Non-symbolic Number Comparison Task Research Articles

A connectome-based neuromarker of nonverbal number acuity and arithmetic skills.

The approximate number system (ANS) is vital for survival and reproduction in animals and is crucial for constructing abstract mathematical abilities in humans. Most previous neuroimaging studies focused on identifying discrete brain regions responsible for the ANS and characterizing their functions in numerosity perception. However, a neuromarker to characterize an individual's ANS acuity is lacking, especially one based on whole-brain functional connectivity (FC). Here, based on the resting-state functional magnetic resonance imaging (rs-fMRI) data obtained from a large sample, we identified a distributed brain network (i.e. a numerosity network) using a connectome-based predictive modeling (CPM) analysis. The summed FC strength within the numerosity network reliably predicted individual differences in ANS acuity regarding behavior, as measured using a nonsymbolic number-comparison task. Furthermore, in an independent dataset of the Human Connectome Project (HCP), we found that the summed FC strength within the numerosity network also specifically predicted individual differences in arithmetic skills, but not domain-general cognitive abilities. Therefore, our findings revealed that the identified numerosity network could serve as an applicable neuroimaging-based biomarker of nonverbal number acuity and arithmetic skills.

Sharpening, focusing, and developing: A study of change in nonsymbolic number comparison skills and math achievement in 1st grade.

Children's ability to discriminate nonsymbolic number (e.g., the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest that it may be due to a sharpening numerical representation or an improved ability to pay attention to number and filter out non-numerical information. We investigate this issue by studying change in children's performance (N=65) on a nonsymbolic number comparison task, where children decide which of two dot arrays has more dots, from the middle to the end of 1st grade (mean age at time 1=6.85 years old). In this task, visual properties of the dot arrays such as surface area are either congruent (the more numerous array has more surface area) or incongruent. Children rely more on executive functions during incongruent trials, so improvements in each congruency condition provide information about the underlying cognitive mechanisms. We found that accuracy rates increased similarly for both conditions, indicating a sharpening sense of numerical magnitude, not simply improved attention to the numerical task dimension. Symbolic number skills predicted change in congruent trials, but executive function did not predict change in either condition. No factor predicted change in math achievement. Together, these findings suggest that nonsymbolic number processing undergoes development related to existing symbolic number skills, development that appears not to be driving math gains during this period. Children's ability to discriminate nonsymbolic number improves throughout development. Competing theories suggest improvement due to sharpening magnitude representations or changes in attention and inhibition. The current study investigates change in nonsymbolic number comparison performance during first grade and whether symbolic number skills, math skills, or executive function predict change. Children's performance increased across visual control conditions (i.e., congruent or incongruent with number) suggesting an overall sharpening of number processing. Symbolic number skills predicted change in nonsymbolic number comparison performance.

Only Approximately the Same: Approximate Number Skills in Typically Developing Children and Children with Down Syndrome

ABSTRACT The approximate number system (ANS) is foundational to numerical cognition. Whereas some studies hint at intact ANS skills in individuals with Down syndrome (DS), others report impaired ANS abilities. To reconcile these discrepant findings, we investigated ANS skills of children with DS and typically developing (TD) children in a non-symbolic number comparison task. Children had to indicate which of two characters possessed more dots. The two sets of dots differed by ratios of 1:2 to 4:5. While overall DS and TD participants’ performance was comparable, accuracy levels differed for the two groups depending on the ratio presented. Both groups performed similarly for ‘easier’ ratios, however, TD children outperformed children with DS when they had to discriminate ‘harder’ ratios. Children with DS may thus face specific problems when discriminating ratios that are more demanding. The deviating ANS skills could potentially be related to problems with other symbolic maths abilities.

