Fact Retrieval Research Articles

Event-related potentials findings differ between children and adults during arithmetic-fact retrieval

Some cognitive abilities of arithmetical calculation depend on retrieval of arithmetic facts from long-term memory. Arithmetic-fact retrieval has been studied in adults through Event-Related Potentials (ERP) experiments. Such information in children, however, has been scarce. It has been reported that from the age of 9 years, children employ a memory retrieval strategy for solving simple multiplication problems. The present study compared arithmetical-fact retrieval in children and adults while they were being subjected to ERP recording. The subjects were asked to make judgments about solutions to simple multiplication problems. Both groups of participants displayed the so-called arithmetic N400 effect for incorrect solutions relative to correct solutions. Adults showed a posterior N400 effect, while children showed a widely distributed N400 effect. Children displayed a larger amplitude and longer latency arithmetic N400 component than adults; this observation could be due to children exerting greater effort involving more widespread cortical activation than adults to solve the experimental problems. The Late Positive Component (LPC), which follows the arithmetic N400 and has been described previously in adult subjects, was observed in the present adult subjects, but was present in children only for correct solutions. These results may indicate that, relative to adults, children showed slower memory retrieval and a different pattern of a verification mechanism for correct and incorrect solutions.

Event-related potentials for simple arithmetic in Arabic digits and Chinese number words: a study of the mental representation of arithmetic facts through notation and operation effects

To test whether the retrieval of arithmetic facts is independent of numerical notations, this study investigated the event-related potentials elicited by single-digit addition and multiplication problems in Arabic digits and Chinese number words. The results showed that, in comparison with addition, multiplication elicited a greater N300-like component at the left anterior electrodes and greater late positive potentials at the right posterior electrodes, regardless of numerical notations. The operation effects lasted from 250 to 900 ms for Arabic digits, but from 250 to 1400 ms for Chinese number words when participants were asked to respond only to false arithmetic equations (experiment one), and lasted from 350 to 1400 ms for Arabic digits and Chinese number words when participants were asked to respond to both true and false arithmetic equations (experiment two). The consistency in the operation effects in ERPs (i.e., a dissociation of brain organization for different arithmetic operations) for different number notations suggests that mental representation and retrieval of arithmetic facts may be relatively independent of numerical notations.

Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders

The contribution of the three core components of working memory (WM) to the development of mathematical skills in young children is poorly understood. The relation between specific WM components and Numerical Operations, which emphasize computation and fact retrieval, and Mathematical Reasoning, which emphasizes verbal problem solving abilities in 48 2nd and 50 3rd graders was assessed using standardized WM and mathematical achievement measures. For 2nd graders, the central executive and phonological components predicted Mathematical Reasoning skills; whereas the visuo-spatial component predicted both Mathematical Reasoning and Numerical Operations skills in 3rd graders. This pattern suggests that the central executive and phonological loop facilitate performance during early stages of mathematical learning whereas visuo-spatial representations play an increasingly important role during later stages. We propose that these changes reflect a shift from prefrontal to parietal cortical functions during mathematical skill acquisition. Implications for learning and individual differences are discussed.

Querying for provenance, trust, uncertainty and other meta knowledge in RDF

The Semantic Web is based on accessing and reusing RDF data from many different-sources, which one may assign different levels of authority and credibility. Existing Semantic Web query languages, like SPARQL, have targeted the retrieval, combination and re-use of facts, but have so far ignored all aspects of meta knowledge, such as origins, authorship, recency or certainty of data. In this paper, we present an original, generic, formalized and implemented approach for managing many dimensions of meta knowledge, like source, authorship, certainty and others. The approach re-uses existing RDF modeling possibilities in order to represent meta knowledge. Then, it extends SPARQL query processing in such a way that given a SPARQL query for data, one may request meta knowledge without modifying the query proper. Thus, our approach achieves highly flexible and automatically coordinated querying for data and meta knowledge, while completely separating the two areas of concern.

