TY - JOUR

T1 - The natural number bias and magnitude representation in fraction comparison by expert mathematicians

AU - Obersteiner, Andreas

AU - Van Dooren, Wim

AU - Van Hoof, Jo

AU - Verschaffel, Lieven

PY - 2013/12

Y1 - 2013/12

N2 - When school students compare the numerical values of fractions, they have frequently been found to be biased by the natural numbers involved (e.g., to believe that 1/4>1/3 because 4>3), thereby considering fractions componentially as two natural numbers rather than holistically as one number. Adult studies have suggested that intuitive processes could be the source of this bias, but also that adults are able to activate holistic rather than componential mental representations of fractions under some circumstances. We studied expert mathematicians on various types of fraction comparison problems to gain further evidence for the intuitive character of the bias, and to test how the mental representations depend on the type of comparison problems. We found that experts still show a tendency to be biased by natural numbers and do not activate holistic representations when fraction pairs have common numerators or denominators. With fraction pairs without common components, we found no natural number bias, and holistic representations were more likely. We discuss both findings in relation to each other, and point out implications for mathematics education.

AB - When school students compare the numerical values of fractions, they have frequently been found to be biased by the natural numbers involved (e.g., to believe that 1/4>1/3 because 4>3), thereby considering fractions componentially as two natural numbers rather than holistically as one number. Adult studies have suggested that intuitive processes could be the source of this bias, but also that adults are able to activate holistic rather than componential mental representations of fractions under some circumstances. We studied expert mathematicians on various types of fraction comparison problems to gain further evidence for the intuitive character of the bias, and to test how the mental representations depend on the type of comparison problems. We found that experts still show a tendency to be biased by natural numbers and do not activate holistic representations when fraction pairs have common numerators or denominators. With fraction pairs without common components, we found no natural number bias, and holistic representations were more likely. We discuss both findings in relation to each other, and point out implications for mathematics education.

KW - Componential representation

KW - Holistic representation

KW - Intuitive reasoning

KW - Rational numbers

KW - Whole number bias

UR - http://www.scopus.com/inward/record.url?scp=84879747887&partnerID=8YFLogxK

U2 - 10.1016/j.learninstruc.2013.05.003

DO - 10.1016/j.learninstruc.2013.05.003

M3 - Article

AN - SCOPUS:84879747887

SN - 0959-4752

VL - 28

SP - 64

EP - 72

JO - Learning and Instruction

JF - Learning and Instruction

ER -