scholarly journals Estimation as analogy-making: Evidence that preschoolers’ analogical reasoning ability predicts their numerical estimation

2020 ◽  
Author(s):  
Joseph Alvarez ◽  
Monica Abdul-Chani ◽  
Paul Michael Deutchman ◽  
Kayla Dibiasie ◽  
Julia Iannucci ◽  
...  
Keyword(s):  
Cognitive Skills ◽  
Analogical Reasoning ◽  
Number System ◽  
Reasoning Ability ◽  
Approximate Number System ◽  
Numerical Estimation ◽  
Structure Mapping ◽  
Number Words ◽  
Number Systems ◽  
Linguistic Representations

All humans and many animals can represent approximate quantities of perceptual objects nonlinguistically by using the Approximate Number System (Dehaene, 1997/2011). Early in life, children in numerate societies also learn to describe this system using number words. How do linguistic representations of number become related to nonlinguistic representations of number? We hypothesize that the analogical process of structure mapping (Gentner, 1983) helps children to form mappings between the linguistic and nonlinguistic number systems on the basis of structural similarities between the two systems. To test this, we tested and analyzed 47 four-and-five year olds’ performance on estimation and analogy tasks. We found that analogical reasoning ability uniquely predicted several components of estimation performance, even when controlling for other domain-general cognitive skills. This provides strong evidence that analogical processes are uniquely related to the development of early estimation.

scholarly journals Electrophysiological Evidence for the Involvement of the Approximate Number System in Preschoolers' Processing of Spoken Number Words

2014 ◽  
Vol 26 (9) ◽  
pp. 1891-1904 ◽  
Author(s):  
Michal Pinhas ◽  
Sarah E. Donohue ◽  
Marty G. Woldorff ◽  
Elizabeth M. Brannon
Keyword(s):  
Number System ◽  
Number Word ◽  
Word Knowledge ◽  
Approximate Number System ◽  
Word Comprehension ◽  
Number Words ◽  
Visual Objects ◽  
Number Representations ◽  
Word Onset ◽  
Neural Underpinnings

Little is known about the neural underpinnings of number word comprehension in young children. Here we investigated the neural processing of these words during the crucial developmental window in which children learn their meanings and asked whether such processing relies on the Approximate Number System. ERPs were recorded as 3- to 5-year-old children heard the words one, two, three, or six while looking at pictures of 1, 2, 3, or 6 objects. The auditory number word was incongruent with the number of visual objects on half the trials and congruent on the other half. Children's number word comprehension predicted their ERP incongruency effects. Specifically, children with the least number word knowledge did not show any ERP incongruency effects, whereas those with intermediate and high number word knowledge showed an enhanced, negative polarity incongruency response (Ninc) over centroparietal sites from 200 to 500 msec after the number word onset. This negativity was followed by an enhanced, positive polarity incongruency effect (Pinc) that emerged bilaterally over parietal sites at about 700 msec. Moreover, children with the most number word knowledge showed ratio dependence in the Pinc (larger for greater compared with smaller numerical mismatches), a hallmark of the Approximate Number System. Importantly, a similar modulation of the Pinc from 700 to 800 msec was found in children with intermediate number word knowledge. These results provide the first neural correlates of spoken number word comprehension in preschoolers and are consistent with the view that children map number words onto approximate number representations before they fully master the verbal count list.

scholarly journals Approximate number system task performance: Associations with domain-general and domain-specific cognitive skills in young children

2018 ◽  
Vol 4 (3) ◽  
pp. 590-612 ◽  
Author(s):  
Mary Wagner Fuhs ◽  
Kimberly Turner Nesbitt ◽  
Connor D. O’Rear
Keyword(s):  
Cognitive Skills ◽  
Visual Cues ◽  
Number System ◽  
Approximate Number System ◽  
Early Environment ◽  
Developmental Models ◽  
General Ability ◽  
Domain Specific ◽  
Research Findings ◽  
System Task

We investigated the associations between young children’s domain-general executive functioning (EF) skills and domain-specific spontaneous focusing on number (SFON) tendencies and their performance on an approximate number system (ANS) task, paying particular attention to variations in associations across different trial types with either congruent or incongruent non-numerical continuous visual cues. We found that children’s EF skills were strongly related to their performance on ANS task trials in which continuous visual cues were incongruent with numerosity. Novel to the current study, we found that children’s SFON tendencies were specifically related to their performance on ANS task trials in which continuous visual cues were congruent with numerosity. Children’s performance on ANS task trials in which children can use both congruent numerical and non-numerical continuous visual cues to approximate large quantities may be related to their unprompted tendency to focus on number in their early environment when there are not salient distractors present. On the other hand, children’s performance on incongruent ANS trials may be less a function of number-specific knowledge but more of children’s domain-general ability to inhibit salient but conflicting or irrelevant stimuli. Importantly, these effects held even when accounting for global math achievement and children’s cardinality knowledge. Overall, results support the consideration of both domain-specific and domain-general cognitive factors in developmental models of children’s early ability to attend to numerosity and provide a possible means for reconciling previous conflicting research findings.