The impact of visuo-spatial number forms on simple arithmetic

Number forms, conscious visuo-spatial representations of the sequence of numbers, are found in around 12% of the population. However, their contribution to numerical cognition is not well understood. In this study we contrast the speeded performance of individuals with number forms versus controls on single digit multiplication, subtraction and addition. Previous research has suggested that multiplication may rely more on retrieval of verbal facts whereas subtraction relies more on online calculation using a putatively spatial ‘mental number line’. If people with number forms rely more heavily on visual-spatial strategies than verbal ones then we hypothesised that multiplication may be disproportionately affected by this strategy relative to subtraction, and this was found.

Mapping arithmetic problem solving strategies in the brain: The role of the left angular gyrus in arithmetic fact retrieval

Mapping arithmetic problem solving strategies in the brain: The role of the left angular gyrus in arithmetic fact retrieval

Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia

The underlying neural mechanisms of developmental dyscalculia (DD) are still far from being clearly understood. Even the behavioral processes that generate or influence this heterogeneous disorder are a matter of controversy. To date, the few studies examining functional brain activation in children with DD mainly focus on number and counting related tasks, whereas studies on more general cognitive domains that are involved in arithmetical development, such as working memory are virtually absent. There are several studies showing a close relationship between DD and spatial working memory [Camos, V. (2008). Low working memory capacity impedes both efficiency and learning of number transcoding in children. Journal of Experimental Child Psychology, 99(1), 37-57; McLean, J. F., & Hitch, G. J. (1999). Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology, 74(3), 240-260; Rosselli, M., Matute, E., Pinto, N., & Ardila, A. (2006). Memory abilities in children with subtypes of dyscalculia. Developmental Neuropsychology, 30(3), 801-818; Siegel, L. S., & Ryan, E. B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60(4), 973-980]. The relationship between these two mechanisms is still matter of debate, but this study follows the assumption that poor spatial working memory capacity may hinder the acquisition of spatial number representations in children with DD [Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345-362; von Aster, M., & Shalev, R. S. (2007). Number development and developmental dyscalculia. Developmental Medicine and Child Neurology, 49(11), 868-873]. Using functional MRI the current study compares brain activity associated with spatial working memory processes in 8-10-year-old children with DD and normally achieving controls. Both groups showed significant spatial working memory related activity in a network including occipital and parietal regions. Children with DD showed weaker neural activation compared to the control group during a spatial working memory task in the right intraparietal sulcus (IPS), the right insula and the right inferior frontal lobe. Performance tests outside the scanner showed impaired working memory proficiency in children with DD. Bringing behavioral performance and neural activity together we found significant correlations of right IPS activity with performance on the verbal digit span forward and the spatial Corsi Block Tapping test. Our findings demonstrate for the first time an involvement of spatial working memory processes in the neural underpinnings of DD. These poor spatial working memory processes may inhibit the formation of spatial number representations (mental numberline) as well as the storage and retrieval of arithmetical facts.

Oscillatory EEG correlates of arithmetic strategy use in addition and subtraction

Adults use different strategies in mental arithmetic. For example, they directly retrieve the answer from memory or calculate by means of procedural strategies. Despite growing insight into the hemodynamic and electrophysiological correlates of these strategies, the functional changes in the oscillatory brain dynamics during the use of these strategies remain unknown. In the present high-resolution electroencephalography (EEG) study, we analysed event-related synchronisation (ERS) and desynchronisation (ERD) in the theta and alpha bands while participants solved addition and subtraction problems, which displayed a high probability of retrieval or procedural strategy use. Findings revealed that arithmetic fact retrieval is reflected in left-hemispheric ERS in the theta band, whereas the application of procedural strategies is accompanied by bilateral parietooccipital ERD in the alpha band. The topographical and frequency specificity of the strategy effects provides a start for the development of electrophysiological indices of strategy use in arithmetic.

