Differences between literates and illiterates on symbolic but not nonsymbolic numerical magnitude processing

The role of the intraparietal sulcus in numeracy: A review of parietal lesion cases

Prominent theories of numeracy link the intraparietal sulcus (IPS) to approximate representations of quantity that undergird basic math abilities. The goal of this review is to better understand the neural basis of mathematical cognition through the lens of acalculia, by identifying numeracy-focused single case studies of patients with parietal lesions and testing for causal relationships between numeracy impairments and the locus of parietal damage. A systematic literature review identified 27 single case studies with left parietal lesions and categorized administered tasks across four numeracy domains: Approximation, Calculation, Ordinality/Cardinality, and Transcoding. We compared published lesion images by drawing a sphere at the inferred center-of-mass and assigning each case to an anatomical group (IPS or Other Parietal damage) based on overlap with left IPS and original anatomical description. We performed Fisher's Exact Test to compare behavioral performance on each numeracy domain between the two groups. As an exploratory follow-up, we used Activation Likelihood Estimation (ALE) to identify sites of damage within parietal cortex preferentially associated with impairments in each domain. We found that Approximation impairments were significantly more frequent in the IPS group (p = .003). The exploratory ALE analysis revealed that only Approximation impairment cases significantly overlapped with the IPS, while impairments in other domains were localized to different regions of the parietal lobe. Based on the pattern of impairments shown across these cases, we conclude that damage to the left IPS is linked to impairments in approximation ability specifically. Our findings support theoretical claims linking IPS to magnitude representation, but do not provide evidence that IPS critically underpins performance across all numeracy tasks. Instead, our findings are more compatible with models of dissociable circuits of numerical processing within the parietal lobe.

Using the Australian Dietary Guidelines 2&5 education message in supermarket shopping trolleys to nudge shoppers to purchase more fruit and vegetables: A feasibility study using an intervention design

Fruit and vegetable (F&V) consumption is associated with a reduced risk of developing chronic diseases; however, only one in 16 Australian adults consume F&Vs at the recommended two servings of fruit and five servings of vegetables per day. What and how much people eat is influenced by their social and physical environments. Supermarkets are a key setting influencing food purchases, and as such, they can shape consumption patterns of F&Vs. Implementing effective strategies to increase F&V intake is crucial. The objective of this research was to test the feasibility of modifying shopper purchasing behaviour to purchase more F&Vs using the Australian Dietary Guidelines 2&5 education message covering one-half of the base of shopping trolleys. Placards giving the message that eating 2 fruits and 5 vegetables every day for good health were placed at the base of shopping trolleys as an educational nudge. Applying an intervention research design, 30 out of ~100 trolleys were fitted with the placards and shopper purchases were measured by collecting paper sales receipts to measure the weight (kg), total spending and F&V-specific spending (Australian dollars) for intervention versus control trolleys for one Saturday. We also conducted a short intercept survey that was administered independently from the research study day on non-trial shoppers. Shoppers who selected trolleys with the 2&5 education nudge placards (n = 101) purchased 1.66 kg less weight of F&Vs (Intervention: mean = 3.89 kg, SD = 3.40 kg, 95% CI = 3.21 kg, 4.56 kg, vs. Control: mean 5.55 kg, SD = 4.16 kg, 95% CI = 4.73 kg, 6.37 kg, p = 0.002) and spent less on F&Vs compared to shoppers in the control group (n = 102; Intervention: mean = $26.00, SD = $21.60, 95% CI = $21.78, $30.32 vs. Control: mean $36.00, SD = $27.00, 95% CI = $30.72, $42.36, p = 0.004). Intervention group shoppers also spent less in total spending between groups (Intervention: mean = $115.40, SD = $68.30, 95% CI = $101.95, $128.95 vs. Control: mean $151.30, SD = $79.40, 95% CI = $135.73, $166.93, p = 0.001). The 2&5 education nudge placard had the opposite effect as intended on shoppers' purchases to buy more F&Vs, although there may have been other differences between the intervention and the control groups since they were not randomised. Larger studies are required to elucidate and confirm these findings over the longer term.

