Portuguese and Brazilian children understanding the inverse relation between quantities: the case of fractions

Abstract

This study compares Portuguese and Brazilian fourth-graders (n=84) understanding of the inverse relation between quantities when fractions are presented in quotient and part-whole interpretations. It addresses three questions: 1) How do children understand this inverse relation in quotient interpretations of fractions? 2) How do children understand this inverse relation in part-whole interpretation of fractions? 3) Are there differences in performance between Brazilian and Portuguese children concerning these issues? A survey by questionnaire was applied and 16 part-whole and quotient problems were analyzed. Results indicate that quotient interpretation promotes more the understanding of this inverse relation; Portuguese and Brazilian children perform differently when solving the fraction problems.