Numerical Abilities and Arithmetic in Infancy

2014 ◽  
Author(s):  
Koleen McCrink ◽  
Wesley Birdsall
Keyword(s):  
Object Tracking ◽  
Statistical Learning ◽  
Tracking System ◽  
Number System ◽  
Approximate Number System ◽  
Numerical Abilities ◽  
Large Numbers ◽  
Mathematical Operations

Numerical Abilities and Arithmetic in Infancy. In this chapter, infants’ capacity to represent and manipulate numerical amounts via a precise system for small numbers (the object-tracking system) and an imprecise system for large numbers (the Approximate Number System, or ANS) is detailed. Of particular interest is the presence of an untrained ability to calculate arithmetic outcomes as a result of mathematical operations. The evidence for addition, subtraction, ordering, multiplication, and division in infancy is reviewed and links to other domains such as statistical learning are explored.

scholarly journals Building blocks for a cognitive science-led epistemology of arithmetic

2021 ◽  
Author(s):  
Stefan Buijsman
Keyword(s):  
Cognitive Science ◽  
Object Tracking ◽  
Mathematical Knowledge ◽  
Tracking System ◽  
Philosophy Of Mathematics ◽  
Building Blocks ◽  
Number System ◽  
Psychological Processes ◽  
Approximate Number System ◽  
Oxford University

AbstractIn recent years philosophers have used results from cognitive science to formulate epistemologies of arithmetic (e.g. Giaquinto in J Philos 98(1):5–18, 2001). Such epistemologies have, however, been criticised, e.g. by Azzouni (Talking about nothing: numbers, hallucinations and fictions, Oxford University Press, 2010), for interpreting the capacities found by cognitive science in an overly numerical way. I offer an alternative framework for the way these psychological processes can be combined, forming the basis for an epistemology for arithmetic. The resulting framework avoids assigning numerical content to the Approximate Number System and Object Tracking System, two systems that have so far been the basis of epistemologies of arithmetic informed by cognitive science. The resulting account is, however, only a framework for an epistemology: in the final part of the paper I argue that it is compatible with both platonist and nominalist views of numbers by fitting it into an epistemology for ante rem structuralism and one for fictionalism. Unsurprisingly, cognitive science does not settle the debate between these positions in the philosophy of mathematics, but I it can be used to refine existing epistemologies and restrict our focus to the capacities that cognitive science has found to underly our mathematical knowledge.

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

Second-order characteristics don't favor a number-representing ANS

2021 ◽  
Vol 44 ◽  
Author(s):  
Stefan Buijsman
Keyword(s):  
Object Tracking ◽  
Sensory Integration ◽  
Tracking System ◽  
Second Order ◽  
Integration Mechanism ◽  
Numerical Magnitudes

Abstract Clarke and Beck argue that the ANS doesn't represent non-numerical magnitudes because of its second-order character. A sensory integration mechanism can explain this character as well, provided the dumbbell studies involve interference from systems that segment by objects such as the Object Tracking System. Although currently equal hypotheses, I point to several ways the two can be distinguished.

“Approximate number system” training: A perceptual learning approach

2018 ◽  
Vol 81 (3) ◽  
pp. 621-636 ◽  
Author(s):  
Aaron Cochrane ◽  
Lucy Cui ◽  
Edward M. Hubbard ◽  
C. Shawn Green
Keyword(s):  
Perceptual Learning ◽  
Number System ◽  
Learning Approach ◽  
Approximate Number System

scholarly journals Compromised approximate number system acuity in extremely preterm school-aged children

2013 ◽  
Vol 55 (12) ◽  
pp. 1109-1114 ◽  
Author(s):  
Kerstin Hellgren ◽  
Justin Halberda ◽  
Lea Forsman ◽  
Ulrika Ådén ◽  
Melissa Libertus
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
School Aged Children ◽  
Extremely Preterm

IoT Enabled RFID Authentication and Secure Object Tracking System for Smart Logistics

2018 ◽  
Vol 104 (2) ◽  
pp. 543-560 ◽  
Author(s):  
S. Anandhi ◽  
R. Anitha ◽  
Venkatasamy Sureshkumar
Keyword(s):  
Object Tracking ◽  
Tracking System ◽  
Smart Logistics

scholarly journals Reconfigurable fuzzy logic system for high-frame rate stereovision object tracking

2021 ◽  
Author(s):  
Oleg Samarin
Keyword(s):  
Fuzzy Logic ◽  
Control System ◽  
Object Tracking ◽  
Fuzzy Logic Control ◽  
Tracking System ◽  
Frame Rate ◽  
Disparity Map ◽  
High Frame Rate ◽  
Logic Control ◽  
Logic System

his study investigates the applicability of fuzzy logic control to high-frame rate stereovision object tracking. The technology developed in this work is based on utilizing a disparity map produced by the Stereovision Tracking System (STS) to identify the object of interest. The coordinates of the object are used by the fuzzy logic control system to provide rotation and focus control for object tracking. The fuzzy logic control was realized as a reconfigurable hardware module and implemented on Virtex-2 FPGA platform of the STS. The fuzzy reasoning was implemented as a reconfigurable look-up table residing in FPGA's internal memory. A set of software tools facilitating creation of loop-up table and reconfiguration of fuzzy logic control system was developed. Finally, the experimental prototype of the system was built and tested.

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