Developmental dyscalculia: A deficit in the approximate number system or an access deficit?

Delayed development of basic numerical skills in children with developmental dyscalculia

Research suggests that children with developmental dyscalculia (DD) have deficits in basic numerical skills. However, there is conflicting evidence on whether basic numerical skills in children with DD are qualitatively different from those in typically developing children (TD) or whether basic numerical skills development in children with DD is simply delayed. In addition, there are also competing hypotheses about deficits in basic numerical skills, assuming (1) a general deficit in representing numerosities (Approximate Number System, ANS), (2) specific deficits in an object-based attentional system (Object Tracking System, OTS), or (3) deficits in accessing numerosities from symbols (Access Deficit, AD). Hence, the purpose of this study was to investigate whether deficits in basic numerical skills in children with DD are more indicative of a developmental delay or a dyscalculia-specific qualitative deviation and whether these deficits result from (selective) impairment of core cognitive systems involved in numerical processing. To address this, we tested 480 children (68 DD and 412 TD) in the 2nd, 3rd, and 4th grades with different paradigms for basic numerical skills (subitizing, counting, magnitude comparison tasks, number sets, and number line estimation tasks). The results revealed that DD children's impairments did not indicate qualitatively different basic numerical skills but instead pointed to a specific developmental delay, with the exception of dot enumeration. This result was corroborated when comparing mathematical profiles of DD children in 4th grade and TD children in 2nd grade, suggesting that DD children were developmentally delayed and not qualitatively different. In addition, specific deficits in core markers of numeracy in children with DD supported the ANS deficit rather than the AD and OTS deficit hypothesis.

[Formula: see text] Domain-general and domain-specific cognitive correlates of developmental dyscalculia: a systematic review of the last two decades' literature

Developmental dyscalculia is a neurodevelopmental disorder, influencing the learning of mathematics in developing children. In the last two decades, continuous growth of research has helped in the advancement of the state of knowledge of dyscalculia. This upsurge in the number of studies makes it relevant to conduct a systematic review, covering all the empirical evidence, but there is a dearth of review studies synthesizing findings of the studies in the recent past. Therefore, the current study aims to systematically review studies investigating the underlying cognitive causal factors associated with developmental dyscalculia in the last two decades. To investigate the underlying cognitive factors associated with dyscalculia, two prominent approaches have been used: domain-general and domain-specific. While the domain-general approach argues for the deficit in general cognitive abilities, the domain-specific approach argues for the deficit in core numerical abilities. In the present review, the PRISMA method is followed. Articles were searched using two methods: firstly, through database sources of Google Scholar, Web of Science, and ScienceDirect, 1738 abstracts were screened, of which 46 articles met the specific inclusion criteria; and secondly, through recently published systematic reviews and meta-analyses, 29 studies were included. A total of 75 studies, 48 studies from domain-general and 27 studies from domain-specific approaches, have been selected. This review discusses domain-general and domain-specific approaches of developmental dyscalculia, along with specific theories associated with both approaches. Based on the discussed findings, visuospatial working memory and symbolic number processing abilities emerged as the best predictor of math ability in children with dyscalculia.

The role of spatial information in an approximate cross-modal number matching task

The approximate number system (ANS) is thought to be an innate cognitive system that allows humans to perceive numbers (>4) in a fuzzy manner. One assumption of the ANS is that numerosity is represented amodally due to a mechanism, which filters out nonnumerical information from stimulus material. However, some studies show that nonnumerical information (e.g., spatial parameters) influence the numerosity percept as well. Here, we investigated whether there is a cross-modal transfer of spatial information between the haptic and visual modality in an approximate cross-modal number matching task. We presented different arrays of dowels (haptic stimuli) to 50 undergraduates and asked them to compare haptically perceived numerosity to two visually presented dot arrays. Participants chose which visually presented array matched the numerosity of the haptic stimulus. The distractor varied in number and displayed a random pattern, whereas the matching (target) dot array was either spatially identical or spatially randomized (to the haptic stimulus). We hypothesized that if a "numerosity" percept is based solely on number, neither spatially identical nor spatial congruence between the haptic and the visual target arrays would affect the accuracy in the task. However, results show significant processing advantages for targets with spatially identical patterns and, furthermore, that spatial congruency between haptic source and visual target facilitates performance. Our results show that spatial information was extracted from the haptic stimuli and influenced participants' responses, which challenges the assumption that numerosity is represented in a truly abstract manner by filtering out any other stimulus features.

