Who can escape the natural number bias in rational number tasks? A study involving students and experts

2015 ◽  
Vol 107 (3) ◽  
pp. 537-555 ◽  
Author(s):  
Andreas Obersteiner ◽  
Jo Van Hoof ◽  
Lieven Verschaffel ◽  
Wim Van Dooren
Keyword(s):  
Natural Number ◽  
Rational Number ◽  
Natural Number Bias

Models for Rational Number Bases

1975 ◽  
Vol 68 (2) ◽  
pp. 113-123
Author(s):  
Jean J. Pedersen ◽  
Frank O. Armbruster
Keyword(s):  
Natural Number ◽  
Rational Number ◽  
Binary Representation ◽  
Base System ◽  
Negative Number

We think it’s important that you have some background on how this article came to be written. One of the authors sometimes plays a game he invented, called “hats,” in which he puts on a funny hat and converts base-ten numerals into another base representation. For example, he puts on a beanie and calls for anyone to say a favorite number. Someone says “six.” He goes to the chalkboard and writes “110,” The object of the game is for the students to figure out what he is doing, Someone who figures it out says, “Gotcha!” And then that person gets to wear the hat until someone else says, “Gotcha!” (In case you haven’t “got it” yet, the beanie hat converts numbers to the binary representation.) Several hats are used in the course of play, and each represents a different number base, but it’s always a natural number base greater than one. Recently we began to wonder if perhaps you can have a negative number base system in which the base is not an integer. And if you can, what will the numerals look like?

Naturally biased? In search for reaction time evidence for a natural number bias in adults

2012 ◽  
Vol 31 (3) ◽  
pp. 344-355 ◽  
Author(s):  
Xenia Vamvakoussi ◽  
Wim Van Dooren ◽  
Lieven Verschaffel
Keyword(s):  
Reaction Time ◽  
Natural Number ◽  
Natural Number Bias

scholarly journals The Interplay Between the Natural Number Bias and Fraction Magnitude Processing in Low-Achieving Students

2020 ◽  
Vol 5 ◽  
Author(s):  
Frank Reinhold ◽  
Andreas Obersteiner ◽  
Stefan Hoch ◽  
Sarah Isabelle Hofer ◽  
Kristina Reiss
Keyword(s):  
Natural Number ◽  
Magnitude Processing ◽  
Low Achieving Students ◽  
Natural Number Bias

Is the Euclidean Algorithm Optimal Among its Peers?

2004 ◽  
Vol 10 (3) ◽  
pp. 390-418 ◽  
Author(s):  
Lou Van Den Dries ◽  
Yiannis N. Moschovakis
Keyword(s):  
Natural Number ◽  
Rational Number ◽  
Time Complexity ◽  
Euclidean Algorithm ◽  
Worst Case ◽  
On Demand ◽  
Recursive Program ◽  
Remainder Function ◽  
Proper Formulation ◽  
Image Position

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem(a, b) is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from (relative to) the remainder function rem, meaning that in computing its time complexity function cε (a, b), we assume that the values rem(x, y) are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch more is known about cε(a, b), but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's (worst case) optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd (x,y) from rem with time complexity cα (x,y), then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα (a,b) > r log2a.

Complex fraction comparisons and the natural number bias: The role of benchmarks

2020 ◽  
Vol 67 ◽  
pp. 101307 ◽  
Author(s):  
Andreas Obersteiner ◽  
Martha Wagner Alibali ◽  
Vijay Marupudi
Keyword(s):  
Natural Number ◽  
Natural Number Bias

Natural number bias in operations with missing numbers

ZDM ◽  
2015 ◽  
Vol 47 (5) ◽  
pp. 747-758 ◽  
Author(s):  
Konstantinos P. Christou
Keyword(s):  
Natural Number ◽  
Natural Number Bias
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