scholarly journals Storage and retrieval of addition facts: The role of number comparison

2001 ◽  
Vol 54 (4) ◽  
pp. 1005-1029 ◽  
Author(s):  
Brian Butterworth ◽  
Marco Zorzi ◽  
Luisa Girelli ◽  
A.R. Jonckheere
Keyword(s):  
Reaction Times ◽  
Naming Task ◽  
Comparison Task ◽  
Single Digit ◽  
Magnitude Comparison ◽  
Comparison Stage ◽  
Storage And Retrieval ◽  
Addition Task ◽  
Three Stages ◽  
Fact Retrieval

It is proposed that arithmetical facts are organized in memory in terms of a principle that is unique to numbers—the cardinal magnitudes of the addends. This implies that sums such as 4 + 2 and 2 + 4 are represented, and searched for, in terms of the maximum and minimum addends. This in turn implies that a critical stage in solving an addition problem is deciding which addend is the larger. The COMP model of addition fact retrieval incorporates a comparison stage, as well as a retrieval stage and a pronunciation stage. Three tasks, using the same subjects, were designed to assess the contribution of these three stages to retrieving the answers to single-digit addition problems. Task 3 was the addition task, which examined whether reaction times (RTs) were explained by the model; Task 1 was a number naming task to assess the contribution of the pronunciation stage; Task 2 was a magnitude comparison task to assess the contribution, if any, of the comparison stage. A regression equation that included just expressions of these three stages was found to account for 71% of the variance. It is argued that the COMP model fits not only the adult RT data better than do alternatives, but also the evidence from development of additional skills.

The Organization of Brain Activations in Number Comparison: Event-Related Potentials and the Additive-Factors Method

1996 ◽  
Vol 8 (1) ◽  
pp. 47-68 ◽  
Author(s):  
Stanislas Dehaene
Keyword(s):  
Cognitive Task ◽  
Reaction Times ◽  
Event Related Potentials ◽  
Normal Subjects ◽  
Imaging Data ◽  
Comparison Task ◽  
Cerebral Lateralization ◽  
Magnitude Comparison ◽  
Number Comparison ◽  
Related Potentials

Measuring reaction times (RTs) using the additive-factors method provides information about the sequence of processing stages in a cognitive task. Here, I describe how the simultaneous recording of event-related potentials (ERPs) in the same task can provide complementary information that cannot be obtained using RTs alone. Most notably, ERP data can reveal the absolute activation time and the coarse brain localization of processing stages. RTs and ERPs can also be used to cross-validate a serial-stage model. These notions were applied to a study of the temporal unfolding of brain activations in a number comparison task. ERPs were recorded from 64 scalp electrodes while normal subjects classified numbers as larger or smaller than 5. Specific scalp signatures and timing data were obtained for stages of word and digit identification, magnitude comparison, response programming, and error capture and correction. The observed localizations were compatible with previous neuropsychological and brain imaging data and provided new insights into the cerebral lateralization and timing of number processing.

scholarly journals Culture-Independent Prerequisites for Early Arithmetic

2018 ◽  
Vol 29 (9) ◽  
pp. 1383-1392 ◽  
Author(s):  
Robert A. Reeve ◽  
Fiona Reynolds ◽  
Jacob Paul ◽  
Brian L. Butterworth
Keyword(s):  
Working Memory ◽  
Cognitive Abilities ◽  
Cultural Practices ◽  
Visuospatial Working Memory ◽  
Single Digit ◽  
Correlation Matrices ◽  
Magnitude Comparison ◽  
Addition Task ◽  
Indigenous Children ◽  
Culture Independent