First fixation duration as a bottom-up measure during symbolic and non-symbolic numerical comparisons (La duración de la primera fijación como medida bottom-up al comparar cantidades simbólicas y no simbólicas)

ABSTRACT The ability to represent quantities, either in a symbolic or non-symbolic format, predicts calculation skills. Recording the saccades during gazing at these stimuli allows us to infer the cognitive processing taking place at that moment. The purpose of this research study was to analyse the duration of the first fixation during symbolic and non-symbolic numerical stimuli. We evaluated 32 university students through symbolic and non-symbolic number comparison tasks while recording their eye movements. In addition, they answered a calculation task. Participants spent more time looking first at the stimulus of greater magnitude during the execution of the comparison task (regardless of the presentation format). This measure was not a predictor of calculation skills. The duration of the first fixation was interpreted as a bottom-up measure during numerical stimuli perception, and therefore during the initial stage of cognitive processing.

NASCO: A new method and program to generate dot arrays for non-symbolic number comparison tasks

Basic numerical abilities are generally assumed to influence more complex cognitive processes involving numbers, such as mathematics. Yet measuring non-symbolic number abilities remains challenging due to the intrinsic correlation between numerical and non-numerical dimensions of any visual scene. Several methods have been developed to generate non-symbolic stimuli controlling for the latter aspects but they tend to be difficult to replicate or implement. In this study, we describe the NASCO method, which is an extension to the method popularized by Dehaene, Izard, and Piazza (2005). Their procedure originally controlled for two visual dimensions that are mediated by Number: Total Area and Item Size (i.e., N = TA/IS). Here, we additionally propose to control for another twofold dimension related to the array extent, which is also mediated by Number: Convex Hull Area and Mean Occupancy (i.e., N = CH/MO). We illustrate the NASCO method with a MATLAB app—NASCO app—that allows easy generation of dot arrays for a visually controlled assessment of non-symbolic numerical abilities. Results from a numerical comparison task revealed that the introduction of this twofold dimension manipulation substantially affected young adults’ performance. In particular, we did not replicate the relation between non-symbolic number abilities and arithmetic skills. Our findings open the debate about the reliability of previous results that did not take into account visual features related to the array extent. We then discuss the strengths of NASCO method to assess numerical ability, as well as the benefits of its straightforward implementation in NASCO app for researchers.

Preschoolers' Associations Between Space and Numbers Can Be Biased by Surface Area

ABSTRACTPeople associate numbers and horizontal space. This association has been demonstrated by the so‐called SNARC (Spatial‐Numerical Association of Response Codes)‐effect, with Western participants responding faster to larger numbers with their right hand and vice versa for smaller numbers. SNARC‐like effects have also been reported for preschoolers. However, it remains unclear whether children's SNARC‐effects are exclusively based on number or whether nonnumerical factors such as surface area can also play a role. To address this question, we asked children to compare quantities in a nonsymbolic number comparison task. On half of the trials, the larger set took up more total surface area (congruent trials), and on the other half, the smaller number had more surface area (incongruent trials). We obtained a significant interaction of SNARC‐like effects and congruency. SNARC‐effects were only observed for congruent trials, demonstrating that preschoolers' spatial‐numerical associations can be affected by nonnumerical magnitude.

Mathematics Competence Level: The Contribution of Non-symbolic and Spatial Magnitude Comparison Skills.

Magnitude comparison skills have been related to mathematics competence, although results in this area vary. The current study aimed to describe the performance of 75 children (aged 4–5 years) in two comparison tasks; and examine the strength of the relationship between each of the two tasks and mathematics competence level (MCL). Participants were assessed with the Early Numeracy Test which provides a global MCL score. Magnitude comparison skills were assessed with two tasks: a non-symbolic number comparison task and a spatial comparison task. Results of the Pearson correlation analysis showed a relationship between the two tasks with better performance in the spatial comparison task. Regression analysis with the stepwise method showed that only the non-symbolic number comparison task had a significant value in the prediction of the MCL pointing to the need to take these kinds of tasks into account in the first years of school.

Dyscalculia and Typical Math Achievement Are Associated With Individual Differences in Number-Specific Executive Function.