Retrieval of Simple Addition Facts

There exists a substantial number of studies that have identified a subset of low-achieving mathematics students who do not develop a reliance on retrieval for simple addition but who continue to use a counting strategy to solve these problems. There are few studies, however, that have focused on how retrieval of simple addition facts may be improved. This study employed a combined methodological approach to examine the effect extended practice had on increasing a reliance on retrieval for simple addition. An intervention aimed at improving the efficiency of extended practice was also piloted. Although most students improved with extended practice, the extent of improvement was not practical for all students and the intervention did not generally improve the effectiveness of extended practice. The findings emphasize the critical importance of continuing such research and draw attention to the complexities involved in addressing retrieval difficulties for simple addition.

Dissociating the solution processes of small, large, and zero multiplications by means of fMRI

The present study investigated the neuroanatomical basis of different solution processes in single-digit multiplication by means of fMRI. Sixteen participants silently produced the solution of three distinct types of multiplication, i.e., problems involving zero (e.g., 3 ⁎ 0), small (e.g., 2 ⁎ 4), or large operands (e.g., 8 ⁎ 7). Zero and small problems are assumed to be solved by rule application and fact retrieval, respectively, and problems with large operands sometimes involve backup strategies when direct retrieval is not sufficient. Small problems, when compared with a high-level baseline not requiring any kind of calculation, activated a network of parietal, subcortical, and frontal areas. This activation pattern supports the hypothesis that arithmetic fact retrieval is mediated by a verbal processing loop including the angular gyrus and the basal ganglia. Problems with larger operands showed increased activation in the anterior cingulate cortex, SMA, and the left inferior frontal gyrus, which could reflect increased conflict during the fact-retrieval process, but also higher demands for controlling and coordinating multiple processing steps when a problem cannot be solved by direct retrieval. Zero problems, in comparison to multiplications with small operands, activated the caudate nucleus and the right inferior frontal cortex, showing that rule application is separable from fact retrieval on a neuroanatomical level, too.

Effects of Fact Retrieval Tutoring on Third‐Grade Students with Math Difficulties with and without Reading Difficulties

The purpose of this study was to assess the efficacy of fact retrieval tutoring as a function of math difficulty (MD) subtype, that is, whether students have MD alone (MD-only) or have concurrent difficulty with math and reading (MDRD). Third graders (n = 139) at two sites were randomly assigned, blocking by site and MD subtype, to four tutoring conditions: fact retrieval practice, conceptual fact retrieval instruction with practice, procedural computation/estimation instruction, and control (no tutoring). Tutoring occurred for 45 sessions over 15weeks for 15-25 minutes per session. Results provided evidence of an interaction between tutoring condition and MD subtype status for assessment of fact retrieval. For MD-only students, students in both fact retrieval conditions achieved comparably and outperformed MD-only students in the control group as well as those in the procedural computation/estimation instruction group. By contrast, for MDRD students, there were no significant differences among intervention conditions.

Fact learning in complex arithmetic and figural‐spatial tasks: The role of the angular gyrus and its relation to mathematical competence

Neuroimaging studies have revealed a strong link between mental calculation and the angular gyrus (AG) which has been interpreted to reflect arithmetic fact retrieval. Moreover, a stronger AG activation in individuals with higher mathematical competence has been reported. The present fMRI study investigates the specificity of the AG for arithmetic fact learning and the interplay between training and mathematical competence on brain activation. Adults of lower and higher mathematical competence underwent a five-day training on sets of complex multiplication and figural-spatial problems. In the following fMRI test session, trained and untrained problems were presented. Similar training effects were observed in both problem types, consisting of AG activation increases bilaterally and wide-spread activation decreases in frontal and parietal regions. This finding indicates that the AG is not specifically involved in the learning of arithmetic facts. Competence-related differences in the AG only emerged in untrained but not in trained multiplication problems. The relation between AG activation and mathematical competence in arithmetic problem solving therefore seems to be due to differences in arithmetic fact retrieval which can be attenuated through training.

