Numerical Cognition Research Articles

Modeling the left digit effect in adult number line estimation

Number line estimation tasks are frequently used to study numerical cognition skills. In a typical version, the bounded number line task, target numerals must be placed on a bounded line labeled only at its endpoints (e.g., with 0 and 100). Placements by adults, while highly accurate, reveal a cyclical pattern of over- and underestimation of target numerals. The pattern suggests use of proportion judgment strategies and is well-captured by cyclical power models. Another systematic number line bias that has recently been observed, but has not yet been considered in modeling efforts, is the left digit effect. Numerals with different leftmost digits (e.g., 39 and 41) are placed farther apart on a line than is warranted. In the current study (N = 60), adult estimates were obtained for all numerals on a 0–100 number line estimation task, and fit of the standard cyclical power model was compared with two modified versions of the model. One modified version included a parameter that underweights the rightward digit's place value (e.g., the ones digit here), and the other used the same parameter to underweight all digits' place values. We found that both modifications provided a considerably better fit for individual and median data than the standard model, and we discuss their relative merits and cognitive interpretations. The data and models suggest how a left digit bias might impact estimates across the number line.

Neurodevelopmental differences in task-evoked number network connectivity: Comparing symbolic and nonsymbolic number discrimination in children and adults

Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., “two”), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects.

Spontaneous anchors bias consumers’ divisions, judgments, and behavior

Consumers often have to make divisions to evaluate attributes. In seven experiments (total N = 3841, six preregistered), this research shows how spontaneous anchors bias divisions. That is, consumers will recruit typical values of the attribute from memory and use them as priors when dividing. This process biases consumers’ judgments and subsequent behavior. When the actual attribute quotient is above the attribute prior, it tends to be underestimated, and when it is below the attribute prior, it tends to be overestimated. This research examines when the attribute of interest is a company’s median wage. Consumers’ intuitive approach results in corresponding changes in the perceived fairness of employee pay and can, in turn, affect downstream company evaluations, willingness-to-pay, and product choice. The authors discuss theoretical implications for consumers’ numerical cognition, anchoring, and perceptions of income inequality. Practical implications for the management of and policymaking around product attribute information communication and for income inequality are also discussed.

PC020 / #794 THE EFFECTS OF ANODAL TRANSCRANIAL DIRECT CURRENT STIMULATION OVER RIGHT PARIETAL AND PREFRONTAL CORTICES ON NUMERICAL COGNITION: E-POSTER VIEWING

Non-invasive brain stimulation (NIBS) is used in basic cognitive science to establish causal models of the relationships between specific neural regions and cognition. In the field of numerical cognition, Transcranial Direct Current Stimulation (tDCS) applied to parietal and prefrontal cortex produce neuromodulatory effects, which translate into measurable behavioral effects affecting magnitude processing (Schroeder, 2017). The improvement of the number sense during early childhood is the foundation for the further development of numerical cognition and mathematical skills.

Preschoolers prior formal mathematics education engage numerical magnitude representation rather than counting principles in symbolic ±1 arithmetic: Evidence from the operational momentum effect.

In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This study is the first to demonstrate OM in symbolic arithmetic in preschoolers. It was modeled on Haman and Lipowska's (2021) non-symbolic arithmetic task, using Arabic numerals instead of visual sets. Seventy-seven children (4-7 years old) who know Arabic numerals and counting principles (CP), but without prior school math education, solved addition and subtraction problems presented as videos with one as the second operand. In principle, such problems may be difficult when involving a non-symbolic approximate number processing system, whereas in symbolic format they can be solved based solely on the successor/predecessor functions and knowledge of numerical orders, without reference to representation of numerical magnitudes. Nevertheless, participants made systematic errors, in particular, overestimating results of addition in line with the typical OM tendency. Moreover, subtraction and addition induced longer response times when primed with left- and right-directed movement, respectively, which corresponds to the reversed spatial form of OM. These results largely replicate those of non-symbolic task and show that children at early stages of mastering symbolic arithmetic may rely on numerical magnitude processing and spatial-numerical associations rather than newly-mastered CP and the concept of an exact number.

