Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction

Br J Educ Psychol. 2018 Sep;88(3):345-362. doi: 10.1111/bjep.12182. Epub 2017 Sep 8.


Background: Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature.

Aim: This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction.

Sample(s): Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school.

Methods: Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later.

Results: In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later.

Conclusions: Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level.

Keywords: approximate number system; fraction instruction; fraction magnitude understanding; mathematics achievement; whole number knowledge.

MeSH terms

  • Academic Success*
  • Child
  • Child Development / physiology*
  • Comprehension / physiology*
  • Female
  • Humans
  • Male
  • Mathematical Concepts*
  • Mathematics* / education
  • Random Allocation
  • Thinking / physiology*