Numerical Processing Tasks Research Articles

Put you in the problem: Effects of self-pronouns on mathematical problem-solving.

Self-cues such as personal pronouns are known to elicit processing biases, such as attention capture and prioritisation in working memory. This may impact the performance of tasks that have a high attentional load like mathematical problem-solving. Here, we compared the speed and accuracy with which children solved numerical problems that included either the self-cue "you," or a different character name. First, we piloted a self-referencing manipulation with N = 52, 7 to 11 year-olds, testing performance on addition and subtraction problems that had either a single referent ("You"/"Sam") or more than one referent. We took into account operation and positioning of the pronoun and also measured performance on attention and working memory tasks. We found a robust accuracy advantage for problems that included "you," regardless of how many characters were included. The accuracy advantage for problems with a self-pronoun was not statistically associated with individual differences in attention or working memory. In our main study (9 to 11 year-olds, N = 144), we manipulated problem difficulty by creating consistently and inconsistently worded addition and subtraction problems. We found significantly higher speed and accuracy for problems that included "you." However, this effect varied by task difficulty, with the self-pronoun effect being strongest in the most difficult inconsistently worded, subtraction problems. The advantage of problems with a self-pronoun was not associated with individual differences in working memory. These findings suggest that self-cues like the pronoun "you" can be usefully applied in numerical processing tasks, an effect that may be attributable to the effects of self-cues on attention.

The relationship between working memory for serial order and numerical development: A longitudinal study.

Despite numerous studies, the link between verbal working memory (WM) and calculation abilities remains poorly understood. The present longitudinal study focuses specifically on the role of serial order retention capacities, based on recent findings suggesting a link between ordinal processing in verbal WM and numerical processing tasks. Children were tested when they were in 3rd-year kindergarten (Time 1 [T1]), 1st grade (Time 2 [T2]), and 2nd grade of primary school (Time 3 [T3]), with WM tasks maximizing retention of serial order or item information, as well as with numerical judgment and calculation tasks. We observed that order WM measures at T1 provided a robust predictor of calculation abilities at T2 and T3. Numerical ordinal and magnitude judgment abilities were also associated with calculation abilities and this, independently of order WM abilities. This study highlights the important role of WM for order in early calculation acquisition, in addition to numerical ordinal and magnitude representations, and provides new perspectives for our understanding of the link between verbal WM and numerical abilities. (PsycINFO Database Record (c) 2014 APA, all rights reserved).

Development of numerical processing in children with typical and dyscalculic arithmetic skills—a longitudinal study

Numerical processing has been demonstrated to be closely associated with arithmetic skills, however, our knowledge on the development of the relevant cognitive mechanisms is limited. The present longitudinal study investigated the developmental trajectories of numerical processing in 42 children with age-adequate arithmetic development and 41 children with dyscalculia over a 2-year period from beginning of Grade 2, when children were 7; 6 years old, to beginning of Grade 4. A battery of numerical processing tasks (dot enumeration, non-symbolic and symbolic comparison of one- and two-digit numbers, physical comparison, number line estimation) was given five times during the study (beginning and middle of each school year). Efficiency of numerical processing was a very good indicator of development in numerical processing while within-task effects remained largely constant and showed low long-term stability before middle of Grade 3. Children with dyscalculia showed less efficient numerical processing reflected in specifically prolonged response times. Importantly, they showed consistently larger slopes for dot enumeration in the subitizing range, an untypically large compatibility effect when processing two-digit numbers, and they were consistently less accurate in placing numbers on a number line. Thus, we were able to identify parameters that can be used in future research to characterize numerical processing in typical and dyscalculic development. These parameters can also be helpful for identification of children who struggle in their numerical development.

Gender Differences in Children’s Arithmetic Performance Are Accounted for by Gender Differences in Language Abilities

Studies have shown that female children, on average, consistently outperform male children in arithmetic. In the research reported here, 1,556 pupils (8 to 11 years of age) from urban and rural regions in the greater Beijing area completed 10 cognitive tasks. Results showed that girls outperformed boys in arithmetic tasks (i.e., simple subtraction, complex multiplication), as well as in numerosity-comparison, number-comparison, number-series-completion, choice reaction time, and word-rhyming tasks. Boys outperformed girls in a mental rotation task. Controlling for scores on the word-rhyming task eliminated gender differences in arithmetic, whereas controlling for scores on numerical-processing tasks (number comparison, numerosity estimation, numerosity comparison, and number-series completion) and general cognitive tasks (choice reaction time, Raven’s Progressive Matrices, and mental rotation) did not. These results suggest that girls’ advantage in arithmetic is likely due to their advantage in language processing.

