A bridge between tools and conventions: a transition to ratio and proportion concepts after ratio table

Overview & Synopsis

This study aims to present taken-as-shared ideas of the students about transitions from ratio table tool to verbal and written symbolic representations of ratio and proportion concepts. The study is part of a dissertation which was guided by educational design research investigating the seventh-grade students’ classroom mathematical practices (CMPs) through ratio and proportion instructional sequence. After 34 lesson hours of observation, five CMPs were extracted from the classroom discussions of 38 students, activity sheets, and teacher-researcher interviews. One of the CMPs extracted from the six hours of classroom discussions indicated a transition of the seventh-grade students to the ratio and proportion verbal and symbolic representation after intensely using the ratio table. This study may contribute to the field in terms of how to transfer learning of using ratio tables into the mathematical procedures and conventions for ratio and proportion.