Inhibition and Retrieval of Facts in Young and Older Adults

Inhibition is considered to have an important role in memory retrieval. However, many experimental results suggest that its efficiency declines with aging. In this study, the authors tested this hypothesis by using the retrieval-practice task. The retrieval-induced forgetting (RIF) observed with this paradigm is normally explained in terms of inhibition. Young (mean age 21.5 years) and older (mean age 71.6 years) adults studied sets of four shared-subject sentences. A retrieval-practice phase required participants to repeatedly recall a subset of the studied sentences. In the final test, participants were provided item-specific cues and told to recall all the studied sentences. RIF was similar for both age groups, suggesting comparable inhibitory efficiency in young and older adults.

Mathematical learning disabilities in children with 22q11.2 deletion syndrome: A review

Mathematical learning disabilities (MLD) occur frequently in children with specific genetic disorders, like Turner syndrome, fragile X syndrome and neurofibromatosis. This review focuses on MLD in children with chromosome 22q11.2 deletion syndrome (22q11DS). This syndrome is the most common known microdeletion syndrome with a prevalence of at least 1:4000 to 1:6000 live births. Although the clinical presentation of 22q11DS is quite variable, its major characteristics include velopharyngeal abnormalities, congenital cardiac anomalies, mild facial dysmorphism and learning difficulties. Children with 22q11DS show considerable difficulties in mathematics, despite relatively normal reading performance. While fact retrieval seems to be preserved, impairments in procedural calculation and word problem solving are particularly prominent. Children with 22q11DS also have substantial difficulties in understanding and representing numerical quantities, possibly related to poor visuospatial attention, which all might stem from their underlying abnormalities in the inferior parietal cortex. This review ends with a discussion on how research on genetic disorders might aid our understanding of MLD in general.

Querying for Provenance, Trust, Uncertainty and Other Meta Knowledge in RDF

The Semantic Web is based on accessing and reusing RDF data from many different sources, which one may assign different levels of authority and credibility. Existing Semantic Web query languages, like SPARQL, have targeted the retrieval, combination and reuse of facts, but have so far ignored all aspects of meta knowledge, such as origins, authorship, recency or certainty of data. In this paper, we present an original, generic, formalized and implemented approach for managing many dimensions of meta knowledge, like source, authorship, certainty and others. The approach re-uses existing RDF modeling possibilities in order to represent meta knowledge. Then, it extends SPARQL query processing in such a way that given a SPARQL query for data, one may request meta knowledge without modifying the query proper. Thus, our approach achieves highly flexible and automatically coordinated querying for data and meta knowledge, while completely separating the two areas of concern.

First-grade predictors of mathematical learning disability: A latent class trajectory analysis

Kindergarten to third grade mathematics achievement scores from a prospective study of mathematical development ( n = 306) were subjected to latent growth trajectory analyses. The four corresponding classes included children with mathematical learning disability (MLD, 6% of sample), and low (LA, 50%), typically (TA, 39%) and high (HA, 5%) achieving children. The groups were administered a battery of intelligence (IQ), working memory, and mathematical-cognition measures in first grade. The children with MLD had general deficits in working memory and IQ and potentially more specific deficits on measures of number sense. The LA children did not have working memory or IQ deficits but showed moderate deficits on these number sense measures and for addition fact retrieval. The distinguishing features of the HA children were a strong visuospatial working memory, a strong number sense, and frequent use of memory-based processes to solve addition problems. Implications for the early identification of children at risk for poor mathematics achievement are considered.

Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study

This article reports results of a four-year longitudinal study that investigated the impact of specific and non-specific precursors on mathematical school achievement. Preschool quantity-number competencies (QNC) predicted mathematical achievement in primary school. Furthermore, basic arithmetic fact retrieval in Grade 1 had an impact on early mathematics school achievement. The influence of socioeconomic status and number naming speed, assessed in kindergarten, became especially important at the end of Grade 4. Particularly, a subgroup of mathematically low-achieving children in Grade 4 had already performed more poorly than normal children in tasks assessing preschool QNC, number naming speed, and basic arithmetic fact retrieval, as well as nonverbal intelligence and socioeconomic status.

Flexible transfer of knowledge in mental arithmetic — An fMRI study

Recent imaging studies could show that fact acquisition in arithmetic is associated with decreasing activation in several frontal and parietal areas, and relatively increasing activation within the angular gyrus, indicating a switch from direct calculation to retrieval of a learned fact from memory. So far, however, little is known about the transfer of learned facts between arithmetic operations. The aim of the present fMRI study was to investigate whether and how newly acquired arithmetic knowledge might transfer from trained multiplication problems to related division problems. On the day before scanning, ten complex multiplication problems were trained. Within the scanner, trained multiplication problems were compared with untrained multiplication problems, and division problems related to multiplication (transfer condition) were compared with unrelated division problems (no-transfer condition). Replicating earlier results, untrained multiplication problems activated several frontal and parietal brain areas more strongly than trained multiplication problems, while trained multiplication problems showed relatively stronger activation in the left angular gyrus than untrained multiplication problems. Concerning division, an ROI analysis indicated that activation in the left angular gyrus was relatively stronger for the transfer condition than for the no-transfer condition. We also observed distinct inter-individual differences with regard to transfer that modulated activation within the left angular gyrus. Activation within the left angular gyrus was generally higher for participants who showed a transfer effect for division problems. In conclusion, the present study yielded some evidence that successful transfer of knowledge between arithmetic operations is accompanied by modifications of brain activation patterns. The left angular gyrus seems not only to be involved in the retrieval of stored arithmetic facts, but also in the transfer between arithmetic operations.

To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving

While there is consistent evidence from neuropsychological and brain imaging studies for an association between the left angular gyrus and mental arithmetic, its specific role in calculation has remained poorly understood. It has been speculated that the angular gyrus mediates the retrieval of arithmetic facts during problem solving, but this hypothesis has not been directly tested. In the present functional Magnetic Resonance Imaging study comprising 28 adults, we used trial-by-trial strategy self-reports to identify brain regions underpinning different strategies in arithmetic problem solving. Analyses revealed stronger activation of the left angular gyrus while solving arithmetic problems for which participants reported fact retrieval whereas the application of procedural strategies was accompanied by widespread activation in a fronto-parietal network. These data directly link the left angular gyrus with arithmetic fact retrieval and show that strategy self-reports can be used to predict differential patterns of brain activation.

Rehabilitation of arithmetic fact retrieval via extensive practice: A combined fMRI and behavioural case-study

The present study investigates the effects of a training of arithmetic fact retrieval in a patient suffering from particular difficulties with multiplication facts. Over a period of four weeks simple multiplication facts were trained extensively. The outcome of the training was assessed behaviourally and changes in cerebral activation patterns were investigated using fMRI. The training led to a change in calculation strategies: Prior to training, the patient used predominantly time-consuming back-up strategies, after training he relied increasingly on the direct retrieval of arithmetic facts from long-term memory. Regarding the fMRI results, prefrontal activations were observed for untrained problems, which can be attributed to the application of back-up strategies strongly relying on fronto-executive functions. Interestingly, significant foci of activation for both trained and untrained items were found in the angular gyrus of the right hemisphere, which, however, differed in their exact localisation. For the trained condition, activations were observed in anterior parts of the angular gyrus which may be related to the training-based automatisation in fact retrieval. Activations in the untrained condition were found in a more posterior portion of the angular gyrus, that might be attributable to one of the patient's back-up strategies, namely to recite a whole multiplication row to get to the correct answer.