Attention to number requires magnitude-specific inhibition

Recent studies have shown that the ability to process number in the face of conflicting dimensions of magnitude is a crucial aspect of numerosity judgments, relying in part on the inhibition of the non-numerical dimensions. Here we report, for the first time, that these inhibitory control processes are specific to the conflicting dimension of magnitude. Using a non-symbolic numerical comparison task adapted to a conflict adaptation paradigm on a group of 82 adults, we show that congruency effects between numerical and non-numerical information were reduced only when the conflicting dimension was the same in the preceding incongruent trial. Attention to number thus involves inhibitory control processes acting at a specific level of information. These results contribute to better characterize the domain general abilities involved in numerical cognition, and provide evidence for a specific interaction between numerosity perception and inhibitory control.

The Dutch Oxford Cognitive Screen (OCS-NL): psychometric properties in Flemish stroke survivors.

The Oxford Cognitive Screen is a stroke-specific screen to evaluate attention, executive functions, memory, praxis, language, and numeric cognition. It was originally validated in England for acute stroke patients. In this study, we examined the psychometric properties of the Dutch OCS (OCS-NL). A total of 193 (99 acute stroke unit, 94 rehabilitation unit) patients were included in our study. A subset of patients (n = 128) completed a retest with the parallel version of the OCS-NL. First, we did not find evidence for a difference in prevalence of impairment between patients in the acute stroke versus rehabilitation unit on all but one of the subtests. For praxis, we observed a 14% lower prevalence of impairment in the rehabilitation than the acute stroke unit. Second, the parallel-form reliability ranged from weak to excellent across subtests. Third, in stroke patients below age 60, the OCS-NL had a 92% sensitivity relative to the MoCA, while the MoCA had a 55% sensitivity relative to the OCS-NL. Last, although left-hemispheric stroke patients performed worse on almost all MoCA subdomains, they performed similarly to right-hemispheric stroke patients on non-language domains on the OCS-NL. Our results suggest that the OCS-NL is a reliable cognitive screen that can be used in acute stroke and rehabilitation units. The OCS-NL may be more sensitive to detect cognitive impairment in young stroke patients and less likely to underestimate cognitive abilities in left-hemispheric stroke patients than the MoCA.

Numerical cognition in black-handed spider monkeys (Ateles geoffroyi)

We assessed two aspects of numerical cognition in a group of nine captive spider monkeys (Ateles geoffroyi). Petri dishes with varying amounts of food were used to assess relative quantity discrimination, and boxes fitted with dotted cards were used to assess discrete number discrimination with equally-sized dots and various-sized dots, respectively. We found that all animals succeeded in all three tasks and, as a group, reached the learning criterion of 70% correct responses within 110 trials in the quantity discrimination task, 160 trials in the numerosity task with equally-sized dots, and 30 trials in the numerosity task with various-sized dots. In all three tasks, the animals displayed a significant correlation between performance in terms of success rate and task difficulty in terms of numerical similarity of the stimuli and thus a ratio effect. The spider monkeys performed clearly better compared to strepsirrhine, catarrhine, and other platyrrhine primates tested previously on both types of numerical cognition tasks and at the same level as chimpanzees, bonobos, and orangutans. Our results support the notion that ecological traits such as a high degree of frugivory and/or social traits such as a high degree of fission-fusion dynamics may underlie between-species differences in cognitive abilities.

Number neurons in the nidopallium of young domestic chicks

Numerical cognition is ubiquitous in the animal kingdom. Domestic chicks are a widely used developmental model for studying numerical cognition. Soon after hatching, chicks can perform sophisticated numerical tasks. Nevertheless, the neural basis of their numerical abilities has remained unknown. Here, we describe number neurons in the caudal nidopallium (functionally equivalent to the mammalian prefrontal cortex) of young domestic chicks. Number neurons that we found in young chicks showed remarkable similarities to those in the prefrontal cortex and caudal nidopallium of adult animals. Thus, our results suggest that numerosity perception based on number neurons might be an inborn feature of the vertebrate brain.

Children’s development of an understanding of number: A model for Grade R teachers

Background: Teachers teach mathematics by focusing on procedural knowledge (what steps to follow when doing mathematics) and pay scant attention to the conceptual understanding that underlies these procedures such as double-digit addition or subtraction and overall additive and multiplicative relations. They teach concepts in a haphazard way instead of looking at them from a convergent perspective of concepts that a child builds, one after the other.Aim: This study explores what Grade R teachers know about young children’s specific developmental numerical cognition and if they infuse their understanding of number concept development in their pedagogy.Setting: Samples of 15 female Grade R teachers were purposefully selected from five schools in what was previously a racially segregated living area in South Africa.Methods: This research design is a descriptive case study. Data were collected using semi-structured interviews and observation notes documented during workshops and when the teachers implemented their learnings in their classrooms.Results: The main finding was that although teachers could reflect on the model of number concept development they had learned, they found it hard to infuse their knowledge into a strictly structured curriculum.Conclusion: Despite the Meerkat Maths programme offered to the teachers, they could not rely on their intuitive pedagogy, coupled with the model of number concept development that they had learned because of the strict demands of the school curriculum content with which they had to comply.