Mental Numerosity Line in the Human’s Approximate Number System

2016 ◽  
Vol 63 (3) ◽  
pp. 169-179 ◽  
Author(s):  
Xinlin Zhou ◽  
Chaoran Shen ◽  
Leinian Li ◽  
Dawei Li ◽  
Jiaxin Cui
Keyword(s):  
Number System ◽  
Spatial Layout ◽  
Matching Task ◽  
Approximate Number System ◽  
Current Experiment ◽  
Number Systems ◽  
Subitizing Range ◽  
Arabic Digits

Abstract. Previous studies have demonstrated existence of a mental line for symbolic numbers (e.g., Arabic digits). For nonsymbolic number systems, however, it remains unresolved whether a spontaneous spatial layout of numerosity exists. The current experiment investigated whether SNARC-like (Spatial-Numerical Association of Response Codes) effects exist in approximate processing of numerosity, as well as of size and density. Participants were asked to judge whether two serially presented stimuli (i.e., dot arrays, pentagons) were the same regarding numbers of dots, sizes of the pentagon, or densities of dots. Importantly, two confounds that were overlooked by most previous studies were controlled in this study: no ordered numerosity was presented, and only numerosity in the approximate number system (beyond the subitizing range) was used. The results demonstrated that there was a SNARC-like effect only in the numerosity-matching task. The results suggest that numerosity could be spontaneously aligned to a left-to-right oriented mental line according to magnitude information in human’s approximate number system.

Children’s mappings between number words and the approximate number system

Cognition ◽  
2015 ◽  
Vol 138 ◽  
pp. 102-121 ◽  
Author(s):  
Darko Odic ◽  
Mathieu Le Corre ◽  
Justin Halberda
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Number Words

scholarly journals Estimation as analogy-making: Evidence that preschoolers’ analogical reasoning ability predicts their numerical estimation

2017 ◽  
Vol 41 ◽  
pp. 73-84 ◽  
Author(s):  
Joseph Alvarez ◽  
Monica Abdul-Chani ◽  
Paul Deutchman ◽  
Kayla DiBiasie ◽  
Julia Iannucci ◽  
...  
Keyword(s):  
Analogical Reasoning ◽  
Reasoning Ability ◽  
Numerical Estimation

scholarly journals Individual Differences Related to College Students’ Course Performance in Calculus II

2017 ◽  
Vol 4 (2) ◽  
Author(s):  
Sara Hart ◽  
Mia Daucourt ◽  
Colleen Ganley
Keyword(s):  
Cognitive Skills ◽  
Student Attitudes ◽  
Math Anxiety ◽  
Recommendation System ◽  
Number System ◽  
Discussion Forum ◽  
Approximate Number System ◽  
Spatial Skills ◽  
Final Grade ◽  
Final Grades

In this study, we explore student achievement in a semester-long flipped Calculus II course, combining various predictor measures related to student attitudes (math anxiety, math confidence, math interest, math importance) and cognitive skills (spatial skills, approximate number system), as well as student engagement with the online system (discussion forum interaction, time to submission of workshop assignments, quiz attempts), in predicting final grades. Data from 85 students enrolled in a flipped Calculus II course was used in dominance analysis to determine which predictors emerged as the most important for predicting final grades. Results indicated that feelings of math importance, approximate number system (ANS) ability, total amount of discussion forum posting, and time grading peer workshop submissions was the best combination of predictors of final grade, accounting for 17% of variance in a student’s final grade. The point of this work was to determine which predictors are the most important in predicting student grade, with the end goal of building a recommendation system that could be implemented to help students in this traditionally difficult class. The methods used here could be used for any class.

scholarly journals Canine sense of quantity: evidence for numerical ratio-dependent activation in parietotemporal cortex

2019 ◽  
Vol 15 (12) ◽  
pp. 20190666 ◽  
Author(s):  
Lauren S. Aulet ◽  
Veronica C. Chiu ◽  
Ashley Prichard ◽  
Mark Spivak ◽  
Stella F. Lourenco ◽  
...  
Keyword(s):  
Neural Mechanism ◽  
Number System ◽  
Neural Mechanisms ◽  
Primate Species ◽  
Approximate Number System ◽  
Numerical Estimation ◽  
Extensive Training ◽  
Ratio Dependent ◽  
Neural Underpinnings ◽  
Number Perception

