The inverse relation between the size and the number of parts

Abstract

This study analyses children’s understanding of the inverse relationship between size and number of parts when fractions and division situations are involved. A survey by questionnaire was conducted with 42 Portuguese fourth-graders trying to address two questions: 1) How do children understand the inverse relation between size and number of parts in partitive and quotitive division situations? And 2) How do children understand the inverse relation when fractions are involved in part-whole and quotient interpretations? Results suggest that these distinct situations have different impacts on children’s understanding of the inverse relations between the size and the number of parts.