Large numbers cause magnitude neglect: The case of government expenditures

Four studies demonstrate that the public's understanding of government budgetary expenditures is hampered by difficulty in representing large numerical magnitudes. Despite orders of magnitude difference between millions and billions, study participants struggle with the budgetary magnitudes of government programs. When numerical values are rescaled as smaller magnitudes (in the thousands or lower), lay understanding improves, as indicated by greater sensitivity to numerical ratios and more accurate rank ordering of expenses. A robust benefit of numerical rescaling is demonstrated across a variety of experimental designs, including policy relevant choices and incentive-compatible accuracy measures. This improved sensitivity ultimately impacts funding choices and public perception of respective budgets, indicating the importance of numerical cognition for good citizenship.

A note on the normality assumption for Bayesian models of constraint in behavioral individual differences

To investigate the structure of individual differences in performance on behavioral tasks, Haaf and Rouder (2017) developed a class of hierarchical Bayesian mixed models with varying levels of constraint on the individual effects. The models are then compared via Bayes factors, telling us which model best predicts the observed data. One common criticism of their method is that the observed data are assumed to be drawn from a normal distribution. However, for most cognitive tasks, the primary measure of performance is a response time, the distribution of which is well known not to be normal. In this paper, I investigate the assumption of normality for two datasets in numerical cognition. Specifically, I show that using a shifted lognormal model for the response times does not change the overall pattern of inference. Further, since the model-estimated effects are now on a logarithmic scale, the interpretation of the modeling becomes more difficult, particularly because the estimated effect is now multiplicative rather than additive. As a result, I recommend that even though response times are not normally distributed in general, the simplification afforded by the Haaf and Rouder's approach provides a pragmatic approach to modeling individual differences in behavioral tasks.

Influences of hand action on the processing of symbolic numbers: A special role of pointing?

Embodied and grounded cognition theories state that cognitive processing is built upon sensorimotor systems. In the context of numerical cognition, support to this framework comes from the interactions between numerical processing and the hand actions of reaching and grasping documented in skilled adults. Accordingly, mechanisms for the processing of object size and location during reach and grasp actions might scaffold the development of mental representations of numerical magnitude. The present study exploited motor adaptation to test the hypothesis of a functional overlap between neurocognitive mechanisms of hand action and numerical processing. Participants performed repetitive grasping of an object, repetitive pointing, repetitive tapping, or passive viewing. Subsequently, they performed a symbolic number comparison task. Importantly, hand action and number comparison were functionally and temporally dissociated, thereby minimizing context-based effects. Results showed that executing the action of pointing slowed down the responses in number comparison. Moreover, the typical distance effect (faster responses for numbers far from the reference as compared to close ones) was not observed for small numbers after pointing, while it was enhanced by grasping. These findings confirm the functional link between hand action and numerical processing, and suggest new hypotheses on the role of pointing as a meaningful gesture in the development and embodiment of numerical skills.

Examining Challenges Associated with Numerical Cognition in Early Years Challenges Associated with Numerical Cognition in Early Years

The current research aims at examining challenges associated with numerical cognition in early years in South Africa. Guided by cognitive learning theory, the current investigation was informed by continuous quest in South Africa. The aim was to respond to unresolved challenges associated with early numerical cognition in terms of numerical cognition through semantics and textual misunderstanding in early numerical problems and concepts. Using survey design, a sample of 80 learners was chosen and tested through descriptive statistics. Data was collected using semi-structured questionnaires. It was revealed that the challenges associated with numerical cognition in early numerical problems and concepts are counting, reading numbers that contain more than one digit, difficulties with copying numbers, mathematical signs confusion, and challenges associated with manipulatives. By implication, the study highlighted that there is a severe lack of numerical literacy and competency among learners. Implying too that teachers need to pay particular attention to both semantics and textual misunderstanding

Discerning Developmental Dyscalculia and Neurodevelopmental Models of Numerical Cognition in a Disadvantaged Educational Context.