The Neuroscience of Time and Number: Untying the Gordian Knot

The Neuroscience of Time and Number: Untying the Gordian Knot

Cortical Areas Involved in Numerical Processing: An Intraoperative Electrostimulation Study

Background: Numerical processing is important in our everyday lives. However, very few attempts have been made to map the numerical processing function areas during lesion surgery. Objective: To identify and protect the cortical areas involved in numerical processing, the authors used the intraoperative brain mapping approach to study numerical processing areas in patients with parietal lobe tumors. Methods: During resection in patients with parietal lobe tumors, local anesthesia was administered and numerical processing mapping was performed. Our mapping procedures were conducted before glioma removal and included somatosensory, language and numerical processing tasks. We focused on the numerical processing task. Results: Different brain sites within the parietal lobe were detected to be specifically related to multiplication or subtraction processing. They displayed precise spatial distribution and overlapped with each other. No brain sites were found to be specifically related to numerical processing in the right hemisphere. Conclusions: To improve the quality of resection while minimizing the neurological deficits, functional boundaries of numerical processing areas should be considered during the removal of a parietal low-grade glioma. Moreover, only the left intraparietal sulcus is necessary for numerical processing, whereas the right intraparietal sulcus does not appear to be critically involved in numerical processing.

Executive function effects and numerical development in children: Behavioural and ERP evidence from a numerical Stroop paradigm

Most research on numerical development in children is behavioural, focusing on accuracy and response time in different problem formats. However, Temple and Posner (1998) used ERPs and the numerical distance task with 5-year-olds to show that the development of numerical representations is difficult to disentangle from the development of the executive components of response organization and execution. Here we use the numerical Stroop paradigm (NSP) and ERPs to study possible executive interference in numerical processing tasks in 6–8-year-old children. In the NSP, the numerical magnitude of the digits is task-relevant and the physical size of the digits is task-irrelevant. We show that younger children are highly susceptible to interference from irrelevant physical information such as digit size, but that access to the numerical representation is almost as fast in young children as in adults. We argue that the developmental trajectories for executive function and numerical processing may act together to determine numerical development in young children.

Basic numerical processing in left intraparietal sulcus (IPS) acalculia

We report a case of a patient, AD, who suffered from acalculia following an infarct restricted to the left IPS (intraparietal sulcus). AD showed deficits in an arithmetic battery and in basic numerical processing tasks. Compared to matched controls, AD showed a larger distance effect in numerical comparisons, an abnormal size congruity indicated by a lack of facilitation by irrelevant numerical values in physical comparisons, a deficiency in counting in comparison tasks, and a deficiency in subitizing in number naming tasks and comparison tasks. This suggests that the underlying deficit in AD is a difficulty in the perception and manipulation of quantity. Moreover, it indicates the essential role of the IPS in basic numerical processing.

Parietal rTMS distorts the mental number line: Simulating ‘spatial’ neglect in healthy subjects

Patients with left-sided visuospatial neglect, typically after damage to the right parietal lobe, show a systematic bias towards larger numbers when asked to bisect a numerical interval. This has been taken as further evidence for a spatial representation of numbers, perhaps akin to a mental number line with smaller numbers represented to the left and larger numbers to the right. Previously, contralateral neglect-like symptoms in physical line bisection have been induced in healthy subjects with repetitive transcranial magnetic stimulation (rTMS) over right posterior parietal lobe. Here we used rTMS over parietal and occipital sites in healthy subjects to investigate spatial representations in a number bisection task. Subjects were asked to name the midpoint of numerical intervals without calculating. On control trials subjects’ behaviour was similar to performance reported in physical line bisection experiments. Subjects underestimated the midpoint of the numerical interval. Repetitive transcranial magnetic stimulation produced representational neglect-like symptoms in number bisection when applied over right posterior parietal cortex (right PPC). Repetitive TMS over right PPC shifted the perceived midpoint of the numerical interval significantly to the right while occipital TMS had no effect on bisection performance. Our study therefore provides further evidence that subjects use spatial representations, perhaps akin to a mental number line, in basic numerical processing tasks. Furthermore, we showed that the right posterior parietal cortex is crucially involved in spatial representation of numbers.

The Expression Processor: A Pipelined, Multiple- Processor Architecture

A nem multiple-processor architecture is described that can exploit the instruction level concurrency in numerical processing tasks. The expression processor contains multiple processing elements (PE's), which can be configured either as an SIMD [8] array or as an expression tree pipeline. An expression tree is the parse tree conctructed by a compiler from an arithmetic or logical expression. The expression tree pipeline, or "X-Pipe," is a binary-tree networks of PE'S upon which expression tress are executed intact.A series of expression trees can be executed in pipelined fashion for enhanced concurrency. With this capability, the expression processor can exploit the concurrency in vector merges and scalar tasks, as well as conventional vector tasks. The architecture is designed for low-cost implementation using large-scale in (LSI) components.

Inner Product Computers

The inner product computer is a special-purpose computational unit intended to be used as an adjunct to a general-purpose digital computer to perform numerical processing tasks which previously exceeded the capacity of the general-purpose computer. The algorithmic structure of the inner product is briefly reviewed in the first section of this paper. Methods are described for computing the inner product of complex vectors with a series of four real inner products. Several hardware implementations of the inner product computer are described and then compared in terms of speed and complexity; a figure of merit is developed to simplify the comparison. The utility of this computational unit is demonstrated via the examination of a large-scale numerical problem, computerized three-dimensional x-ray reconstruction (computerized tomography) arising in the biomedical sciences. Finally, a comparison is given of the size of a general-purpose computer required to execute a large-scale processing task with that of an inner product computer to execute the same task. The inner product computer greatly reduces computational costs for the solution of a large class of problems, including computerized tomography, image restoration, weather forecasting, and economic modeling.