Deficits in numerical magnitude perception characterize the mathematics learning disability developmental dyscalculia (DD), but recent studies suggest the relation stems from inhibitory control demands from incongruent visual cues in the nonsymbolic number comparison task. This study investigated the relation among magnitude perception during differing congruency conditions, executive function, and mathematics achievement measured longitudinally in children (n=448) from ages 4 to 13. This relation was investigated across achievement groups and as it related to mathematics across the full range of achievement. Only performance on incongruent trials related to achievement. Findings indicate that executive function in a numerical context, beyond magnitude perception or executive function in a non-numerical context, relates to DD and mathematics across a wide range of achievement.

Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics.

The ability to intuitively and quickly compare the number of items in collections without counting is thought to rely on the Approximate Number System (ANS). To assess individual differences in the precision of peoples’ ANS representations, researchers often use non-symbolic number comparison tasks in which participants quickly choose the numerically larger of two arrays of dots. However, some researchers debate whether this task actually measures the ability to discriminate approximate numbers or instead measures the ability to discriminate other continuous magnitude dimensions that are often confounded with number (e.g., the total surface area of the dots or the convex hull of the dot arrays). In this study, we used hierarchical linear models (HLMs) to predict 132 adults’ accuracy on each trial of a non-symbolic number comparison task from a comprehensive set of trial-level characteristics (including numerosity ratio, surface area, convex hull, and temporal and spatial variations in presentation format) and participant-level controls (including cognitive abilities such as visual-short term memory, working memory, and math ability) in order to gain a more nuanced understanding of how individuals complete this task. Our results indicate that certain trial-level characteristics of the dot arrays contribute to our ability to compare numerosities, yet numerosity ratio, the critical marker of the ANS, remains a highly significant predictor of accuracy above and beyond trial-level characteristics and across individuals with varying levels of math ability and domain-general cognitive abilities.

Attention to number: The convergence of numerical magnitude processing, attention, and mathematics in the inferior frontal gyrus.

Research indicates that the neurocognitive system representing nonsymbolic numerical magnitudes is foundational for the development of mathematical competence. However, recent studies found that the most common task used to measure numerical acuity, the nonsymbolic number comparison task, is heavily influenced by non-numerical visual parameters of stimuli that increase executive function demands. Further, this influence may be a confound invalidating theoretical accounts of the relation between number comparison performance and mathematical competence. Instead of acuity, the relation may depend on one's ability to attend to numerical information in the face of competing, non-numerical cues. The current study investigated this issue by measuring neural activity associated with numerical magnitude processing acuity, domain-general attention, and selective attention to number via functional magnetic resonance imaging while children 8-11 years old completed a nonsymbolic number comparison task and a flanker task. Results showed that activation in the right inferior frontal gyrus during incongruent versus congruent trials of the comparison task, our construct for attention to number, predicted mathematics achievement after controlling for verbal IQ, flanker accuracy rate, and the neural congruency effect from the flanker task. In contrast, activity in frontal and parietal regions responding to differences in difficulty of numerical comparisons, our construct for numerical magnitude processing acuity, did not correlate with achievement. Together, these findings suggest a need to reframe existing models of the relation between number processing and math competence to include the interaction between attention and use of numerical information, or in other words "attention to number."

Expanding the Home Numeracy Model to Chilean children: Relations among parental expectations, attitudes, activities, and children’s mathematical outcomes

We used structural equation modeling to evaluate an enhanced version of the Home Numeracy Model proposed by Skwarchuk and colleagues (2014, Journal of Experimental Child Psychology, 121, 63–84). Participants were 390 Chilean preschool children and their parents. Children completed numeracy and literacy tasks at the beginning of preschool (mean age: 4 years and 7 months) and approximately 8 months later. Parents reported on the home numeracy activities they engaged in with their children, including formal (i.e., mapping and operational), informal (i.e., parents’ number-game knowledge), and home literacy activities (i.e., code-related and meaning-related), as well as on numeracy and literacy attitudes and expectations for children’s performance prior to Grade 1. We found that parents with more positive numeracy attitudes and higher academic expectations reported a higher frequency of formal numeracy (mapping and operational) activities. In turn, formal operational activities predicted number line estimation and applied problem-solving skills. In contrast, informal activities (i.e., parents’ number-game knowledge) predicted children’s non-symbolic arithmetic and non-symbolic number comparison tasks, as well as their applied problem-solving skills. The links between home activities and numeracy outcomes were domain specific: Parents’ reports of literacy activities did not predict early numeracy skills. We discuss how our results support the enhanced Home Numeracy Model and thus provide a more complete framework connecting parents’ engagement in numeracy activities and children’s mathematical outcomes.