What Skills Could Distinguish Developmental Dyscalculia and Typically Developing Children: Evidence From a 2-Year Longitudinal Screening

Developmental dyscalculia (DD) is a mathematics learning disorder that affects approximately 5% to 7% of the population. This study aimed to detect the underlying domain-specific and domain-general differences between DD and typically developing (TD) children. We recruited 9-year-old primary school children to form the DD group via a 2-year longitudinal screening process. In total, 75 DD children were screened from 1,657 children after the one-time screening, and 13 DD children were screened from 1,317 children through a consecutive 2-year longitudinal screening. In total, 13 experimental tasks were administered to assess their cognitive abilities to test the domain-specific magnitude representation hypothesis (including symbolic and nonsymbolic magnitude comparisons) and four alternative domain-general hypotheses (including working memory, executive function, attention, and visuospatial processing). The DD group had worse performance than the TD group on the number sense task, finger sense task, shifting task, and one-back task after both one-time and two-time screening. Logistic regressions further indicated the differences on the shifting task and the nonsymbolic magnitude comparison task could distinguish DD and TD children. Our findings suggest that domain-specific nonsymbolic magnitude representation and domain-general executive function both contribute to DD. Thus, both domain-specific and domain-general abilities will be necessary to investigate and to intervene in DD groups in the future.

Get in touch with numbers - an approximate number comparison task in the haptic modality

The Approximate Number System (ANS) is conceptualized as an innate cognitive system that allows humans to perceive numbers of objects or events (>4) in a fuzzy, imprecise manner. The representation of numbers is assumed to be abstract and not bound to a particular sense. In the present study, we test the assumption of a shared cross-sensory system. We investigated approximate number processing in the haptic modality and compared performance to that of the visual modality. We used a dot comparison task (DCT), in which participants compare two dot arrays and decide which one contains more dots. In the haptic DCT, 67 participants had to compare two simultaneously presented dot arrays with the palms of their hands; in the visual DCT, participants inspected and compared dot arrays on a screen. Tested ratios ranged from 2.0 (larger/smaller number) to 1.1. As expected, in both the haptic and the visual DCT responses similarly depended on the ratio of the numbers of dots in the two arrays. However, on an individual level, we found evidence against medium or stronger positive correlations between “ANS acuity” in the visual and haptic DCTs. A regression model furthermore revealed that besides number, spacing-related features of dot patterns (e.g., the pattern’s convex hull) contribute to the percept of numerosity in both modalities. Our results contradict the strong theory of the ANS solely processing number and being independent of a modality. According to our regression and response prediction model, our results rather point towards a modality-specific integration of number and number-related features.

Do children with mathematical learning disabilities use the inversion principle to solve three-term arithmetic problems?: The impact of presentation mode

Numerical inversion is the ability to understand that addition is the opposite of subtraction and vice versa. Three-term arithmetic problems can be solved without calculation using this conceptual shortcut. To verify that this principle is used, inverse problems (a + b - b) can be compared with standard problems (a + b - c). If this principle is used, performance on inverse problems will be higher than performance on standard problems because no calculation is required. To our knowledge, this principle has not been previously studied in children with mathematical learning disabilities (MLD). Our objectives were (a) to study whether 10-year-olds with MLD are able to use this conceptual principle in three-term arithmetic problems and (b) to evaluate the impact of the presentation mode. A total of 64 children with or without MLD solved three-term arithmetic problems (inverse and standard) in two presentation modes (symbolic and picture). The results showed that even though children with MLD have difficulties in performing arithmetic problems, they can do so when the inverse problem is presented with pictures. The picture presentation mode allowed children with MLD to efficiently identify and use the conceptual inversion shortcut and thus to achieve a similar performance to that of typically developing children. These results provide interesting perspectives for the care of children with MLD.

Nonsymbolic and Symbolic Numerical Magnitude Processing in the Brazilian Children with Mathematics Difficulties

It is still debated if the main deficit in mathematical difficulties (MD) is nonsymbolic or symbolic numerical magnitude processing.

Impaired large numerosity estimation and intact subitizing in developmental dyscalculia

It is believed that the approximate estimation of large sets and the exact quantification of small sets (subitizing) are supported by two different systems, the Approximate Number System (ANS) and Object Tracking System (OTS), respectively. It is a current matter of debate whether they are both impaired in developmental dyscalculia (DD), a specific learning disability in symbolic number processing and calculation. Here we tackled this question by asking 32 DD children and 32 controls to perform a series of tasks on visually presented sets, including exact enumeration of small sets as well as comparison of large, uncountable sets. In children with DD, we found poor sensitivity in processing large numerosities, but we failed to find impairments in the exact enumeration of sets within the subitizing range. We also observed deficits in visual short-term memory skills in children with dyscalculia that, however, did not account for their low ANS acuity. Taken together, these results point to a dissociation between quantification skills in dyscalculia, they highlight a link between DD and low ANS acuity and provide support for the notion that DD is a multifaceted disability that covers multiple cognitive skills.

