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

• Response times on fraction comparison problems varied in spite of very high accuracy rates.
• Overcoming the natural number bias seems impossible on fraction pairs with common components.
• No natural number bias was found on fraction pairs without common components.
• Experts use holistic representations of fractions only when this is effective.

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.