The effect of mathematics anxiety on the processing of numerical magnitude

In an effort to understand the origins of mathematics anxiety, we investigated the processing of symbolic magnitude by high mathematics-anxious (HMA) and low mathematics-anxious (LMA) individuals by examining their performance on two variants of the symbolic numerical comparison task. In two experiments, a numerical distance by mathematics anxiety (MA) interaction was obtained, demonstrating that the effect of numerical distance on response times was larger for HMA than for LMA individuals. These data support the claim that HMA individuals have less precise representations of numerical magnitude than their LMA peers, suggesting that MA is associated with low-level numerical deficits that compromise the development of higher level mathematical skills.     

The effect of mathematics anxiety on the processing of numerical magnitude

In an effort to understand the origins of mathematics anxiety, we investigated the processing of symbolic magnitude by high mathematics-anxious (HMA) and low mathematics-anxious (LMA) individuals by examining their performance on two variants of the symbolic numerical comparison task. In two experiments, a numerical distance by mathematics anxiety (MA) interaction was obtained, demonstrating that the effect of numerical distance on response times was larger for HMA than for LMA individuals. These data support the claim that HMA individuals have less precise representations of numerical magnitude than their LMA peers, suggesting that MA is associated with low-level numerical deficits that compromise the development of higher level mathematical skills.     

Reevaluating the two-representation model of numerical magnitude processing

One debate in mathematical cognition centers on the single-representation model versus the two-representation model. Using an improved number Stroop paradigm (i.e., systematically manipulating physical size distance), in the present study we tested the predictions of the two models for number magnitude processing. The results supported the single-representation model and, more importantly, explained how a design problem (failure to manipulate physical size distance) and an analytical problem (failure to consider the interaction between congruity and task-irrelevant numerical distance) might have contributed to the evidence used to support the two-representation model. This study, therefore, can help settle the debate between the single-representation and two-representation models.     

A test of a two-stage model of magnitude judgment

It has been suggested that the power law J = aⁿ, describing the relationship between numerical magnitude judgments and physical magnitudes, confounds a sensory or input function with an output function flawing to do with O’s use of numbers. Judged magnitudes of differences between stimuli offer some opportunity for separating these functions. We obtained magnitude judgments of differences between paired weights, as well as magnitude judgments of the weights making up the pairs. From the former we calculated simultaneously an input exponent and an output exponent, working upon Attneave’s assumption that both transformations are describable as power functions. The inferred input and output functions, in combination, closely predict the judgments of individual weights by the same Os. Although pooled data (geometric means of judgments) conform fairly well to a linear output function, individual data do not; i.e., individual Os deviate quite significantly fromlinearity and from one another in their use of numbers. Individual values of the inferred sensory exponent, k, show significantly better uniformity over Os than do values of the phenotypica! magnitude exponent previously found to describe interval judgments of weight.     

Automaticity for numerical magnitude of two-digit Arabic numbers in children

This paper examines the automatic processing of the numerical magnitude of two-digit Arabic numbers using a Stroop-like task in school-aged children. Second, third, and fourth graders performed physical size judgments on pairs of two-digit numbers varying on both physical and numerical dimensions. To investigate the importance of synchrony between the speed of processing of the numerical magnitude and the physical dimensions on the size congruity effect (SCE), we used masked priming: numerical magnitude was subliminally primed in half of the trials, while neutral priming was used in the other half. The results indicate a SCE in physical judgments, providing the evidence of automatic access to the magnitude of two-digit numbers in children. This effect was modulated by the priming type, as a SCE only appeared when the numerical magnitude was primed. This suggests that young children needed a relative synchronization of numerical and physical dimensions to access the magnitude of two-digit numbers automatically.     

