Processing Of Numerical Information Research Articles

Mathematical Anxiety and mathematical learning: Multidimensional approach

Research suggests that mathematical anxiety is a complex phenomenon related to mathematical achievement, developmental dyscalculia, strategies of numerical information processing, and negative emotional states. The goal of this currently on-going large-scale study is to implement a mixed method approach towards assessment of mathematical anxiety across the school grades. The methods include: a picture-based assessment; a questionnaire measuring attitudes towards mathematics; and a computerized test-battery measuring mathematics related cognitive processes. This mixed method approach addresses mathematical anxiety as a multidimensional, multi-faceted and dynamic manifestation of individual differences in a specific educational context. The research also allows exploring interrelations between non-cognitive and cognitive processes involved in mathematical anxiety. Here we present the results of the first wave of the investigation, involving data from 3 different age groups, assessed in several schools in Russia and the UK. The results suggest the importance of accounting for educational contexts in measuring and treating mathematical anxiety.

Price Number Relationships and Deal Processing Fluency: The Effects of Approximation Sequences and Number Multiples

This research investigates how the relationships among pieces of numerical information in a price promotional offer (i.e., regular price, sale price, absolute discount, and relative discount) affect deal processing fluency. Across four studies (including a field study involving purchase data collected from an online group-buying website), the authors show that when the numbers constitute an approximation sequence or are multiples of one another, deal processing fluency is increased, which influences deal liking and ultimately has an impact on consumers’ price promotion predilection. In addition, this article demonstrates that when consumers are not highly motivated to process numerical information, they may choose deals that offer less economic value but feature a combination of numbers that they can more fluently process. This research has important implications for the type of numerical information marketers should include in price promotional offers.

How Disclosure Features of Corporate Social Responsibility Reports Interact with Investor Numeracy to Influence Investor Judgments

Firms’ Corporate Social Responsibility (CSR) reports typically frame their strategies in terms of either community or global efforts (i.e., “strategy frame”). Further, the style used to depict CSR performance in reports often highlights either pictures or words (i.e., “presentation style”). These two prominent disclosure features of CSR reports promote a natural fit or misfit in the focus (relatively low-level or high-level focus) investors adopt when thinking about the firm and its CSR efforts. Further, these disclosure features likely have different effects on investors depending on their numeracy or, in other words, the way that they naturally process numerical information. In this study we predict and find that a fit between the strategy frame and the presentation style of a firm’s CSR report causes less numerate investors to be more willing to invest than when a fit is not present. Specifically, we find that a fit leads less numerate investors to experience subjective feelings of processing fluency and, in turn, positive affect that serves as a cue that the positive CSR performance information can be relied upon, which positively influences willingness to invest. Our results have implications for both CSR reports as well as other types of firm disclosures that increasingly vary along similar disclosure characteristics. Our results also contribute to both the growing literature on presentation effects in accounting, as well as the broader business literature on CSR reporting.

Leftmost-digit-bias in an enumerated public sector? An experiment on citizens’ judgment of performance information

AbstractNumerical performance information is increasingly important to political decision-making in the public sector. Some have suggested that biases in citizens’ processing of numerical information can be exploited by politicians to skew citizens’ perception of performance. I report on an experiment on how citizens evaluate numerical performance information from a public school context. The experiment is conducted with a large and diverse sample of the Danish population (N=1156). The analysis shows a strong leftmost-digit-bias in citizens’ evaluation of school grading information. Thus, very small changes in reported average grades, which happen to shift the leftmost grade digit, can lead to very large shifts in citizens’ evaluation of performance. The rightmost digit on the grade is almost fully ignored.

The Countability Effect: Comparative versus Experiential Reactions to Reward Distributions

The effect of inequity on satisfaction—people who are underbenefited are less satisfied than those who are overbenefited—is robust across many domains. However, various factors may moderate this effect, and a key perspective centers on value sensitivity. The present research demonstrates that countability (how easily a product or service can be counted using simple whole numbers) feeds into value sensitivity and thus moderates the impact of inequity on satisfaction. Across nine experiments, we show that when rewards are less easily counted, the effect of inequity on satisfaction is diminished. Further, this effect is rooted to a mechanism in which less countable rewards shift cognitive focus from value comparison to consumption experience. This research contributes to literature on value sensitivity, comparative thinking, numerical information processing, fairness, and happiness.