The developmental relationship between nonsymbolic and symbolic fraction abilities

A fundamental research question in quantitative cognition concerns the developmental relationship between nonsymbolic and symbolic quantitative abilities. This study examined this developmental relationship in abilities to process nonsymbolic and symbolic fractions. There were 99 6th graders (M_age = 11.86 years), 101 10th graders (M_age = 15.71 years), and 102 undergraduate and graduate students (M_age = 21.97 years) participating in this study, and their nonsymbolic and symbolic fraction abilities were measured with nonsymbolic and symbolic fraction comparison tasks, respectively. Nonsymbolic and symbolic fraction abilities were significantly correlated in all age groups even after controlling for the ability to process nonsymbolic absolute quantity and general cognitive abilities, including working memory and inhibitory control. Moreover, the strength of nonsymbolic-symbolic correlations was higher in 6th graders than in 10th graders and adults. These findings suggest a weakened association between nonsymbolic and symbolic fraction abilities during development, and this developmental pattern may be related with participants' increasing proficiency in symbolic fractions.

Cultural factors weaken but do not reverse left-to-right spatial biases in numerosity processing: Data from Arabic and English monoliterates and Arabic-English biliterates

Directional response biases due to a conceptual link between space and number, such as a left-to-right hand bias for increasing numerical magnitude, are known as the SNARC (Spatial-Numerical Association of Response Codes) effect. We investigated how the SNARC effect for numerosities would be influenced by reading-writing direction, task instructions, and ambient visual environment in four literate populations exemplifying opposite reading-writing cultures-namely, Arabic (right-to-left script) and English (left-to-right script). Monoliterates and biliterates in Jordan and the U.S. completed a speeded numerosity comparison task to assess the directionality and magnitude of a SNARC effect in their numerosity processing. Monoliterates' results replicated previously documented effects of reading-writing direction and task instructions: the SNARC effect found in left-to-right readers was weakened in right-to-left readers, and the left-to-right group exhibited a task-dependency effect (SNARC effect in the smaller condition, reverse SNARC effect in the larger condition). Biliterates' results did not show a clear effect of environment; instead, both biliterate groups resembled English monoliterates in showing a left-to-right, task-dependent SNARC effect, albeit weaker than English monoliterates'. The absence of significant biases in all Arabic-reading groups (biliterates and Arabic monoliterates) points to a potential conflict between distinct spatial-numerical mapping codes. This view is explained in terms of the proposed Multiple Competing Codes Theory (MCCT), which posits three distinct spatial-numerical mapping codes (innate, cardinal, ordinal) during numerical processing-each involved at varying levels depending on individual and task factors.

Domain-general cognitive functions fully explained growth in nonsymbolic magnitude representation but not in symbolic representation in elementary school children

In this study, we aimed to compare developmental changes in nonsymbolic and symbolic magnitude representations across the elementary school years. For this aim, we used a four-wave longitudinal study with a one-year interval in schoolchildren in grades 1-4 in Russia and Kyrgyzstan (N = 490, mean age was 7.65 years at grade 1). The results of mixed-effects growth models revealed that growth in the precision of symbolic representation was larger than in the nonsymbolic representation. Moreover, growth in nonsymbolic representation was fully explained by growth in fluid intelligence (FI), visuospatial working memory (VSWM) and processing speed (PS). The analysis demonstrated that growth in nonsymbolic magnitude representation was significant only for pupils with a high level of FI and PS, whereas growth in precision of symbolic representation did not significantly vary across pupils with different levels of FI or VSWM.