Intergenerational associations of the approximate number system in toddlers and their parents.

From birth, humans are able to discriminate quantities using the approximate number system (ANS). However, previous methods have only been suitable to examine ANS functioning in infancy and older children. The goals of this study were twofold: first, to modify an existing method of assessing ANS functioning for toddlerhood; and second, to investigate individual differences in toddlers' ANS performance by examining correlations with their parents' ANS acuity. Using a preferential looking paradigm, we found that 1- to 3-year-olds (N=46) looked significantly longer to numerically changing images compared to numerically constant ones suggesting that the paradigm is a suitable measure of ANS functioning in toddlerhood. Furthermore, we found a positive relation between toddlers' ANS performance and that of their parents (assessed using a non-symbolic number comparison task) independent of children's vocabulary or parents' perceived math ability or preference for math. These findings are consistent with a specific intergenerational transmission of the ANS. Statement of contribution What is already known on this subject? Past methods used to examine ANS functioning were only suitable for infants and older children. Little research has examined sources underlying individual difference in ANS acuity. What does this study add? We developed a preferential looking task to assess ANS functioning in toddlerhood. Individual differences in toddlers' ANS functioning are correlated with their parents' ANS acuity.

Altered Parietal Activation during Non-symbolic Number Comparison in Children with Prenatal Alcohol Exposure.

Number processing is a cognitive domain particularly sensitive to prenatal alcohol exposure, which relies on intact parietal functioning. Alcohol-related alterations in brain activation have been found in the parietal lobe during symbolic number processing. However, the effects of prenatal alcohol exposure on the neural correlates of non-symbolic number comparison and the numerical distance effect have not been investigated. Using functional magnetic resonance imaging (fMRI), we examined differences in brain activation associated with prenatal alcohol exposure in five parietal regions involved in number processing during a non-symbolic number comparison task with varying degrees of difficulty. fMRI results are presented for 27 Cape Colored children (6 fetal alcohol syndome (FAS)/partial FAS, 5 heavily exposed (HE) non-sydromal, 16 controls; mean age ± SD = 11.7 ± 1.1 years). Fetal alcohol exposure was assessed by interviewing mothers using a timeline follow-back approach. Separate subject analyses were performed in each of five regions of interest, bilateral horizontal intraparietal sulci (IPS), bilateral posterior superior parietal lobules (PSPL), and left angular gyrus (left AG), using the general linear model with predictors for number comparison and difficulty level. Mean percent signal change for each predictor was extracted for each subject for each region to examine group differences and associations with continuous measures of alcohol exposure. Although groups did not differ in performance, controls activated the right PSPL more during non-symbolic number comparison than exposed children, but this was not significant after controlling for maternal smoking, and the right IPS more than children with fetal alcohol syndrome (FAS) or partial FAS. More heavily exposed children recruited the left AG to a greater extent as task difficulty increased, possibly to compensate, in part, for impairments in function in the PSPL and IPS. Notably, in non-syndromal heavily exposed children activation was impaired in the right PSPL, but spared in the right IPS. These results extend previous findings of poor right IPS recruitment during symbolic number processing in FAS/PFAS, indicating that mental representation of relative quantity is affected by prenatal alcohol exposure for both symbolic and non-symbolic representations of quantity.