Numerical processing efficiency improved in experienced mental abacus children

Experienced mental abacus (MA) users are able to perform mental arithmetic calculations with unusual speed and accuracy. However, it remains unclear whether their extraordinary gains in mental arithmetic ability are accompanied by an improvement in numerical processing efficiency. To address this question, the present study, using a numerical Stroop paradigm, examined the numerical processing efficiency of experienced MA children, MA beginners and their respective peers. The results showed that experienced MA children were less influenced than their peers by physical size information when intentionally processing numerical magnitude information, but they were more influenced than their peers by numerical magnitude information when intentionally processing physical size information. By contrast, MA beginners and peers showed no differences in the reciprocal influences between the two conflicting dimensions. These findings indicate that substantial gains in numerical processing efficiency could be achieved through long-term intensive MA training. Implications for numerical magnitude representations and for training students with mathematical learning disabilities are discussed.

Dyscalculia: Characteristics, Causes, and Treatments

Developmental Dyscalculia (DD) is a learning disorder affecting the ability to acquire school-level arithmetic skills, affecting approximately 3-6% of individuals. Progress in understanding the root causes of DD and how best to treat it have been impeded by lack of widespread research and variation in characterizations of the disorder across studies. However, recent years have witnessed significant growth in the field, and a growing body of behavioral and neuroimaging evidence now points to an underlying deficit in the representation and processing of numerical magnitude information as a potential core deficit in DD. An additional product of the recent progress in understanding DD is the resurgence of a distinction between ‘primary’ and ‘secondary’ developmental dyscalculia. The first appears related to impaired development of brain mechanisms for processing numerical magnitude information, while the latter refers to mathematical deficits stemming from external factors such as poor teaching, low socio-economic status, and behavioral attention problems or domain-general cognitive deficits. Increased awareness of this distinction going forward, in combination with longitudinal empirical research, offers great potential for deepening our understanding of the disorder and developing effective educational interventions.

Language‐Switching Costs in Bilingual Mathematics Learning

Behavioral studies on bilingual learning have revealed cognitive costs (lower accuracy and/or higher processing time) when the language of application differs from the language of learning. The aim of this functional magnetic resonance imaging (fMRI) study was to provide insights into the cognitive underpinnings of these costs (so‐called language‐switching costs) in mathematics. Twenty‐nine bilingual adults underwent a 4‐day arithmetic training in one language, followed by an fMRI test session in which they had to solve the trained problems in both languages. Language‐switching costs were accompanied by increased activation in areas associated with magnitude processing (intraparietal sulcus), visuo‐spatial imagery (precuneus), numerical stimulus recognition (fusiform gyrus) and executive functions (frontal areas). These findings suggest that language‐switching costs in arithmetic are due to additional numerical information processing. Bilingual education programs need to take these findings into account to reduce language‐switching costs in order to fully exploit the potential of bilingual learning.

Eating breakfast enhances the efficiency of neural networks engaged during mental arithmetic in school-aged children

To determine the influence of a morning meal on complex mental functions in children (8–11y), time–frequency analyses were applied to electroencephalographic (EEG) activity recorded while children solved simple addition problems after an overnight fast and again after having either eaten or skipped breakfast. Power of low frequency EEG activity [2Hertz (Hz) bands in the 2–12Hz range] was determined from recordings over frontal and parietal brain regions associated with mathematical thinking during mental calculation of correctly answered problems. Analyses were adjusted for background variables known to influence or reflect the development of mathematical skills, i.e., age and measures of math competence and math fluency. Relative to fed children, those who continued to fast showed greater power increases in upper theta (6–8Hz) and both alpha bands (8–10Hz; 10–12Hz) across sites. Increased theta suggests greater demands on working memory. Increased alpha may facilitate task-essential activity by suppressing non-task-essential activity. Fasting children also had greater delta (2–4Hz) and greater lower-theta (4–6Hz) power in left frontal recordings—indicating a region-specific emphasis on both working memory for mental calculation (theta) and activation of processes that suppress interfering activity (delta). Fed children also showed a significant increase in correct responses while children who continued to fast did not. Taken together the findings suggest that neural network activity involved in processing numerical information is functionally enhanced and performance is improved in children who have eaten breakfast, whereas greater mental effort is required for this mathematical thinking in children who skip breakfast.