Developmental Dyscalculia (DD) signifies a failure in representing quantities, which impairs the performance of basic math operations and schooling achievement during childhood. The lack of specificity in assessment measures and respective cut-offs are the most challenging factors to identify children with DD, particularly in disadvantaged educational contexts. This research is focused on a numerical cognition battery for children, designed to diagnose DD through 12 subtests. The aims of the present study were twofold: to examine the prevalence of DD in a country with generally low educational attainment, by comparing z-scores and percentiles, and to test three neurodevelopmental models of numerical cognition based on performance in this battery. Participants were 304 Brazilian school children aged 7–12 years of both sexes (143 girls), assessed by the Zareki-R. Performances on subtests and the total score increase with age without gender differences. The prevalence of DD was 4.6% using the fifth percentile and increased to 7.4% via z-score (in total 22 out of 304 children were diagnosed with DD). We suggest that a minus 1.5 standard deviation in the total score of the Zareki-R is a useful criterion in the clinical or educational context. Nevertheless, a percentile ≤ 5 seems more suitable for research purposes, especially in developing countries because the socioeconomic environment or/and educational background are strong confounder factors to diagnosis. The four-factor structure, based on von Aster and Shalev’s model of numerical cognition (Number Sense, Number Comprehension, Number Production and Calculation), was the best model, with significant correlations ranging from 0.89 to 0.97 at the 0.001 level.

Enumeration takes time: Accuracy improves even after stimuli disappear

Numerical cognition is widespread among animal species and present from birth in humans. Laboratory studies show that longer stimulus duration improves numerical discrimination accuracy (Inglis & Gilmore, 2013; Wood & Spelke, 2005). Inglis and Gilmore (2013) suggested that longer durations allow subjects to resample the stimulus image multiple times, resulting in a more accurate final estimate. The current study tested this “multiple sampling” model alongside two competing models – “serial foveal accumulator” (Cheyette & Piantadosi, 2019) and “longer processing time” – to determine how stimulus duration relates to accuracy. Adult subjects completed a fully within-subject, 2AFC task in which they judged which of two arrays had more dots; accuracy was the dependent measure. Experiment 1 revealed higher accuracy in the 500 ms stimulus duration condition compared to the 100 ms condition, replicating previous results. Experiments 2 and 4 extended this finding. When stimulus duration was held constant at 100 ms, adding a 400 ms delay between stimulus offset and mask onset improved accuracy. Accuracy was similar in the 500 ms stimulus duration condition (E1) and the 100 ms duration + 400 ms mask delay conditions (E2 and E4), indicating that post-stimulus processing time improves accuracy, rather than stimulus duration per se. This contrasts with both the multiple sampling model and the serial foveal model, although we cannot exclude the possibility that sampling continues in iconic memory. Numerosity was a significant factor in all four experiments, suggesting a serial component in the enumeration process. These findings shed light on the cognitive processes underlying nonverbal number representation in humans.

Sub-cortical areas process physical size but not numerical value.

A robust finding in the numerical cognition literature is that the physical size and the numerical value of two to-be-compared digits interact, resulting in a size congruity effect (SiCE). The current study focuses on the possible role of prestriate areas in a digit comparison Stroop-like task. In the visual pathway, prestriate areas refer to regions from the retina up to the primary visual cortex (V1). I hypothesized that processing of physical size, but not numerical value, begins already in prestriate areas. This is because physical size is a basic visual feature while the numerical value of a symbol is a learned convention that should be retrieved from long-term memory. Adult participants compared the size or the numerical value of two digits. Without participants' awareness, I projected the digits either to the same eye, or each digit to a different eye. The latter type of presentation prevents prestriate areas from taking part in comparing the digits. Therefore, slower aresponse time under this condition hints atthe involvement of prestriate areas. Evidence confirmed the initial hypothesis, demonstrating slower performance when the stimuli are segregated between the eyes but only for physical size comparisons. This finding suggests that at least the initial processing of physical size, when relevant, is done before, and by different neural substrate than numerical value. The implications of the study and future directions are discussed.

Magnitude comparison and automaticity in number processing in adolescents with prenatal alcohol exposure: An event-related potentials study.