The many ways quantifiers count: Children’s quantifier comprehension and cardinal number knowledge are not exclusively related

Children’s comprehension of quantifiers (like all, many, some) correlates with their cardinal number knowledge. However, it is unclear whether children’s quantifier comprehension is exclusively related to cardinal number knowledge or whether the relationship extends to approximate number skills. To find out, we tested German-speaking children in a quantifier comprehension task, a ‘Give-n task’, and a non-symbolic number comparison task (‘ANS task’). While we observed a significant correlation between quantifier and number knowledge in German-speaking children (age- and IQ-controlled), quantifiers did not mediate the relationship between cardinal number knowledge and age. This result suggests that quantifiers do not support number acquisition, contrasting with previous findings in English. Our results also revealed links between quantifier knowledge and approximate number skills, suggesting that quantifier and cardinal number skills are not exclusively related. Rather, children’s quantifier knowledge seems to be linked to number skills in a more general way, including approximate number skills.

Deficits in Approximate Number System Acuity and Mathematical Abilities in 6.5-Year-Old Children Born Extremely Preterm.

Preterm children are at increased risk for poor academic achievement, especially in math. In the present study, we examined whether preterm children differ from term-born children in their intuitive sense of number that relies on an unlearned, approximate number system (ANS) and whether there is a link between preterm children’s ANS acuity and their math abilities. To this end, 6.5-year-old extremely preterm (i.e., <27 weeks gestation, n = 82) and term-born children (n = 89) completed a non-symbolic number comparison (ANS acuity) task and a standardized math test. We found that extremely preterm children had significantly lower ANS acuity than term-born children and that these differences could not be fully explained by differences in verbal IQ, perceptual reasoning skills, working memory, or attention. Differences in ANS acuity persisted even when demands on visuo-spatial skills and attention were reduced in the ANS task. Finally, we found that ANS acuity and math ability are linked in extremely preterm children, similar to previous results from term-born children. These results suggest that deficits in the ANS may be at least partly responsible for the deficits in math abilities often observed in extremely preterm children.

Accumulation of non-numerical evidence during nonsymbolic number processing in the brain: An fMRI study.

Behavioral evidence has shown that when performing a nonsymbolic number comparison task (e.g., deciding which of two dot arrays contains more dots), participants' responses are sensitive to affected by both numerical (e.g., number of items) and non-numerical magnitudes (i.e., area, density, etc.). Thus far it is unclear what brain circuits support this process of accumulating non-numerical variables during nonsymbolic number processing. To investigate this, 21 adult participants were asked to engage in a dot comparison task. To measure the neural correlates of accumulating numerical and non-numerical variables, we manipulated the number of the non-numerical magnitudes that were congruent (correlated with number) or incongruent (anticorrelated with number). In a control task, participants were asked to choose the darker of two gray rectangles (brightness task). The tasks were matched in terms of their difficulty. The results of a whole brain analysis for regions sensitive to the congruity of numerical and non-numerical magnitudes revealed a region in the right inferior frontal gyrus (rIFG). Activation in this region was found to be correlated with the relative congruency of numerical and non-numerical magnitudes. In contrast, this region was not modulated by difficulty of the brightness control task. Accordingly in view of these findings, we suggest that the rIFG supports the accumulation of non-numerical magnitudes that are positively correlated with number. Therefore taken together, this study reveals a brain region whose pattern of activity is influenced by the congruency between numerical and non-numerical variables during nonsymbolic number judgments. Hum Brain Mapp 38:4908-4921, 2017. © 2017 Wiley Periodicals, Inc.

The Approximate Number System Acuity Redefined: A Diffusion Model Approach.