Symbolic and non symbolic numerical representation in adults with and without developmental dyscalculia

BackgroundThe question whether Developmental Dyscalculia (DD; a deficit in the ability to process numerical information) is the result of deficiencies in the non symbolic numerical representation system (e.g., a group of dots) or in the symbolic numerical representation system (e.g., Arabic numerals) has been debated in scientific literature. It is accepted that the non symbolic system is divided into two different ranges, the subitizing range (i.e., quantities from 1-4) which is processed automatically and quickly, and the counting range (i.e., quantities larger than 4) which is an attention demanding procedure and is therefore processed serially and slowly. However, so far no study has tested the automaticity of symbolic and non symbolic representation in DD participants separately for the subitizing and the counting ranges.MethodsDD and control participants undergo a novel version of the Stroop task, i.e., the Enumeration Stroop. They were presented with a random series of between one and nine written digits, and were asked to name either the relevant written digit (in the symbolic task) or the relevant quantity of digits (in the non symbolic task) while ignoring the irrelevant aspect.ResultDD participants, unlike the control group, didn't show any congruency effect in the subitizing range of the non symbolic task.ConclusionThese findings suggest that DD may be impaired in the ability to process symbolic numerical information or in the ability to automatically associate the two systems (i.e., the symbolic vs. the non symbolic). Additionally DD have deficiencies in the non symbolic counting range.

Subitizing and visual short-term memory in human and non-human species: a common shared system?

Subitizing and visual short-term memory in human and non-human species: a common shared system?

Proficiency in a second language influences the processing of number words

We evaluated whether proficiency in a second language (L2) influenced the processing of numerical information. In Experiment 1, two groups of German/English bilinguals, one less proficient in English (L2) and the other more proficient in L2, performed two-digit number comparison tasks while the unit–decade compatibility was evaluated. All participants presented compatibility effect with Arabic digits regardless of their L2 proficiency. However, when bilinguals with less proficiency in L2 performed verbal number comparison tasks they showed regular compatibility effect in German and reverse compatibility effect in English, whereas more proficient bilinguals did not show compatibility effects in either German or English. In Experiment 2, the same pattern of results was obtained with highly proficient bilinguals after controlling their working memory span. These results indicate that L2 proficiency influences the processing of two-digit number words.

Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made “ordered” or “non-ordered” judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.

Factors Influencing Cancer Risk Perception in High Risk Populations: A Systematic Review

BackgroundPatients at higher than average risk of heritable cancer may process risk information differently than the general population. However, little is known about clinical, demographic, or psychosocial predictors that may impact risk perception in these groups. The objective of this study was to characterize factors associated with perceived risk of developing cancer in groups at high risk for cancer based on genetics or family history.MethodsWe searched Ovid MEDLINE, Ovid Embase, Ovid PsycInfo, and Scopus from inception through April 2009 for English-language, original investigations in humans using core concepts of "risk" and "cancer." We abstracted key information and then further restricted articles dealing with perceived risk of developing cancer due to inherited risk.ResultsOf 1028 titles identified, 53 articles met our criteria. Most (92%) used an observational design and focused on women (70%) with a family history of or contemplating genetic testing for breast cancer. Of the 53 studies, 36 focused on patients who had not had genetic testing for cancer risk, 17 included studies of patients who had undergone genetic testing for cancer risk. Family history of cancer, previous prophylactic tests and treatments, and younger age were associated with cancer risk perception. In addition, beliefs about the preventability and severity of cancer, personality factors such as "monitoring" personality, the ability to process numerical information, as well as distress/worry also were associated with cancer risk perception. Few studies addressed non-breast cancer or risk perception in specific demographic groups (e.g. elderly or minority groups) and few employed theory-driven analytic strategies to decipher interrelationships of factors.ConclusionsSeveral factors influence cancer risk perception in patients at elevated risk for cancer. The science of characterizing and improving risk perception in cancer for high risk groups, although evolving, is still relatively undeveloped in several key topic areas including cancers other than breast and in specific populations. Future rigorous risk perception research using experimental designs and focused on cancers other than breast would advance the field.

A Novel Marketing Strategy Based on Information Technology

Marketing is the process of performing market research, selling products and/or services to customers and promoting them via advertising to further enhance sales. It generates the strategy that underlies sales techniques, business communication, and business developments. Information technology is the acquisition, processing, storage and dissemination of vocal, pictorial, textual and numerical information by a microelectronics-based combination of computing and telecommunications.

Symbolic number: the integration of magnitude and spatial representations in children aged 6 to 8 years.