Innate or Acquired? - Disentangling Number Sense and Early Number Competencies

The clinical profile termed developmental dyscalculia (DD) is a fundamental disability affecting children already prior to arithmetic schooling, but the formal diagnosis is often only made during school years. The manifold associated deficits depend on age, education, developmental stage, and task requirements. Despite a large body of studies, the underlying mechanisms remain dubious. Conflicting findings have stimulated opposing theories, each presenting enough empirical support to remain a possible alternative. A so far unresolved question concerns the debate whether a putative innate number sense is required for successful arithmetic achievement as opposed to a pure reliance on domain-general cognitive factors. Here, we outline that the controversy arises due to ambiguous conceptualizations of the number sense. It is common practice to use early number competence as a proxy for innate magnitude processing, even though it requires knowledge of the number system. Therefore, such findings reflect the degree to which quantity is successfully transferred into symbols rather than informing about quantity representation per se. To solve this issue, we propose a three-factor account and incorporate it into the partly overlapping suggestions in the literature regarding the etiology of different DD profiles. The proposed view on DD is especially beneficial because it is applicable to more complex theories identifying a conglomerate of deficits as underlying cause of DD.

Individual differences influence two-digit number processing, but not their analog magnitude processing: a large-scale online study

Symbolic magnitude comparison is one of the most well-studied cognitive processes in research on numerical cognition. However, while the cognitive mechanisms of symbolic magnitude processing have been intensively studied, previous studies have paid less attention to individual differences influencing symbolic magnitude comparison. Employing a two-digit number comparison task in an online setting, we replicated previous effects, including the distance effect, the unit-decade compatibility effect, and the effect of cognitive control on the adaptation to filler items, in a large-scale study in 452 adults. Additionally, we observed that the most influential individual differences were participants' first language, time spent playing computer games and gender, followed by reported alcohol consumption, age and mathematical ability. Participants who used a first language with a left-to-right reading/writing direction were faster than those who read and wrote in the right-to-left direction. Reported playing time for computer games was correlated with faster reaction times. Female participants showed slower reaction times and a larger unit-decade compatibility effect than male participants. Participants who reported never consuming alcohol showed overall slower response times than others. Older participants were slower, but more accurate. Finally, higher grades in mathematics were associated with faster reaction times. We conclude that typical experiments on numerical cognition that employ a keyboard as an input device can also be run in an online setting. Moreover, while individual differences have no influence on domain-specific magnitude processing-apart from age, which increases the decade distance effect-they generally influence performance on a two-digit number comparison task.

Data-driven heterogeneity in mathematical learning disabilities based on the triple code model

Many classifications of heterogeneity in mathematical learning disabilities (MLD) have been proposed over the past four decades, however no empirical research has been conducted until recently, and none of the classifications are derived from Triple Code Model (TCM) postulates. The TCM proposes MLD as a heterogeneous disorder, with two distinguishable profiles: a representational subtype and a verbal subtype. A sample of elementary school 3rd to 6th graders was divided into two age cohorts (3rd - 4th grades, and 5th - 6th grades). Using data-driven strategies, based on the cognitive classification variables predicted by the TCM, our sample of children with MLD clustered as expected: a group with representational deficits and a group with number-fact retrieval deficits. In the younger group, a spatial subtype also emerged, while in both cohorts a non-specific cluster was produced whose profile could not be explained by this theoretical approach.

Distinct influences of affective and cognitive factors on children's non-verbal and verbal mathematical abilities

Individual differences in children's math performance have been associated with math anxiety, attention problems, working memory (WM), and reading skills, but the mechanisms by which these factors jointly contribute to children's math achievement are unknown. Here, we use structural equation modeling to characterize the relation between these factors and their influence on non-verbal Numerical Operations (NO) and verbal Math Reasoning (MR) in 330 children (M=8.34years). Our findings indicate that WM plays a central role in both non-verbal NO and verbal MR, whereas math anxiety and reading comprehension have unique and more pronounced influences on MR, compared to NO. Our study elucidates how affective and cognitive factors distinctly influence non-verbal and verbal mathematical problem solving.