While all humans are capable of non-verbally representing numerical quantity using so-called the approximate number system (ANS), there exist considerable individual differences in its acuity. For example, in a non-symbolic number comparison task, some people find it easy to discriminate brief presentations of 14 dots from 16 dots while others do not. Quantifying individual ANS acuity from such a task has become an essential practice in the field, as individual differences in such a primitive number sense is thought to provide insights into individual differences in learned symbolic math abilities. However, the dominant method of characterizing ANS acuity—computing the Weber fraction (w)—only utilizes the accuracy data while ignoring response times (RT). Here, we offer a novel approach of quantifying ANS acuity by using the diffusion model, which accounts both accuracy and RT distributions. Specifically, the drift rate in the diffusion model, which indexes the quality of the stimulus information, is used to capture the precision of the internal quantity representation. Analysis of behavioral data shows that w is contaminated by speed-accuracy tradeoff, making it problematic as a measure of ANS acuity, while drift rate provides a measure more independent from speed-accuracy criterion settings. Furthermore, drift rate is a better predictor of symbolic math ability than w, suggesting a practical utility of the measure. These findings demonstrate critical limitations of the use of w and suggest clear advantages of using drift rate as a measure of primitive numerical competence.

Inhibitory control may not explain the link between approximation and math abilities in kindergarteners from middle class families

Past research suggests that individual differences in the acuity of the approximate number system (ANS) are associated with children’s math abilities. However, some recent work has argued that these associations can be explained through shared reliance on inhibitory control. Here, we test this claim in two separate experiments. In Experiment 1, forty-two 5- and 6-year-old children completed a non-symbolic number comparison task to assess ANS acuity as well as standardized experimenter-administered assessments for inhibitory control and math ability. Children’s accuracy in the number comparison task and scores on the math assessment were significantly correlated, even when controlling for performance on the inhibitory control task. To rule out that our findings were due to the nature of the inhibitory control task, in Experiment 2, we administered a different, computerized inhibitory control task, and similar tasks to assess ANS acuity and math ability as in Experiment 1 to children aged 3–6 years (N = 169). Similar to the result of Experiment 1, we found that associations between accuracy in the number comparison task and math ability persisted when controlling for performance on the inhibitory control task. Together these results suggest that ANS acuity is uniquely associated with early math abilities, independent of the effect of inhibitory control at least in children from middle- to high-SES families.

The Approximate Number System is not Predictive for Symbolic Number Processing in Kindergarteners

The relation between the approximate number system (ANS) and symbolic number processing skills remains unclear. Some theories assume that children acquire the numerical meaning of symbols by mapping them onto the preexisting ANS. Others suggest that in addition to the ANS, children also develop a separate, exact representational system for symbolic number processing. In the current study, we contribute to this debate by investigating whether the nonsymbolic number processing of kindergarteners is predictive for symbolic number processing. Results revealed no association between the accuracy of the kindergarteners on a nonsymbolic number comparison task and their performance on the symbolic comparison task six months later, suggesting that there are two distinct representational systems for the ANS and numerical symbols.

Impaired acuity of the approximate number system in 22q11.2 microdeletion syndrome.

A magnitude comparison deficit has been frequently observed in velocardiofacial syndrome (Del22q11.2). We hypothesized that this deficit extends to impairments in the acuity of the approximate number system (ANS). Three groups of children aged 8-14 years were investigated: Del22q11.2 children (n = 12), low cognitive ability children (LCA; n = 12), and matched typically developing children (TD; n = 28). All children were assessed with a simple reaction time task and symbolic and nonsymbolic number comparison tasks. To estimate the acuity of the ANS, the Weber fraction (w) was calculated from the nonsymbolic comparison task. The Del22q11.2 group exhibited a significantly higher w compared with the other groups. Importantly, no significant differences were found in w between the TD and LCA groups. The performance pattern of the Del22q11.2 group was similar to the TD group in the symbolic comparison task, and both of these groups had better performance than the LCA group. The impairment of ANS acuity observed in individuals with Del22q11.2 cannot be explained by deficits in general processing speed because no significant group differences were found in the simple reaction time task. These results suggest that lower acuity of the ANS should be added to the behavioral phenotype of Del22q11.2. The absence of impaired ANS acuity in the LCA group is consistent with the hypothesis that number sense is a relatively specific and autonomous domain. Investigations of low ANS acuity in mathematics learning difficulties and Del22q11.2 should be intensified.