The process of learning symbolic Arabic digits in early childhood requires that magnitude and spatial information integrates with the concept of symbolic digits. Previous research has separately investigated the development of automatic access to magnitude and spatial information from symbolic digits. However, developmental trajectories of symbolic number knowledge cannot be fully understood when considering components in isolation. In view of this, we have synthesized the existing lines of research and tested the use of both magnitude and spatial information with the same sample of British children in Years 1, 2, and 3 (6–8 years of age). The physical judgment task of the numerical Stroop paradigm demonstrated that automatic access to magnitude was present from Year 1 and the distance effect signaled that a refined processing of numerical information had developed. Additionally, a parity judgment task showed that the onset of the spatial–numerical association of response codes effect occurs in Year 2. These findings uncover the developmental timeline of how magnitude and spatial representations integrate with symbolic number knowledge during early learning of Arabic digits and resolve inconsistencies between previous developmental and experimental research lines.

Numerical information processing under the global rule expressed by the Euler–Riemann ζ function defined in the complex plane

When nonzero, the ζ function is intimately connected with numerical information processing. Two other functions play a key role, namely, η(s)=∑n≥1(-1)n+1/ns and λ(s)=∑(n≥0)1/(2n+1)s. The paper opens on a survey of some of the seminal work of Euler [Mémoires Acad. Sci., Berlin 1768, 83 (1749)] and of the amazing theorem by Voronin [Math. USSR, Izv. 9, 443 (1975)] Then, as a follow-up of Chatelin [Qualitative Computing. A Computational Journey into Nonlinearity (World Scientific, Singapore, in press)], we present a fresh look at the triple (η,ζ,λ) which suggests an elementary analysis based on the distances of the three complex numbers z, z/2, and 2/z to 0 and 1. This metric approach is used to contextualize any nonlinear computation when it is observed at a point describing a complex plane. The results applied to ζ, η, and λ shed a new epistemological light about the critical line. The suggested interpretation related to ζ carries computational significance.

The Long and Short of It: Why Are Stocks with Shorter Runs Preferred?

This article examines how consumers process graphical financial information to estimate risk. We propose that consumers sample the local maxima and minima of a graph to infer the variation around a trend line, which is used to estimate risk. The local maxima and minima are more extreme the higher the run length of the stocks (the consecutive number of upward or downward movements of a price series with identical mean, variance, skewness, and kurtosis). Three experiments show that this leads to stocks with higher run lengths being perceived as riskier: the run-length effect. Importantly, the run-length effect is greater for investors who are more educated, are employed full time, trade more frequently, have had longer experience trading, and trade a wider range of financial instruments. Implications for the communication of financial products, public policy, and consumer welfare are discussed, as are theoretical implications for the processing of visual and financial information and behavioral finance.

Bidirectionality in Synesthesia

Color-grapheme synesthetes automatically perceive achromatic numbers as colored (e.g., 7 is turquoise). Up until recently, synesthesia was believed to be unidirectional. For instance, the number 7 gives rise to the percept of turquoise but the perception of turquoise does not trigger the number 7. However, some recent studies argue for bidirectional connections Cohen Kadosh et al., 2005; Johnson et al., 2007; Knoch et al., 2005). In this study, a multiplication verification task (e.g., 7 x 2 = 14, true/false?) was used to test bidirectionality. In agreement with previous studies we observed that the presentation of colors evokes numerical magnitudes. The current findings add two important notions to previous studies: (a) The influence of color on the processing of numerical information can be extended to multiplication verification tasks and (b) The perception of color can both facilitate and interfere with the processing of digit-related information.

On the evolution of calculation abilities

Some numerical knowledge, such as the immediate recognition of small quantities, is observed in animals. The development of arithmetical abilities found in man's evolution as well as in child's development represents a long process following different stages. Arithmetical abilities are relatively recent in human history and are clearly related with counting, i.e., saying aloud a series of number words that correspond to a collection of objects. Counting probably began with finger sequencing, and that may explain the 10-base found in most numerical systems. From a neuropsychological perspective, there is a strong relationship between numerical knowledge and finger recognition, and both are impaired in cases of left posterior parietal damage (angular or Gerstmann's syndrome). Writing numbers appeared earlier in human history than written language. Positional digit value is clearly evident in Babylonians, and around 1,000 BC the zero was introduced. Contemporary neuroimaging techniques, specifically fMRI, have demonstrated that the left parietal lobe, particularly the intraparietal sulcus, is systematically activated during a diversity of tasks; other areas, particularly the frontal lobe, are also involved in processing numerical information and solving arithmetical problems. It can be conjectured that numerical abilities continue evolving due to advances in mathematical knowledge and the introduction of new technologies.