A quantitative review of the guilty knowledge test

The guilty knowledge polygraph test (GKT; D. T. Lykken, 1959, 1960) is a psychophysiological method of identifying suspects with concealed information about a crime. A meta-analysis of 50 treatment groups drawn from 22 laboratory simulation studies (total N = 1,247) was conducted to provide a comprehensive estimate of GKT accuracy under controlled conditions. Electrodermal measures correctly identified 76% of participants with concealed knowledge and 83% of those without information. Informed participants were detected at rates significantly in excess of chance, with a mean weighted effect size of .57. Enactment of mock crimes increased the hit rate to 82%. The rates of false-positive error among noninformed treatment groups did not significantly exceed chance. Applications and research directions are discussed.     

Testwiseness: some evidence for the effect of personality testing on subsequent test results

The assumption is presented of the test-taker as a hypothesis-generating organism who can become "testwise." Testwiseness is defined as a stable skill, acquired by test-taking experiences, by which an individual can make test responses conform to a desired response pattern. Forty-three college students completed two forms of The Personality Research Form (PRF) and a rank ordering of their predicted personality need pattern. Results show significantly higher correlations of PRF predictions in the second administration. Analyses show PRF profiles, not predictions, to have been modified. Furthermore, high testwise subjects had higher needs for Understanding and Nurturance, and lower needs for Aggression and Defendence than low testwise persons. The importance of considering testwiseness, given trends in society encouraging access to psychological records, is discussed.     

The predictive value of numerical magnitude comparison for individual differences in mathematics achievement

Although it has been proposed that the ability to compare numerical magnitudes is related to mathematics achievement, it is not clear whether this ability predicts individual differences in later mathematics achievement. The current study addressed this question in typically developing children by means of a longitudinal design that examined the relationship between a number comparison task assessed at the start of formal schooling (mean age = 6 years 4 months) and a general mathematics achievement test administered 1 year later. Our findings provide longitudinal evidence that the size of the individual’s distance effect, calculated on the basis of reaction times, was predictively related to mathematics achievement. Regression analyses showed that this association was independent of age, intellectual ability, and speed of number identification.     

A scale for the psychological magnitude of number

A scale of the “psychological magnitude” of number was constructed from similarity ratings of the 45 number pairs that can be obtained from a set of 10 integers. A nonmetric analysis of these similarity ratings showed that “psychological number” was a power function of number.     

Grasping numbers: evidence for automatic influence of numerical magnitude on grip aperture

Previous research has shown that the fingers’ aperture during grasp is affected by the numerical values of numbers embedded in the grasped objects: Numerically larger digits lead to larger grip apertures than do numerically smaller digits during the initial stages of the grasp. The relationship between numerical magnitude and visuomotor control has been taken to support the idea of a common underlying neural system mediating the processing of magnitude and the computation of object size for motor control. The purpose of the present study was to test whether the effect of magnitude on motor preparation is automatic. During grasping, we asked participants to attend to the colors of the digit while ignoring numerical magnitude. The results showed that numerical magnitude affected grip aperture during the initial stages of the grasp, even when magnitude information was irrelevant to the task at hand. These findings suggest that magnitude affects grasping preparation in an automatic fashion.     

Supplementary knowledge of results

Children learned to respond differentially to four tones when correct responses were indicated by re-sounding the tone and flashing a signal lamp (simple knowledge of results). Correct responses were then made to advance a display counter. With this procedure, rate of response increased, but accuracy decreased. Mild punishment-points subtracted from the count-was then arranged for incorrect responses. Accuracy returned to or above its previous level. Response rate tended to remain above its initial level. These results indicate that when supplementary reinforcers are employed, precise contingencies must be arranged to ensure desired behavior.     

The representational space of numerical magnitude: Illusions of length

In recent years, a growing amount of evidence concerning the relationships between numerical and spatial representations has been interpreted, by and large, in favour of the mental number line hypothesis—namely, the analogue continuum where numbers are spatially represented (Dehaene, 1992 Dehaene, S. 1992. Varieties of numerical abilities. Cognition, 44: 1–42. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Dehaene, Piazza, Pinel, & Cohen, 2003 Dehaene, S., Piazza, M., Pinel, P. and Cohen, L. 2003. Three parietal circuits of number processing. Cognitive Neuropsychology, 20: 487–506. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). This numerical representation is considered the core of number meaning and, accordingly, needs to be accessed whenever numbers are semantically processed. The present study explored, by means of a length reproduction task, whether besides the activation of lateralized spatial codes, numerical processing modulates the mental representation of a horizontal spatial extension. Mis-estimations of length induced by Arabic numbers are interpreted in terms of a cognitive illusion, according to which the elaboration of magnitude information brings about an expansion or compression of the mental representation of spatial extension. These results support the hypothesis that visuo-spatial resources are involved in the representation of numerical magnitude.     