In numerate societies, early arithmetic development is associated with visuospatial working memory, executive functions, nonverbal intelligence, and magnitude-comparison abilities. To what extent do these associations arise from cultural practices or general cognitive prerequisites? Here, we administered tests of these cognitive abilities (Corsi Blocks, Raven’s Colored Progressive Matrices, Porteus Maze) to indigenous children in remote northern Australia, whose culture contains few counting words or counting practices, and to nonindigenous children from an Australian city. The indigenous children completed a standard nonverbal addition task; the nonindigenous children completed a comparable single-digit addition task. The correlation matrices among variables in the indigenous and nonindigenous children showed similar patterns of relationships, and parallel regression analyses showed that visuospatial working memory was the main predictor of addition performance in both groups. Our findings support the hypothesis that the same cognitive capacities promote competence for learners in both numerate and nonnumerate societies.

scholarly journals Magnitude integration in the Archerfish

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tali Leibovich-Raveh ◽  
Ashael Raveh ◽  
Dana Vilker ◽  
Shai Gabay
Keyword(s):  
Animal Model ◽  
Grocery Store ◽  
The Body ◽  
Water Tank ◽  
Comparison Task ◽  
Magnitude Comparison ◽  
Mathematical Abilities ◽  
In The Wild ◽  
Numerical Magnitudes ◽  
Shortest Queue

AbstractWe make magnitude-related decisions every day, for example, to choose the shortest queue at the grocery store. When making such decisions, which magnitudes do we consider? The dominant theory suggests that our focus is on numerical quantity, i.e., the number of items in a set. This theory leads to quantity-focused research suggesting that discriminating quantities is automatic, innate, and is the basis for mathematical abilities in humans. Another theory suggests, instead, that non-numerical magnitudes, such as the total area of the compared items, are usually what humans rely on, and numerical quantity is used only when required. Since wild animals must make quick magnitude-related decisions to eat, seek shelter, survive, and procreate, studying which magnitudes animals spontaneously use in magnitude-related decisions is a good way to study the relative primacy of numerical quantity versus non-numerical magnitudes. We asked whether, in an animal model, the influence of non-numerical magnitudes on performance in a spontaneous magnitude comparison task is modulated by the number of non-numerical magnitudes that positively correlate with numerical quantity. Our animal model was the Archerfish, a fish that, in the wild, hunts insects by shooting a jet of water at them. These fish were trained to shoot water at artificial targets presented on a computer screen above the water tank. We tested the Archerfish's performance in spontaneous, untrained two-choice magnitude decisions. We found that the fish tended to select the group containing larger non-numerical magnitudes and smaller quantities of dots. The fish selected the group containing more dots mostly when the quantity of the dots was positively correlated with all five different non-numerical magnitudes. The current study adds to the body of studies providing direct evidence that in some cases animals’ magnitude-related decisions are more affected by non-numerical magnitudes than by numerical quantity, putting doubt on the claims that numerical quantity perception is the most basic building block of mathematical abilities.

The processing of blend words in naming and sentence reading

2018 ◽  
Vol 72 (4) ◽  
pp. 847-857
Author(s):  
Rebecca L Johnson ◽  
Sarah Rose Slate ◽  
Allison R Teevan ◽  
Barbara J Juhasz
Keyword(s):  
Eye Movements ◽  
Eye Movement ◽  
Reaction Times ◽  
Naming Task ◽  
Compound Words ◽  
Processing Times ◽  
Sentence Reading ◽  
Word Familiarity ◽  
Complex Words ◽  
Eye Movements During Reading

Research exploring the processing of morphologically complex words, such as compound words, has found that they are decomposed into their constituent parts during processing. Although much is known about the processing of compound words, very little is known about the processing of lexicalised blend words, which are created from parts of two words, often with phoneme overlap (e.g., brunch). In the current study, blends were matched with non-blend words on a variety of lexical characteristics, and blend processing was examined using two tasks: a naming task and an eye-tracking task that recorded eye movements during reading. Results showed that blend words were processed more slowly than non-blend control words in both tasks. Blend words led to longer reaction times in naming and longer processing times on several eye movement measures compared to non-blend words. This was especially true for blends that were long, rated low in word familiarity, but were easily recognisable as blends.

