scholarly journals The relationship between children’s approximate number certainty and symbolic mathematics

2020 ◽  
Vol 6 (1) ◽  
pp. 50-65
Author(s):  
Carolyn Baer ◽  
Darko Odic
Keyword(s):  
Large Body ◽  
Number System ◽  
Math Performance ◽  
Approximate Number System ◽  
Mathematical Skills ◽  
Math Ability ◽  
Positive Correlations ◽  
Number Perception ◽  
The Relationship ◽  
Symbolic Number

Why do some children excel in mathematics while others struggle? A large body of work has shown positive correlations between children’s Approximate Number System (ANS) and school-taught symbolic mathematical skills, but the mechanism explaining this link remains unknown. One potential mediator of this relationship might be children’s numerical metacognition: children’s ability to evaluate how sure or unsure they are in understanding and manipulating numbers. While previous work has shown that children’s math abilities are uniquely predicted by symbolic numerical metacognition, we focus on the extent to which children’s non-symbolic/ANS numerical metacognition, in particular sensitivity to certainty, might be predictive of math ability, and might mediate the relationship between the ANS and symbolic math. A total of 72 children aged 4–6 years completed measures of ANS precision, ANS metacognition sensitivity, and the Test of Early Mathematical Ability (TEMA-3). Our results replicate many established findings in the literature, including the correlation between ANS precision and the TEMA-3, particularly on the Informal subtype questions. However, we did not find that ANS metacognition sensitivity was related to TEMA-3 performance, nor that it mediated the relationship between the ANS and the TEMA-3. These findings suggest either that metacognitive calibration may play a larger role than metacognitive sensitivity, or that metacognitive differences in the non-symbolic number perception do not robustly contribute to symbolic math performance.

Ordinal structure of the symbolic number system mediates refinement of the approximate number system

2020 ◽  
Author(s):  
Christian Peake ◽  
Carolina Briones ◽  
Cristina Rodríguez
Keyword(s):  
Developmental Psychology ◽  
Number System ◽  
First Year ◽  
Approximate Number System ◽  
Parallel Development ◽  
School Year ◽  
System P ◽  
Underlying Mechanisms ◽  
The Relationship ◽  
Symbolic Number

Interest in the relationship between the Approximate Number System (ANS, an early cognitive system to process non-symbolic quantities) and the Symbolic Number System (SNS, learned through instruction or intense exposure) is currently growing among researchers in developmental psychology. This research contrasted the two main hypotheses regarding the issue: the traditional mapping account, which states that the ANS underlies the learning of numerical symbols; and the parallel development account, which argues that the SNS develops independently from the ANS and, in fact, serves to refine it during mapping between them, as the ANS is approximate in nature. Moreover, this study focused on the underlying mechanisms that mediate the relationship between the ANS and the SNS. A sample of 200 children in first year of preschool (4 to 5 years old) were followed over the course of the school year. Symbolic and non-symbolic comparison tasks and estimation tasks where applied at the beginning (T1) and end (T2) of the school year. A cardinality task was administered at T1 and an ordinality task at T2. This allowed us to run two serial multiple mediator models to test both hypotheses with multiple longitudinal mediators. Results showed a bidirectional causal relationship between the ANS and the SNS that was interpreted as supporting the parallel development account. Importantly, ordinality mediated the relationship between the SNS at T1 and the ANS at T2, even when controlling for the development of translation skills from the SNS to the ANS and cardinality. This is the first evidence that knowledge of the relationship between number symbols, addressed in terms of their ordinal structure, is the cognitive mechanism that underlies the refinement of the ANS. As such, it supports the idea that the two systems develop independently, although they may impact each other at early stages of learning.

scholarly journals The effect of gender stereotypes on young girls’ intuitive number sense

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258886
Author(s):  
Antonya Marie Gonzalez ◽  
Darko Odic ◽  
Toni Schmader ◽  
Katharina Block ◽  
Andrew Scott Baron
Keyword(s):  
Gender Stereotypes ◽  
Number Sense ◽  
Number System ◽  
Math Performance ◽  
Approximate Number System ◽  
Math Ability ◽  
Young Girls ◽  
And Gender ◽  
Math Test ◽  
The Impact

Despite the global importance of science, engineering, and math-related fields, women are consistently underrepresented in these areas. One source of this disparity is likely the prevalence of gender stereotypes that constrain girls’ and women’s math performance and interest. The current research explores the developmental roots of these effects by examining the impact of stereotypes on young girls’ intuitive number sense, a universal skill that predicts later math ability. Across four studies, 762 children ages 3–6 were presented with a task measuring their Approximate Number System accuracy. Instructions given before the task varied by condition. In the two control conditions, the task was described to children either as a game or a test of eyesight ability. In the experimental condition, the task was described as a test of math ability and that researchers were interested in whether boys or girls were better at math and counting. Separately, we measured children’s explicit beliefs about math and gender. Results conducted on the combined dataset indicated that while only a small number of girls in the sample had stereotypes associating math with boys, these girls performed significantly worse on a test of Approximate Number System accuracy when it was framed as a math test rather than a game or an eyesight test. These results provide novel evidence that for young girls who do endorse stereotypes about math and gender, contextual activation of these stereotypes may impair their intuitive number sense, potentially affecting their acquisition of formal mathematics concepts and developing interest in math-related fields.