Differences in arithmetic performance between Chinese and German adults are accompanied by differences in processing of non-symbolic numerical magnitude

Human beings are assumed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information. The ANS is assumed to be fundamental to arithmetic learning and has been shown to be associated with arithmetic performance. It is, however, still a matter of debate whether better arithmetic skills are reflected in the ANS. To address this issue, Chinese and German adults were compared regarding their performance in simple arithmetic tasks and in a non-symbolic numerical magnitude comparison task. Chinese participants showed a better performance in solving simple arithmetic tasks and faster reaction times in the non-symbolic numerical magnitude comparison task without making more errors than their German peers. These differences in performance could not be ascribed to differences in general cognitive abilities. Better arithmetic skills were thus found to be accompanied by a higher speed of retrieving non-symbolic numerical magnitude knowledge but not by a higher precision of non-symbolic numerical magnitude representations. The group difference in the speed of retrieving non-symbolic numerical magnitude knowledge was fully mediated by the performance in arithmetic tasks, suggesting that arithmetic skills shape non-symbolic numerical magnitude processing skills.

New Evidence on Causal Relationship between Approximate Number System (ANS) Acuity and Arithmetic Ability in Elementary-School Students: A Longitudinal Cross-Lagged Analysis

Approximate number system (ANS) acuity and mathematical ability have been found to be closely associated in recent studies. However, whether and how these two measures are causally related still remain less addressed. There are two hypotheses about the possible causal relationship: ANS acuity influences mathematical performances, or access to math education sharpens ANS acuity. Evidences in support of both hypotheses have been reported, but these two hypotheses have never been tested simultaneously. Therefore, questions still remain whether only one-direction or reciprocal causal relationships existed in the association. In this work, we provided a new evidence on the causal relationship between ANS acuity and arithmetic ability. ANS acuity and mathematical ability of elementary-school students were measured sequentially at three time points within one year, and all possible causal directions were evaluated simultaneously using cross-lagged regression analysis. The results show that ANS acuity influences later arithmetic ability while the reverse causal direction was not supported. Our finding adds a strong evidence to the causal association between ANS acuity and mathematical ability, and also has important implications for educational intervention designed to train ANS acuity and thereby promote mathematical ability.

Cognitive and brain systems underlying early mathematical development

We review current debate regarding the core competencies that support early mathematics learning, focusing on the contributions of the inherent system for representing approximate magnitudes, and domain-general systems that facilitate learning across academic domains. The latter include the executive control system that enables explicit processing of quantitative symbols, such as Arabic numerals, and the logical problem-solving abilities (intelligence) that facilitate learning the relations among numerals. The neural systems that underlie these abilities, as related to mathematical learning, are also discussed, albeit briefly. We place the contributions of inherent quantitative abilities and domain-general mechanisms in an evolutionary context and provide some discussion as to how they interact during the learning of evolutionarily novel mathematics.

Shopper marketing nutrition interventions: Social norms on grocery carts increase produce spending without increasing shopper budgets

Objectives

We assessed the efficacy of an easy-to-implement shopper marketing nutrition intervention in a pilot and two additional studies to increase produce demand without decreasing store profitability or increasing shopper budgets.

Methods

We created grocery cart placards that detailed the number of produce items purchased (i.e., descriptive norm) at particular stores (i.e., provincial norm). The effect of these placards on produce spending was assessed across 971,706 individual person grocery store transactions aggregated by day. The pilot study designated a baseline period (in both control and intervention store) followed by installation of grocery cart placards (in the intervention store) for two weeks. The pilot study was conducted in Texas in 2012. In two additional stores, we designated baseline periods followed by 28 days of the same grocery cart placard intervention as in the pilot. Additional interventions were conducted in New Mexico in 2013.