Failure to replicate the benefit of approximate arithmetic training for symbolic arithmetic fluency in adults

Previous research reported that college students’ symbolic addition and subtraction fluency improved after training with non-symbolic, approximate addition and subtraction. These findings were widely interpreted as strong support for the hypothesis that the Approximate Number System (ANS) plays a causal role in symbolic mathematics, and that this relation holds into adulthood. Here we report four experiments that fail to find evidence for this causal relation. Experiment 1 examined whether the approximate arithmetic training effect exists within a shorter training period than originally reported (2 vs 6 days of training). Experiment 2 attempted to replicate and compare the approximate arithmetic training effect to a control training condition matched in working memory load. Experiments 3 and 4 replicated the original approximate arithmetic training experiments with a larger sample size. Across all four experiments (N = 318) approximate arithmetic training was no more effective at improving the arithmetic fluency of adults than training with control tasks. Results call into question any causal relationship between approximate, non-symbolic arithmetic and precise symbolic arithmetic.

The association between visual attention and arithmetic competence: The mediating role of enumeration

The current study aimed at clarifying the nature of relation between visual attention and arithmetic competence. A group of 301 Chinese second graders was assessed. Children's visual attention was measured using two versions of a visual search task, with efficient visual search (the similarity between the target and the distractors is low) tapping automatic, stimulus-driven visual attention and inefficient visual search (the similarity between the target and the distractors is high) tapping effortful, goal-directed visual attention. Children's arithmetic competence, enumeration skills (assessed in about half of the participants), and other domain-general cognitive abilities were also assessed. The results suggest that only inefficient visual search significantly predicted children's arithmetic competence, and such a relation was mediated through their enumeration skills. The findings highlight the role of fundamental cognitive capacities in mathematics learning and provide insights into potential interventions for improving children's arithmetic competence.

Development of early domain-specific and domain-general cognitive precursors of high and low math achievers in grade 6

This study investigated from a longitudinal retrospective perspective what characterizes and predicts 6th graders (M_age = 12.95, SD = 0.27) with low (LMA) or high (HMA) math achievement concerning the development of early domain-specific and domain-general cognitive abilities. They were examined and compared to average achievers (n = 88) at four-time points from kindergarten (M_age = 6.58, SD = 0.36) to third grade (M_age = 9.53, SD = 0.33). The LMA (n = 27) or HMA (n = 41) children exhibited persistent multi-weakness and multi-strength profiles, respectively, present already prior to formal schooling. The cognitive profiles of the two groups, and their development, were mostly qualitatively similar, but there were also important qualitative differences. Logistic regression analyzes showed that superior verbal arithmetic, logical reasoning, and executive functions are vital for developing superior mathematical skills while inferior verbal arithmetic, logical reasoning, and spatial processing ability constitute unique potential risk factors for low mathematical skills.

Associative Cognitive Factors of Math Problems in Students Diagnosed With Developmental Dyscalculia

The Dutch protocol, 'Dyscalculia: Diagnostics for Behavioral Professionals' (DDBP protocol; Van Luit et al., 2014), describes how behavioral experts can examine whether a student has developmental dyscalculia (DD), based on three criteria: severity, discrepancy, and resistance. In addition to distinguishing the criteria necessary for diagnosis, the protocol provides guidance on formulating hypotheses by describing and operationalising four possible associative cognitive factors of math problems: planning skills, naming speed, short-term and/or working memory, and attention. The current exploratory and descriptive research aims to describe the frequency of these four primary associative cognitive factors in students with DD from the Netherlands. Descriptive data from 84 students aged 8-18 years showed that deficits in naming speed (in particular, in naming numbers) were the most frequent explanation of math problems in children with DD, followed by deficits in short-term/working memory and planning skills. Deficits in attention were the least frequent. The findings are explained in light of current literature, and suggestions for follow-up research are presented.

Comparing Numerical Comparison Tasks: A Meta-Analysis of the Variability of the Weber Fraction Relative to the Generation Algorithm

Since more than 15 years, researchers have been expressing their interest in evaluating the Approximate Number System (ANS) and its potential influence on cognitive skills involving number processing, such as arithmetic. Although many studies reported significant and predictive relations between ANS and arithmetic abilities, there has recently been an increasing amount of published data that failed to replicate such relationship. Inconsistencies lead many researchers to question the validity of the assessment of the ANS itself. In the current meta-analysis of over 68 experimental studies published between 2004 and 2017, we show that the mean value of the Weber fraction (w), the minimal amount of change in magnitude to detect a difference, is very heterogeneous across the literature. Within young adults, w might range from < 10 to more than 60, which is critical for its validity for research and diagnostic purposes. We illustrate here the concern that different methods controlling for non-numerical dimensions lead to substantially variable performance. Nevertheless, studies that referred to the exact same method (e.g., Panamath) showed high consistency among them, which is reassuring. We are thus encouraging researchers only to compare what is comparable and to avoid considering the Weber fraction as an abstract parameter independent from the context. Eventually, we observed that all reported correlation coefficients between the value of w and general accuracy were very high. Such result calls into question the relevance of computing and reporting at all the Weber fraction. We are thus in disfavor of the systematic use of the Weber fraction, to discourage any temptation to compare given data to some values of w reported from different tasks and generation algorithms.

