The Approximate Number System (ANS) and Discriminating Magnitudes

2020 ◽  
pp. 127-139
Author(s):  
Ellen Peters
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Arithmetic Operations ◽  
Simple Arithmetic ◽  
Math Ability ◽  
Intuitive Sense

This chapter, “The Approximate Number System (ANS) and Discriminating Magnitudes,” discusses our intuitive, rather than deliberative, understanding of numbers. Humans are born with an innate sense of number and an ability to perform simple arithmetic operations with sets of objects without counting. We share this intuitive sense of numeric magnitude (how big one quantity is relative to another) with other species. Non-human animals cannot count as humans do. However, they have a keen sense of quantity that allows them to tell quickly and efficiently which quantity is bigger so that they can make better choices about food, mates, and safety. In humans, this intuitive sense of numbers develops from infancy to adulthood, and it appears to underlie the emergence of symbolic math ability (objective numeracy) in children.

scholarly journals Step Pyramid Distribution for Prime Numbers

2022 ◽  
Vol 14 (1) ◽  
pp. 55
Author(s):  
Shaimaa said soltan
Keyword(s):  
Number System ◽  
Prime Numbers ◽  
Classification Algorithm ◽  
Algorithm Complexity ◽  
Arithmetic Operations ◽  
Simple Arithmetic ◽  
Simpler Algorithm

In this document, we will present a new way to visualize the distribution of Prime Numbers in the number system to spot Prime numbers in a subset of numbers using a simpler algorithm. Then we will look throw a classification algorithm to check if a number is prime using only 7 simple arithmetic operations with an algorithm complexity less than or equal to O (7) operations for any number.

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.

scholarly journals Attentional bias induced by stimulus control (ABC) impairs measures of the approximate number system

2021 ◽  
Author(s):  
Marcus Lindskog ◽  
Leo Poom ◽  
Anders Winman
Keyword(s):  
Attentional Bias ◽  
Stimulus Control ◽  
Number System ◽  
Approximate Number System ◽  
Math Ability ◽  
Overt Attention ◽  
Number Discrimination ◽  
Presentation Time ◽  
Item Size ◽  
Individual Size

AbstractPervasive congruency effects characterize approximate number discrimination tasks. Performance is better on congruent (the more numerous stimulus consists of objects of larger size that occupy a larger area) than on incongruent (where the opposite holds) items. The congruency effects typically occur when controlling for nonnumeric variables such as cumulative area. Furthermore, only performance on incongruent stimuli seems to predict math abilities. Here, we present evidence for an attentional-bias induced by stimulus control (ABC) where preattentive features such as item size reflexively influence decisions, which can explain these congruency effects. In three experiments, we tested predictions derived from the ABC. In Experiment 1, as predicted, we found that manipulation of size introduced congruency effects and eliminated the correlation with math ability for congruent items. However, performance on incongruent items and neutral, nonmanipulated items were still predictive of math ability. A negative correlation between performance on congruent and incongruent items even indicated that they measure different underlying constructs. Experiment 2 demonstrated, in line with the ABC account, that increasing presentation time reduced congruency effects. By directly measuring overt attention using eye-tracking, Experiment 3 revealed that people direct their first gaze toward the array with items of larger individual size, biasing them towards these arrays. The ABC explains why the relation between performance on approximate number discrimination tasks and math achievement has been fragile and suggests that stimulus control manipulations have contaminated the results. We discuss the importance of using stimuli that are representative of the environment.

Discriminating Numbers Allows for Better Decisions

2020 ◽  
pp. 153-168
Author(s):  
Ellen Peters
Keyword(s):  
Decision Making ◽  
Proportional Reasoning ◽  
Number System ◽  
Approximate Number System ◽  
Intuitive Sense

This chapter, “Discriminating Numbers Allows for Better Decisions,” focuses on the role of our intuitive sense of numbers in decision making. Humans have evolved beyond these intuitions about quantities to know modern numeric abstractions. However, the evolutionarily old approximate number system (ANS) nonetheless remains pivotal to human decisions. Just as non-human animals use the proportional reasoning and estimation skills that come from the ANS, so do humans. The chapter introduces three systematic properties of the ANS that can explain differences in how people make decisions. These numeric intuitions, independent of objective ability, relate to having superior numeric memory and (usually) more accurate perceptions of value. Sometimes, however, the ANS’s reliance on proportional reasoning can produce what looks like worse decisions. The Appendix to this chapter describes ANS measures.

scholarly journals Preschool acuity of the approximate number system correlates with school math ability

2011 ◽  
Vol 14 (6) ◽  
pp. 1292-1300 ◽  
Author(s):  
Melissa E. Libertus ◽  
Lisa Feigenson ◽  
Justin Halberda
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Math Ability

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.

scholarly journals The approximate number system and domain-general abilities as predictors of math ability in children with normal hearing and hearing loss

2017 ◽  
Vol 36 (2) ◽  
pp. 236-254 ◽  
Author(s):  
Rebecca Bull ◽  
Marc Marschark ◽  
Emily Nordmann ◽  
Patricia Sapere ◽  
Wendy A. Skene
Keyword(s):  
Hearing Loss ◽  
Number System ◽  
Normal Hearing ◽  
Approximate Number System ◽  
Math Ability
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