Confounding Whole-Number and Fraction Concepts When Building on Informal Knowledge

This study examined the development of students' understanding of fractions during instruction with respect to the ways students' prior knowledge of whole numbers influenced the meanings and representations students constructed for fractions as they built on their informal knowledge of fractions. Four third-grade and three fourth-grade students received individualized instruction on addition and subtraction of fractions in a one-to-one setting for 3 weeks. As students attempted to construct meaning for symbolic representations of fractions, they overgeneralized the meanings of symbolic representations for whole numbers to fractions, and they overgeneralized the meanings of symbolic representations for fractions to whole numbers.