The Approximate Number System is not Predictive for Symbolic Number Processing in Kindergarteners

2014 ◽  
Vol 67 (2) ◽  
pp. 271-280 ◽  
Author(s):  
Delphine Sasanguie ◽  
Emmy Defever ◽  
Bieke Maertens ◽  
Bert Reynvoet
Keyword(s):  
Number System ◽  
Number Processing ◽  
Approximate Number System ◽  
Symbolic Number

scholarly journals Intensive math training does not affect approximate number acuity: Evidence from a three-year longitudinal curriculum intervention

2016 ◽  
Vol 2 (2) ◽  
pp. 57-76 ◽  
Author(s):  
Jessica Sullivan ◽  
Michael C. Frank ◽  
David Barner
Keyword(s):  
Number System ◽  
Math Performance ◽  
Cognitive Tasks ◽  
Approximate Number System ◽  
Math Intervention ◽  
Math Success ◽  
Large N ◽  
Curriculum Intervention ◽  
Induced Changes ◽  
Longitudinal Dataset

Does nonverbal, approximate number acuity predict mathematics performance? Some studies report a correlation between acuity of representations in the Approximate Number System (ANS) and early math achievement, while others do not. Few previous reports have addressed (1) whether reported correlations remain when other domain-general capacities are considered, and (2) whether such correlations are causal. In the present study, we addressed both questions using a large (N = 204) 3-year longitudinal dataset from a successful math intervention, which included a wide array of non-numerical cognitive tasks. While we replicated past work finding correlations between approximate number acuity and math success, these correlations were very small when other domain-general capacities were considered. Also, we found no evidence that changes to math performance induced changes to approximate number acuity, militating against one class of causal accounts.

Spontaneous Focusing on Numerosity Is Linked to Numerosity Discrimination in Children and Adults

2020 ◽  
Author(s):  
Mattan S. Ben-Shachar ◽  
Svetlana Lisson ◽  
Dalit Shotts-Peretz ◽  
Minna Hannula-Sormunen ◽  
Andrea Berger
Keyword(s):  
Number System ◽  
Fine Tuning ◽  
Developmental Pathways ◽  
Approximate Number System ◽  
Numerosity Discrimination ◽  
Stable Domain ◽  
Domain Specific ◽  
Mathematical Abilities ◽  
Academic Achievements ◽  
The Relationship

Spontaneous focusing on numerosity (SFON) is the tendency to spontaneously address exact numerosity in the environment without prompting. While previous studies have found children’s SFON to be a stable, domain-specific predictor of mathematical abilities throughout development, it is unclear whether SFON reflects individual differences in quantitative processing. This study examined the relationship between SFON and the acuity of the Approximate Number System (ANS) in children and adults. To measure adults’ SFON, we developed a numerosity bias task (NBT). In children and adults, better ANS acuity was related to higher tendency to spontaneously focus on numerosity. Additionally, in adults, SFON was related to higher mathematical academic achievements. These findings suggest an interplay between SFON and ANS acuity, indicating a mechanism where increased ANS acuity makes numerosity elements in the environment more salient, while early self-initiated numerical practice promotes fine-tuning of the ANS. Possible implications of these reciprocal developmental pathways are discussed.

The Relationship Between Approximate Number System and Mathematics Competency in Indonesian Primary School Children

2018 ◽  
Vol 24 (8) ◽  
pp. 6259-6264
Author(s):  
Kevin Wijaya ◽  
Fransiskus X Ivan ◽  
Adre Mayza
Keyword(s):  
Response Time ◽  
Primary School ◽  
School Children ◽  
Weber Fraction ◽  
Number System ◽  
Primary School Children ◽  
Methodological Aspect ◽  
Approximate Number System ◽  
And Mathematics ◽  
The Relationship

The purpose of this study is to investigate the relationship between Approximate Number System (ANS), a cognitive system which represents and estimates the cardinality of a set, and mathematics competency of primary school children. Many findings on ANS and its relations with mathematics competency showed inconsistency. This research is the first of its kind in Indonesia. 318 fourth and fifth-grade primary school students were instructed to perform non-symbolic (dots) comparison task to measure their Weber fraction (w), accuracy (percentage correct), and response time (ms) which are the measurement for ANS acuity. Mathematics competencies of the students were taken from school’s report card and the data were standardized for each school separately. Correlation and regression linear analysis were conducted to find the relationship between ANS acuity and mathematics’ competency. Analysis showed there was a weak but significant (p < 0.05) correlation between two measurements of ANS acuity, namely the Weber fraction and accuracy, with mathematics competency, but not response time (p > 0.05). Further analysis with linear regression showed there was no relationship between the two variables and mathematics score, which disproves this correlation. This study shows that there is no relationship between children’s ANS acuity and mathematics competency. Intrinsic factors such as children’s attention, engagement, and motivation, also methodological aspect needed further consideration. Future studies are needed to investigate the methodological aspect related to the measurement of ANS and mathematics’ competency as there is no ‘gold standard’ yet to measure ANS.

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