Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities

Yıl 2016, Cilt: 15 Sayı: 1, 0 - 0, 07.01.2016

İbrahim Burak Ölmez

https://doi.org/10.17051/io.2016.94175

https://izlik.org/JA43SP57JK

Öz

The purpose of this study is to investigate how pre-service teachers’ formation of additive and multiplicative relationships support and constrain their understandings of ratios and proportional relationships in terms of quantities. Six pre-service teachers were selected purposefully based on their performances in a previous course. An explanatory case study with multiple cases was used to make comparisons within and across cases. A semi-structured interview was conducted with pairs of pre-service teachers. The results revealed that pre-service teachers’ heavy reliance on additive or multiplicative relationships critically shaped their reasoning about ratios from the two perspectives. Pre-service teachers who only attended to multiplicative relationships were found to have a robust understanding of proportional relationships. Pre-service teachers, who did attend to additive relationships, even if they used multiplicative relationships, struggled to form appropriate proportional relationships from the two perspectives.