The Effects of Case Mixing on Word Recognition: Evidence from a PET Study

2001 ◽  
Vol 13 (6) ◽  
pp. 844-853 ◽  
Author(s):  
Kate Mayall ◽  
Glyn W. Humphreys ◽  
Andrea Mechelli ◽  
Andrew Olson ◽  
Cathy J. Price
Keyword(s):  
Word Recognition ◽  
Feature Detection ◽  
Reaction Times ◽  
Naming Task ◽  
Attentional Processing ◽  
Mixed Case ◽  
Behavioral Studies ◽  
The Right ◽  
Implicit And Explicit ◽  
Language Areas

The early stages of visual word recognition were investigated by scanning participants using PET as they took part in implicit and explicit reading tasks with visually disrupted stimuli. CaSe MiXiNg has been shown in behavioral studies to increase reaction times (RTs) in naming and other word recognition tasks. In this study, we found that during both an implicit (feature detection) task and an explicit word-naming task, mixed-case words compared to same-case words produced increased activation in an area of the right parietal cortex previously associated with visual attention. No effect of case was found in this area for pseudowords or consonant strings. Further, lowering the contrast of the stimuli slowed RTs as much as case mixing, but did not lead to the same increase in right parietal activation. No significant effect of case mixing was observed in left-hemisphere language areas. The results suggest that reading mixed-case words requires increased attentional processing. However, later word recognition processes may be relatively unaffected by the disruption in presentation.

scholarly journals Fact retrieval or compacted procedures in arithmetic – a neurophysiological investigation of two hypotheses

2020 ◽  
Author(s):  
Roland H. Grabner ◽  
Clemens Brunner ◽  
Valerie Lorenz ◽  
Stephan E. Vogel ◽  
Bert De Smedt
Keyword(s):  
Problem Solving ◽  
Cognitive Processes ◽  
High Sensitivity ◽  
List Type ◽  
Single Digit ◽  
Frequency Bands ◽  
Eeg Data ◽  
Neurophysiological Test ◽  
Problem Solving Strategies ◽  
Fact Retrieval

ABSTRACTThere is broad consensus that adults solve single-digit multiplication problems almost exclusively by fact retrieval (i.e., retrieval of the solution from an arithmetic fact network). In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. The fact-retrieval account postulates that these are solved through fact retrieval, just like multiplications, whereas the compacted-procedure account proposes that solving very small additions (i.e., problems with operands between 1 and 4) involves highly automatized and unconscious compacted procedures. In the present electroencephalography (EEG) study, we put these two accounts to the test by comparing neurophysiological correlates of solving very small additions and multiplications. A sample of 40 adults worked on an arithmetic production task involving all (non-tie) single-digit additions and multiplications. Afterwards, participants completed trial-by-trial strategy self-reports. In our EEG analyses, we focused on induced activity (event-related synchronization/desynchronization, ERS/ERD) in three frequency bands (theta, lower alpha, upper alpha). Across all frequency bands, we found higher evidential strength for similar rather than different neurophysiological processes accompanying the solution of very small addition and multiplication problems. This was also true when n + 1 and n × 1 problems were excluded from the analyses. In two additional analyses, we showed that ERS/ERD can differentiate between self-reported problem-solving strategies (retrieval vs. procedure) and even between n + 1 and n + m problems in very small additions, demonstrating its high sensitivity to cognitive processes in arithmetic. The present findings clearly support the fact-retrieval account, suggesting that both very small additions and multiplications are solved through fact retrieval.HIGHLIGHTSNeurophysiological test of fact retrieval and compacted procedures accountInduced EEG data are sensitive to cognitive processes in arithmetic problem solvingBoth very small additions and multiplications are solved through fact retrieval

scholarly journals Neural state space alignment for magnitude generalisation in humans and recurrent networks

2020 ◽  
Author(s):  
Hannah Sheahan ◽  
Fabrice Luyckx ◽  
Stephanie Nelli ◽  
Clemens Teupe ◽  
Christopher Summerfield
Keyword(s):  
Model Systems ◽  
Recurrent Networks ◽  
Comparison Task ◽  
State Spaces ◽  
Magnitude Comparison ◽  
Relational Patterns ◽  
Relational Knowledge ◽  
Neural Representations ◽  
Brain Signals ◽  
Relational Concepts

