Examining the role of number sense on seventh grade students' proportional reasoning

Number sense is the general understanding of a person about the numbers, and related operations, and this person's tendency to use this understanding in variable contexts in order to create effective plans and sound mathematical conclusions (Reys et al., 1997). In this context, considering teaching learning process of mathematics, number sense provides both students and teachers with in-depth understanding for mathematics subjects (Cain et al., 2007). This study examined number sense in the context of proportional reasoning, which is an essential mathematics subject related to higher mathematics (Lesh, Post, & Behr, 1988). In this study which was conducted with the participation of 328 7th grade students, the aim was to determine number sense levels of the students, to investigate whether proportional reasoning of the students differentiate based on their number sense levels, and to display how these students use their number sense on the proportional reasoning problems. Explanatory sequential design, a mixed method design, was conducted. Quantitative data were collected through Number Sense Scale and Proportional Reasoning Test, while qualitative data were collected through audio-recorded interviews that include various proportional reasoning problems. The results of the study revealed that the students have a low-level number sense in total, and proportional reasoning statistically and significantly differentiates based on number sense levels of students. Also, the findings of the qualitative data revealed that students with both good level number sense and proportional reasoning were at forefront in applying different strategies for certain proportional situations.