"The aim of this study is to examine the proportional reasoning strategies used by middle school students and the ability of teachers and teacher candidates to predict these strategies. The participants include 252 middle school students from a public school in Istanbul, 5 teachers working at the same school, and 9 mathematics teacher candidates from a public university. During the research process, students were first given 6 problems involving proportional reasoning, and their solutions were analyzed based on proportional reasoning strategies. Additionally, teachers and teacher candidates were asked to predict how students solved these problems. According to the results of the study, sixth and eighth-grade students used more accurate strategies compared to fifth and seventh-grade students. Mathematics teacher candidates predicted a wide range of strategies, regardless of whether they were correct or incorrect. On the other hand, mathematics teachers were generally able to accurately predict the strategies their own students used. However, they faced difficulties in predicting the most frequently used strategies according to grade level."

propotional reasoning, proportional reasoning strategies, noticing, middle school students, mathematics teachers