Results

The pilot study resulted in a significant difference between average produce spending per day per person across treatment periods (i.e., intervention versus same time period in control) (16%) and the difference between average produce spending per day per person across stores in the control periods (4%); Furthermore, the same intervention in two additional stores resulted in significant produce spending increases of 12.4% and 7.5% per day per person respectively. In all stores, total spending did not change.

Conclusions

Descriptive and provincial social norm messages (i.e., on grocery cart placards) may be an overlooked tool to increase produce demand without decreasing store profitability and increasing shopper budgets.

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Using social norm-based messaging in grocery carts can increase produce demand.

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Shopper marketing nutrition interventions are sustainable for grocery stores.

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Shopper marketing nutrition interventions are sustainable for grocery shoppers.

Modeling individual differences in response time and accuracy in numeracy

In the study of numeracy, some hypotheses have been based on response time (RT) as a dependent variable and some on accuracy, and considerable controversy has arisen about the presence or absence of correlations between RT and accuracy, between RT or accuracy and individual differences like IQ and math ability, and between various numeracy tasks. In this article, we show that an integration of the two dependent variables is required, which we accomplish with a theory-based model of decision making. We report data from four tasks: numerosity discrimination, number discrimination, memory for two-digit numbers, and memory for three-digit numbers. Accuracy correlated across tasks, as did RTs. However, the negative correlations that might be expected between RT and accuracy were not obtained; if a subject was accurate, it did not mean that they were fast (and vice versa). When the diffusion decision-making model was applied to the data (Ratcliff, 1978), we found significant correlations across the tasks between the quality of the numeracy information (drift rate) driving the decision process and between the speed/accuracy criterion settings, suggesting that similar numeracy skills and similar speed-accuracy settings are involved in the four tasks. In the model, accuracy is related to drift rate and RT is related to speed-accuracy criteria, but drift rate and criteria are not related to each other across subjects. This provides a theoretical basis for understanding why negative correlations were not obtained between accuracy and RT. We also manipulated criteria by instructing subjects to maximize either speed or accuracy, but still found correlations between the criteria settings between and within tasks, suggesting that the settings may represent an individual trait that can be modulated but not equated across subjects. Our results demonstrate that a decision-making model may provide a way to reconcile inconsistent and sometimes contradictory results in numeracy research.

The association between higher education and approximate number system acuity

Humans are equipped with an approximate number system (ANS) supporting non-symbolic numerosity representation. Studies indicate a relationship between ANS-precision (acuity) and math achievement. Whether the ANS is a prerequisite for learning mathematics or if mathematics education enhances the ANS remains an open question. We investigated the association between higher education and ANS acuity with university students majoring in subjects with varying amounts of mathematics (mathematics, business, and humanities), measured either early (First year) or late (Third year) in their studies. The results suggested a non-significant trend where students taking more mathematics had better ANS acuity and a significant improvement in ANS acuity as a function of study length that was mainly confined to the business students. The results provide partial support for the hypothesis that education in mathematics can enhance the ANS acuity.

Spontaneous versus trained numerical abilities. A comparison between the two main tools to study numerical competence in non-human animals

A large body of experimental evidence shows that animals as diverse as mammals, birds, and fish are capable of processing numerical information. Considerable differences have been reported in some cases among species and a wide debate currently surrounds the issue of whether all vertebrates share the same numerical systems or not. Part of the problem is due to the fact that these studies often use different methods, a circumstance that potentially introduces confounding factors in a comparative analysis. In most studies, two main methodological approaches have been used: spontaneous choice tests and training procedures. The former approach consists of presenting to the subjects two groups of biologically-relevant stimuli (e.g., food items or social companions) differing in numerosity with the assumption that if they are able to discriminate between the two quantities, they are expected to spontaneously select the larger/smaller quantity. In the latter approach, subjects undergo extensive training in which some neutral stimuli (e.g., a quantity of dots) are associated with a reward and the capacity to learn a numerical rule is taken as evidence of numerical abilities. We review the literature on this topic, highlighting the relevance, and potential weaknesses in controlling confounding factors obtained with either approach.

