An examination of elementary and lower secondary level Japanese and Turkish mathematics curricula through quantitative and (co)variational reasoning in terms of the treatment of functional relationships

Abstract

This study investigated the similarities and differences between Japanese and Turkish curriculum materials, i.e. the course of study, teachers’ guides, and textbooks, in terms of quantitative and covariational reasoning depicted in the concepts of functional relationships, i.e. linear functions, proportions, rate, and ratio. The analysis was focused on the overall structures of textbooks and the learning opportunities of functional relationships in regard to quantitative and covariational reasoning in the curriculum materials. The tasks, problem situations, questions asked of students, and the use of representations were examined as potential learning opportunities. The finding showed that Japanese textbooks allocated more pages to introduce functional relationships than Turkish textbooks regardless of grade level. Findings also displayed that Japanese curriculum has a spiral nature in terms of covariational reasoning, ratio conception, and task variables. In particular, it has a clear focus on supporting learners’ quantitative reasoning and covariational reasoning which seems to gradually raise up to continuous covariation. Whereas Turkish curriculum seems to support students to reach up to coordination of values level of covariational reasoning. Moreover, in terms of ratio and proportion, the Japanese curriculum starts with supporting students’ additive strategies on tasks and gradually introduces multiplicative strategies; whereas Turkish curriculum materials do not cover all multiplicative strategies and do not seem to have spiral nature in terms of ratio conception.