AbstractA prerequisite for intelligent behaviour is to understand how stimuli are related and to generalise this knowledge across contexts. Generalisation can be challenging when relational patterns are shared across contexts but exist on different physical scales. Here, we studied neural representations in humans and recurrent neural networks performing a magnitude comparison task, for which it was advantageous to generalise concepts of “more” or “less” between contexts. Using multivariate analysis of human brain signals and of neural network hidden unit activity, we observed that both systems developed parallel neural “number lines” for each context. In both model systems, these number state spaces were aligned in a way that explicitly facilitated generalisation of relational concepts (more and less). These findings suggest a previously overlooked role for neural normalisation in supporting transfer of a simple form of abstract relational knowledge (magnitude) in humans and machine learning systems.

Effects of syllable structure on reaction times in a delayed naming task

2008 ◽  
Vol 123 (5) ◽  
pp. 3883-3883
Author(s):  
Christine Mooshammer ◽  
Louis Goldstein ◽  
Mark Tiede ◽  
Hosung Nam ◽  
Man Gao
Keyword(s):  
Reaction Times ◽  
Naming Task ◽  
Syllable Structure

Processing of Spanish Preterite Regular and Irregular Verbs: The Role of Neighborhood Density

2012 ◽  
Vol 15 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Eva Rodríguez-González
Keyword(s):  
Language Processing ◽  
Word Processing ◽  
Native Speakers ◽  
Reaction Times ◽  
Naming Task ◽  
Phonological Similarity ◽  
Neighborhood Density ◽  
Inflectional Morphology ◽  
Irregular Verbs

Research into lexical processes shows that frequency and phonological similarity (neighborhood density) affect word processing and retrieval. Previous studies on inflectional morphology have examined the influence of frequency of occurrence in speech production on the inflectional verb paradigm in English. Limited work has been done to examine the influence of phonological similarity in languages with a more complex morphological system than English. The present study examined the influence of neighborhood density on the processing of Spanish Preterite regular and irregular verbs as produced by thirty native speakers of Spanish. The results of a naming task showed that regular verbs were processed faster and more accurately than irregular ones. Similar to what has been observed in English, a facilitative effect of neighborhood density for –ir verbs was observed in both regular and irregular verbs, such that –ir verbs with dense neighborhoods were produced faster and more accurately than –ir verbs with sparse neighborhoods. However, no neighborhood density effects were observed for –ar verbs (regular and irregular) in reaction times and accuracy rates. Thus, the activation of a specific –ir verb was facilitated by similar sounding verbs regardless of being regular and irregular. Implications for models of morphology language processing are discussed.

Mental Representations in Fraction Comparison

2011 ◽  
Vol 58 (6) ◽  
pp. 480-489 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Benton H. Pierce
Keyword(s):  
Mental Representations ◽  
Reaction Times ◽  
Cross Product ◽  
Numerical Distance ◽  
Regression Analyses ◽  
Problem Size ◽  
Comparison Task ◽  
Strategy Types ◽  
Problem Size Effect ◽  
Fraction Comparison

In this study, we investigated the mental representations used in a fraction comparison task. Adults were asked to quickly and accurately pick the larger of two fractions presented on a computer screen and provide trial-by-trial reports of the types of strategies they used. We found that adults used a variety of strategies to compare fractions, ranging among just knowing the answer, using holistic knowledge of fractions to determine the answer, and using component-based procedures such as cross multiplication. Across all strategy types, regression analyses identified that reaction times were significantly predicted by numerical distance between fractions, indicating that the participants used a magnitude-based representation to compare the fraction magnitudes. In addition, a variant of the problem-size effect (e.g., Ashcraft, 1992) appeared, whereby reaction times were significantly predicted by the average cross product of the two fractions. This effect was primarily found for component-based strategies, indicating a role for strategy choice in the formation of mental representations of fractions.

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