The proportional reasoning ability of preservice mathematics teachers: A mixed method study

The aim of the current study was to investigate preservice mathematics teachers' (PSMTs) proportional reasoning. The study was conducted in five public universities in Turkey, during the spring semester of 2018-2019 academic year. A total of 261 junior and senior university students from middle and secondary school mathematics teaching programs participated in the study. Proportional Reasoning Instrument (PRI) which is prepared by the researcher based on six components among characteristics of proportional reasoners outlined by Lamon (2005, 2007) and task-based interviews with selected participants were used as data sources. Quantitative analysis results revealed that although PSMTs had relatively high scores on PRI, they experienced difficulties in reasoning about the multiplicative relationships in both direct and inverse proportions, realizing and understanding the invariance and covariance structures of proportional relationships, evaluating students' alternative strategies and developing proper language for ratio and proportion. Results from the qualitative analysis showed that highest scorers on PRI provide conceptual explanations about the answers more than average and lowest scorers. It was also concluded that all PSMTs in the clinical interviews regardless of their performances on PRI, had difficulty in proper use of ratio and proportion language and overgeneralized use of cross-multiplication algorithm even for non-proportional and inverse proportion situations. While highest scorers overused the algorithm for inverse proportion situations, others used the algorithm frequently for both situations