The approximate number system (ANS), which supports the rapid estimation of quantity, emerges early in human development and is widespread across species. Neural evidence from both human and non-human primates suggests the parietal cortex as a primary locus of numerical estimation, but it is unclear whether the numerical competencies observed across non-primate species are subserved by similar neural mechanisms. Moreover, because studies with non-human animals typically involve extensive training, little is known about the spontaneous numerical capacities of non-human animals. To address these questions, we examined the neural underpinnings of number perception using awake canine functional magnetic resonance imaging. Dogs passively viewed dot arrays that varied in ratio and, critically, received no task-relevant training or exposure prior to testing. We found evidence of ratio-dependent activation, which is a key feature of the ANS, in canine parietotemporal cortex in the majority of dogs tested. This finding is suggestive of a neural mechanism for quantity perception that has been conserved across mammalian evolution.

scholarly journals Do children's number words begin noisy?

2018 ◽  
Author(s):  
Katherine Wagner ◽  
Junyi Chu ◽  
David Barner
Keyword(s):  
Number System ◽  
Number Word ◽  
Approximate Number System ◽  
Word Meanings ◽  
Number Words ◽  
System P ◽  
Number Representations ◽  
Lively Debate ◽  
Early Number ◽  
Made In

How do children acquire exact meanings for number words like three or forty-seven? In recent years, a lively debate has probed the cognitive systems that support learning, with some arguing that an evolutionarily ancient “approximate number system” drives early number word meanings, and others arguing that learning is supported chiefly by representations of small sets of discrete individuals. This debate has centered around findings generated by Wynn’s (1990, 1992) Give-a-Number task, which she used to categorize children into discrete “knower level” stages. Early reports confirmed Wynn’s analysis, and took these stages to support the “small sets” hypothesis. However, more recent studies have disputed this analysis, and have argued that Give-a-Number data reveal a strong role for approximate number representations. In the present study, we use previously collected Give-a-Number data to replicate the analyses of these past studies, and to show that differences between past studies are due to assumptions made in analyses, rather than to differences in data themselves. We also show how Give-a-Number data violate the assumptions of parametric tests used in past studies. Based on simple non-parametric tests and model simulations, we conclude that (1) before children learn exact meanings for words like one, two, three, and four, they first acquire noisy preliminary meanings for these words, (2) there is no reliable evidence of preliminary meanings for larger meanings, and (3) Give-a- Number cannot be used to readily identify signatures of the approximate number system.

scholarly journals Canine sense of quantity: evidence for numerical ratio-dependent activation in parietotemporal cortex

2019 ◽  
Author(s):  
Lauren S. Aulet ◽  
Veronica C. Chiu ◽  
Ashley Prichard ◽  
Mark Spivak ◽  
Stella F. Lourenco ◽  
...  
Keyword(s):  
Neural Mechanism ◽  
Number System ◽  
Neural Mechanisms ◽  
Primate Species ◽  
Approximate Number System ◽  
Numerical Estimation ◽  
Extensive Training ◽  
Ratio Dependent ◽  
Neural Underpinnings ◽  
Number Perception

AbstractThe approximate number system, which supports the rapid estimation of quantity, emerges early in human development and is widespread across species. Neural evidence from both human and non-human primates suggests the parietal cortex as a primary locus of numerical estimation, but it is unclear whether the numerical competencies observed across non-primate species are subserved by similar neural mechanisms. Moreover, because studies with non-human animals typically involve extensive training, little is known about the spontaneous numerical capacities of non-human animals. To address these questions, we examined the neural underpinnings of number perception using awake canine functional magnetic resonance imaging. Dogs passively viewed dot arrays that varied in ratio and, critically, received no task-relevant training or exposure prior to testing. We found evidence of ratio-dependent activation, which is a key feature of the approximate number system, in canine parietotemporal cortex in the majority of dogs tested. This finding is suggestive of a neural mechanism for quantity perception that has been conserved across mammalian evolution.

scholarly journals The precision of mapping between number words and the approximate number system predicts children’s formal math abilities

2016 ◽  
Vol 150 ◽  
pp. 207-226 ◽  
Author(s):  
Melissa E. Libertus ◽  
Darko Odic ◽  
Lisa Feigenson ◽  
Justin Halberda
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Number Words
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