Early informal fraction knowledge matters: a longitudinal investigation between first and second grades

Eighty children were studied from the start of first grade (mean age = 6.68, range 6.03–7.48) through to the end of second grade to characterize initial informal fraction knowledge and its relation to later informal fraction knowledge and mathematics achievement. Children’s understanding of informal fractions grew across first and second grade, despite little formal fraction instruction. Children showed relatively higher performance in nonsymbolic fraction items compared with symbolic items. Gains in understanding the concept of ‘half’ characterized first grade, with higher gains in understanding “thirds” and “fourths” in second grade. There were large individual differences at all timepoints in informal fraction knowledge. Variation in informal fraction knowledge at the start of first grade predicted later mathematics achievement at the end of second grade, even when including number sense in the model. These findings suggest that early informal fraction knowledge is a foundational number skill, whose growth is intertwined with growth in facility with integers.