Influence of initial mathematical competencies on the effectiveness of a classroom-based intervention

BACKGROUND

Students commonly struggle with mathematics and mathematical problem-solving. Therefore, it is necessary to design and implement interventions aimed at improving these essential components of learning. Furthermore, the outcomes of these interventions can vary significantly and appear to be a function of a student's initial competencies in mathematics.

AIM

This study attempts to analyse the influence of initial levels of mathematics competency with respect to the benefits of a specific intervention known as the Integrated Dynamic Representation (IDR).

SAMPLE

Participants were 288 students (aged 6-8 years) who were divided according to their levels of mathematics competency (low-medium-high).

METHODS

Students were assigned to the two primary intervention groups, experimental group (EG; students who received the IDR intervention) and control group (CG; students who followed the traditional instructional methods). All participants completed the Test of Early Mathematics Abilities (TEMA-3) both before and after the intervention.

RESULTS AND CONCLUSIONS

Although all the three competency levels of the EG improved, the progression was different for each level. Results showed that students with low competency level improved substantially more than the students with medium and/or high baseline competency level.

Effects of non-symbolic arithmetic training on symbolic arithmetic and the approximate number system

The approximate number system (ANS) is an innate cognitive template that allows for the mental representation of approximate magnitude, and has been controversially linked to symbolic number knowledge and math ability. A series of recent studies found that an approximate arithmetic training (AAT) task that draws upon the ANS can improve math skills, which not only supports the existence of this link, but suggests it may be causal. However, no direct transfer effects to any measure of the ANS have yet been reported, calling into question the mechanisms by which math improvements may emerge. The present study investigated the effects of a 7-day AAT and successfully replicated previously reported transfer effects to math. Furthermore, our exploratory analyses provide preliminary evidence that certain ANS-related skills may also be susceptible to training. We conclude that AAT has reproducible effects on math performance, and provide avenues for future studies to further explore underlying mechanisms - specifically, the link between improvements in math and improvements in ANS skills.

(Non-)symbolic magnitude processing in children with mathematical difficulties: A meta-analysis

Symbolic and non-symbolic magnitude representations, measured by digit or dot comparison tasks, are assumed to underlie the development of arithmetic skills. The comparison distance effect (CDE) has been suggested as a hallmark of the preciseness of mental magnitude representations. It implies that two magnitudes are harder to discriminate when the numerical distance between them is small, and may therefore differ in children with mathematical difficulties (MD), i.e. low mathematical achievement or dyscalculia. However, empirical findings on the CDE in children with MD are heterogeneous, and only few studies assess both symbolic and non-symbolic skills. This meta-analysis therefore integrates 44 symbolic and 48 non-symbolic response time (RT) outcomes reported in nineteen studies (N=1630 subjects, aged 6-14 years). Independent of age, children with MD show significantly longer mean RTs than typically achieving controls, particularly on symbolic (Hedges' g=0.75; 95% CI [0.51; 0.99]), but to a significantly lower extent also on non-symbolic (g=0.24; 95% CI [0.13; 0.36]) tasks. However, no group differences were found for the CDE. Extending recent work, these meta-analytical findings on children with MD corroborate the diagnostic importance of magnitude comparison speed in symbolic tasks. By contrast, the validity of CDE measures in assessing MD is questioned.

Approximate number sense correlates with math performance in gifted adolescents

Nonhuman animals, human infants, and human adults all share an Approximate Number System (ANS) that allows them to imprecisely represent number without counting. Among humans, people differ in the precision of their ANS representations, and these individual differences have been shown to correlate with symbolic mathematics performance in both children and adults. For example, children with specific math impairment (dyscalculia) have notably poor ANS precision. However, it remains unknown whether ANS precision contributes to individual differences only in populations of people with lower or average mathematical abilities, or whether this link also is present in people who excel in math. Here we tested non-symbolic numerical approximation in 13- to 16-year old gifted children enrolled in a program for talented adolescents (the Center for Talented Youth). We found that in this high achieving population, ANS precision significantly correlated with performance on the symbolic math portion of two common standardized tests (SAT and ACT) that typically are administered to much older students. This relationship was robust even when controlling for age, verbal performance, and reaction times in the approximate number task. These results suggest that the Approximate Number System is linked to symbolic math performance even at the top levels of math performance.