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

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.CIEC - Centro de Investigação em Estudos da Criança, IE, UMinho (UI 317 da FCT), PortugalFundos Nacionais através da FCT (Fundação para a Ciência e a Tecnologia) e cofinanciado pelo Fundo Europeu de Desenvolvimento Regional (FEDER) através do COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) com a referência POCI-01-0145-FEDER-007562