Timed magnitude comparisons of numerical and nonnumerical expressions of uncertainty

Two experiments involving paired comparisons of numerical and nonnumerical expressions of uncertainty are reported. Subjects were timed under two opposing sets of instructions ("choose higher probability" vs. "choose lower probability"). Numerical comparisons were consistently faster and easier than their nonnumerical counterparts. Consistent distance and congruity effects were obtained, illustrating that both numerical and nonnumerical expressions of uncertainty contain subjective magnitude information, and suggesting that similar processes are employed in manipulating and comparing numerical and verbal terms. To account for the general pattern of results obtained, Holyoak's reference point model (1978) was generalized by explicitly including the vagueness of the nonnumerical expressions. This generalized model is based on the notion that probability expressions can be represented by membership functions (Wallsten, Budescu, Rapoport, Zwick, & Forsyth, 1986) from which measures of location for each word, and measures of overlap for each pair can be derived. A good level of fit was obtained for this model at the individual level.     

The representational space of numerical magnitude: illusions of length

In recent years, a growing amount of evidence concerning the relationships between numerical and spatial representations has been interpreted, by and large, in favour of the mental number line hypothesis--namely, the analogue continuum where numbers are spatially represented (Dehaene, 1992; Dehaene, Piazza, Pinel, & Cohen, 2003). This numerical representation is considered the core of number meaning and, accordingly, needs to be accessed whenever numbers are semantically processed. The present study explored, by means of a length reproduction task, whether besides the activation of lateralized spatial codes, numerical processing modulates the mental representation of a horizontal spatial extension. Mis-estimations of length induced by Arabic numbers are interpreted in terms of a cognitive illusion, according to which the elaboration of magnitude information brings about an expansion or compression of the mental representation of spatial extension. These results support the hypothesis that visuo-spatial resources are involved in the representation of numerical magnitude.     

The effect of texture oil the magnitude of

The magnitude of simultaneous brightness contrast was measured while the coarseness of the textural overlay was varied. Remits from 10 Ss indicate that as the size of elements in the texture increases, the amount of obtained contrast decreases. An interpretation of these results in terms of the spread of lateral inhibitory effects is offered.     

A second type of magnitude effect: Reinforcer magnitude differentiates delay discounting between substance users and controls

Basic research on delay discounting, examining preference for smaller–sooner or larger–later reinforcers, has demonstrated a variety of findings of considerable generality. One of these, the magnitude effect, is the observation that individuals tend to exhibit greater preference for the immediate with smaller magnitude reinforcers. Delay discounting has also proved to be a useful marker of addiction, as demonstrated by the highly replicated finding of greater discounting rates in substance users compared to controls. However, some research on delay discounting rates in substance users, particularly research examining discounting of small‐magnitude reinforcers, has not found significant differences compared to controls. Here, we hypothesize that the magnitude effect could produce ceiling effects at small magnitudes, thus obscuring differences in delay discounting between groups. We examined differences in discounting between high‐risk substance users and controls over a broad range of magnitudes of monetary amounts ($0.10, $1.00, $10.00, $100.00, and $1000.00) in 116 Amazon Mechanical Turk workers. We found no significant differences in discounting rates between users and controls at the smallest reinforcer magnitudes ($0.10 and $1.00) and further found that differences became more pronounced as magnitudes increased. These results provide an understanding of a second form of the magnitude effect: That is, differences in discounting between populations can become more evident as a function of reinforcer magnitude.