbolic format is the basic format of processing, one would expect that the processing of non-symbolic numerosities would not differ between purely non-symbolic tasks and mapping tasks, resulting in similar ERP waveforms for both tasks. Our results show that the processing of non-symbolic numerosities does differ between the tasks, indicating that processing of non-symbolic number is dependent on task format. This provides evidence against the ANS mapping account. Alternative theories for both the processing of non-symbolic numerosities and symbolic numbers are discussed

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

Strategy Use on Bounded and Unbounded Number Lines in Typically Developing Adults and Adults With Dyscalculia:An Eye-Tracking Study

Contains fulltext : 195024.pdf (publisher's version ) (Open Access)Recent research suggests that bounded number line tasks, often used to measure number sense, measure proportion estimation instead of pure number estimation. The latter is thought to be measured in recently developed unbounded number line tasks. Children with dyscalculia use less mature strategies on unbounded number lines than typically developing children. In this qualitative study, we explored strategy use in bounded and unbounded number lines in adults with (N = 8) and without dyscalculia (N = 8). Our aim was to gain more detailed insights into strategy use. Differences in accuracy and strategy use between individuals with and without dyscalculia on both number lines may enhance our understanding of the underlying deficits in individuals with dyscalculia. We combined eye-tracking and Cued Retrospective Reporting (CRR) to identify strategies on a detailed level. Strategy use and performance were highly similar in adults with and without dyscalculia on both number lines, which implies that adults with dyscalculia may have partly overcome their deficits in number sense. New strategies and additional steps and tools used to solve number lines were identified, such as the use of the previous target number. We provide gaze patterns and descriptions of strategies that give important first insights into new strategies. These newly defined strategies give a more in-depth view on how individuals approach a number lines task, and these should be taken into account when studying number estimations, especially when using the unbounded number line.23 p

Strategy use in bounded and unbounded number lines in MLD

Number line estimation (NLE) tasks typically measure number placements on a bounded number line. Recently, the unbounded NLE task was introduced in which only the starting point of the number line and unit are given, but no endpoint. This type of task is thought to be a more direct measure of understanding numerical quantity. Performance, development, and strategy use differ between the bounded and unbounded NLE tasks in the general population. Research has shown that individuals with mathematical learning disability (MLD) lag behind in bounded NLE tasks. In the current research, we examined whether they also lag behind in the unbounded NLE task and whether they use different strategies as compared to individuals without MLD. In the first qualitative study, four strategies were identified for estimations on the unbounded NLE task. These strategies were used by adults with and without MLD. In the second study, performance and strategy use of children with and without MLD on the unbounded number line is compared. The results of these studies give additional 72 insights into the deficits in adults and children with MLD and possible strategies that may improve their number line estimations

On the Difference Between Numerosity Processing and Number Processing

The ANS theory on the processing of non-symbolic numerosities and the ANS mapping account on the processing of symbolic numbers have been the most popular theories on numerosity and number processing, respectively, in the last 20 years. Recently, both the ANS theory and the ANS mapping account have been questioned. In the current study, we examined two main assumptions of both the ANS theory and the ANS mapping account. ERPs were measured in 21 participants during four same-different matchto-sample tasks, involving non-symbolic stimuli, symbolic stimuli, or a combination of symbolic and non-symbolic stimuli (i.e., mapping tasks). We strictly controlled the visual features in the non-symbolic stimuli. Based on the ANS theory, one would expect an early distance effect for numerosity in the non-symbolic task. However, the results show no distance effect for numerosity. When analyzing the stimuli based on visual properties, an early distance effect for area subtended by the convex hull was found. This finding is in line with recent claims that the processing of non-symbolic stimuli may be dependent on the processing of visual properties instead of on numerosity (only). With regards to the processing of symbolic numbers, the ANS mapping account states that symbolic numbers are first mapped onto their non-symbolic representations before further processing, since the non-symbolic representation is at the basis of processing the symbolic number. If the non-symbolic format is the basic format of processing, one would expect that the processing of non-symbolic numerosities would not differ between purely non-symbolic tasks and mapping tasks, resulting in similar ERP waveforms for both tasks. Our results show that the processing of non-symbolic numerosities does differ between the tasks, indicating that processing of non-symbolic number is dependent on task format. This provides evidence against the ANS mapping account. Alternative theories for both the processing of non-symbolic numerosities and symbolic numbers are discussed

Tekorten in vergelijken van getallen bij kinderen met ernstige rekenproblemen en dyscalculie

Kinderen met ernstige rekenproblemen en dyscalculie (ERD) hebben vaak problemen met rekenen door tekorten in getalbegrip en/of het werkgeheugen. Dit getalbegrip wordt vaak gemeten met de vergelijkingstaak, een taak die een hoge voorspellende waarde heeft voor rekenvaardigheden (De Smedt et al., 2013). Om op de vergelijkingstaak goed te presteren, zijn verschillende vaardigheden van belang. Het doel van het huidige onderzoek is inzicht krijgen in welke onderliggende vaardigheid van getalsvergelijking het probleem vormt voor kinderen met ERD. Daarnaast zal worden gekeken naar de strategieën die kinderen met en zonder ERD op deze taken gebruiken. Ook wordt de rol van verbaal en visuo-spatieel werkgeheugen onderzocht. De resultaten van dit onderzoek kunnen mogelijk bijdragen aan betere remediatie bij kinderen met ERD

Deficits in digit comparison by children with mathematical learning disability

Kinderen met ernstige rekenproblemen en dyscalculie (ERD) hebben vaak problemen met rekenen door tekorten in getalbegrip en/of het werkgeheugen. Dit getalbegrip wordt vaak gemeten met de vergelijkingstaak, een taak die een hoge voorspellende waarde heeft voor rekenvaardigheden (De Smedt et al., 2013). Om op de vergelijkingstaak goed te presteren, zijn verschillende vaardigheden van belang. Het doel van het huidige onderzoek is inzicht krijgen in welke onderliggende vaardigheid van getalsvergelijking het probleem vormt voor kinderen met ERD. Daarnaast zal worden gekeken naar de strategieën die kinderen met en zonder ERD op deze taken gebruiken. Ook wordt de rol van verbaal en visuo-spatieel werkgeheugen onderzocht. De resultaten van dit onderzoek kunnen mogelijk bijdragen aan betere remediatie bij kinderen met ERD

Analysis of variance for the mean ERP amplitudes in the N1, N2, N3 and P3 window for all conditions.

<p><i>Note.</i> *<i>p</i><.05,</p>**<p><i>p</i><.01,</p>***<p><i>p</i><.001.</p