Association between individual differences in non-symbolic number acuity and math performance: a meta-analysis

Many recent studies have examined the association between number acuity, which is the ability to rapidly and non-symbolically estimate the quantity of items appearing in a scene, and symbolic math performance. However, various contradictory results have been reported. To comprehensively evaluate the association between number acuity and symbolic math performance, we conduct a meta-analysis to synthesize the results observed in previous studies. First, a meta-analysis of cross-sectional studies (36 samples, N = 4705) revealed a significant positive correlation between these skills (r = 0.20, 95% CI = [0.14, 0.26]); the association remained after considering other potential moderators (e.g., whether general cognitive abilities were controlled). Moreover, a meta-analysis of longitudinal studies revealed 1) that number acuity may prospectively predict later math performance (r = 0.24, 95% CI = [0.11, 0.37]; 6 samples) and 2) that number acuity is retrospectively correlated to early math performance as well (r = 0.17, 95% CI = [0.07, 0.26]; 5 samples). In summary, these pieces of evidence demonstrate a moderate but statistically significant association between number acuity and math performance. Based on the estimated effect sizes, power analyses were conducted, which suggested that many previous studies were underpowered due to small sample sizes. This may account for the disparity between findings in the literature, at least in part. Finally, the theoretical and practical implications of our meta-analytic findings are presented, and future research questions are discussed.

Neurobiological underpinnings of math and reading learning disabilities

The primary goal of this review is to highlight current research and theories describing the neurobiological basis of math (MD), reading (RD), and comorbid math and reading disability (MD+RD). We first describe the unique brain and cognitive processes involved in acquisition of math and reading skills, emphasizing similarities and differences in each domain. Next we review functional imaging studies of MD and RD in children, integrating relevant theories from experimental psychology and cognitive neuroscience to characterize the functional neuroanatomy of cognitive dysfunction in MD and RD. We then review recent research on the anatomical correlates of MD and RD. Converging evidence from morphometry and tractography studies are presented to highlight distinct patterns of white matter pathways which are disrupted in MD and RD. Finally, we examine how the intersection of MD and RD provides a unique opportunity to clarify the unique and shared brain systems which adversely impact learning and skill acquisition in MD and RD, and point out important areas for future work on comorbid learning disabilities.

Semantic and Perceptual Processing of Number Symbols: Evidence from a Cross-linguistic fMRI Adaptation Study

The ability to process the numerical magnitude of sets of items has been characterized in many animal species. Neuroimaging data have associated this ability to represent nonsymbolic numerical magnitudes (e.g., arrays of dots) with activity in the bilateral parietal lobes. Yet the quantitative abilities of humans are not limited to processing the numerical magnitude of nonsymbolic sets. Humans have used this quantitative sense as the foundation for symbolic systems for the representation of numerical magnitude. Although numerical symbol use is widespread in human cultures, the brain regions involved in processing of numerical symbols are just beginning to be understood. Here, we investigated the brain regions underlying the semantic and perceptual processing of numerical symbols. Specifically, we used an fMRI adaptation paradigm to examine the neural response to Hindu-Arabic numerals and Chinese numerical ideographs in a group of Chinese readers who could read both symbol types and a control group who could read only the numerals. Across groups, the Hindu-Arabic numerals exhibited ratio-dependent modulation in the left IPS. In contrast, numerical ideographs were associated with activation in the right IPS, exclusively in the Chinese readers. Furthermore, processing of the visual similarity of both digits and ideographs was associated with activation of the left fusiform gyrus. Using culture as an independent variable, we provide clear evidence for differences in the brain regions associated with the semantic and perceptual processing of numerical symbols. Additionally, we reveal a striking difference in the laterality of parietal activation between the semantic processing of the two symbols types.