Individuals with fetal alcohol spectrum disorders may exhibit a distinct pattern of dysmorphic facial features, growth restriction, and cognitive deficits, particularly in arithmetic. Magnitude comparison, a fundamental element of numerical cognition, is modulated by the numerical distance effect, with numbers closer in value more difficult to compare than those further apart, and by the automaticity of the association of numerical values with their symbolic representations (Arabic numerals). We examined event-related potentials acquired during the Numerical Stroop numerical and physical tasks administered to 24 alcohol-exposed adolescents (eight fetal alcohol syndrome (FAS), eight partial FAS (PFAS), eight heavily exposed (HE) nonsyndromal) and 23 typically developing (TD), same- age controls. The distance effect was assessed on the numerical task to examine differences in reaction time (RT) and accuracy when two numbers are close in value (e.g., 1 vs. 2) compared to when the numbers are less close (e.g., 1 vs. 6). Automaticity was assessed in the physical task by examining the degree to which RT and accuracy are reduced when the relative physical size of two numerals is incongruent with their numerical values (e.g., 1 vs. 6). Adolescents in all four groups performed behaviorally as expected on these relatively simple magnitude comparison tasks, but accuracy was poorer and RT was slower on both tasks in the FAS and PFAS than the HE and TD groups. At the neurophysiological level, in the numerical task, a higher level of prenatal alcohol exposure was associated with smaller P2p amplitude. In the physical task, only the TD and nonsyndromal HE groups exhibited the expected smaller P300 amplitude in the incongruent than the congruent condition. These findings suggest that magnitude comparison in alcohol-exposed individuals may be mediated by recruitment of alternative neural pathways that are likely to be inefficient when number processing becomes more challenging.

Understanding the Effects of Transcranial Electrical Stimulation in Numerical Cognition: A Systematic Review for Clinical Translation.

Atypical development of numerical cognition (dyscalculia) may increase the onset of neuropsychiatric symptoms, especially when untreated, and it may have long-term detrimental social consequences. However, evidence-based treatments are still lacking. Despite plenty of studies investigating the effects of transcranial electrical stimulation (tES) on numerical cognition, a systematized synthesis of results is still lacking. In the present systematic review (PROSPERO ID: CRD42021271139), we found that the majority of reports (20 out of 26) showed the effectiveness of tES in improving both number (80%) and arithmetic (76%) processing. In particular, anodal tDCS (regardless of lateralization) over parietal regions, bilateral tDCS (regardless of polarity/lateralization) over frontal regions, and tRNS (regardless of brain regions) strongly enhance number processing. While bilateral tDCS and tRNS over parietal and frontal regions and left anodal tDCS over frontal regions consistently improve arithmetic skills. In addition, tACS seems to be more effective than tDCS at ameliorating arithmetic learning. Despite the variability of methods and paucity of clinical studies, tES seems to be a promising brain-based treatment to enhance numerical cognition. Recommendations for clinical translation, future directions, and limitations are outlined.

Laterality in simple multiplication: Assessing hemispheric specialization of arithmetic fact retrieval in a visual hemifield paradigm.

The prominent view in numerical cognition is that highly overlearned arithmetic facts are verbally mediated and unilaterally processed in a left-hemispheric network, including language areas. However, this view has recently been challenged. Here, we evaluated the hemispheric specialization of verbal arithmetic fact retrieval and number magnitude processing using two verification tasks (i.e., multiplication and number magnitude comparison) in a divided hemifield paradigm in healthy participants (n = 35). In the number comparison task, we replicated bilateral processing advantages for the unit-decade compatibility effect. Magnitude processing was facilitated after bilateral compared with a unilateral presentation. In the multiplication task, lateralized presentation to the left hemisphere yielded processing advantages in arithmetic fact retrieval when the required interhemispheric transitions from the input, processing, and output stages were considered. Crucially, we observed a systematic processing advantage in left visual hemifield stimuli presentation (i.e., initial right-hemisphere processing). Our findings corroborate the assumption that arithmetic fact retrieval is subserved by left-lateralized verbal/linguistic processing. Thereby, they suggest a distinction between unilateral left-hemispheric linguistic processing of arithmetic fact retrieval and bilateral number magnitude processing. Interestingly, however, our data present right-hemispheric processing advantages in identifying early processed visual symbolic numerical stimuli. (PsycInfo Database Record (c) 2022 APA, all rights reserved).