Is There a Gap or Congruency Effect? A Cross-Sectional Study in Students’ Fraction Comparison

Abstract

Many studies have addressed the natural number bias in fraction comparison, focusing on the role of congruency. However, the congruency effect has been observed to operate in the opposite direction, suggesting that a deeper explanation must underlie students’ different reasoning. We extend previous research by examining students’ reasoning and by studying the effect of a gap condition in students’ answers. A cross-sectional study was conducted on 438 students from 5th to 10th grade. Results showed that the gap effect could explain differences between congruent and incongruent items. Moreover, students’ use of gap thinking decreased towards the end of Secondary Education.

Keywords

• Rational numbers, natural number bias, fraction comparison, gap thinking