Students’ Quantitative Reasoning while Engaging in a Mathematical Modeling Task Designed for Learning Linear Function

It is important for students to think the quantities related to the linear functions, to construct new quantities and to relate the different representations of linear functions through quantitative reasoning. The purpose of this study is to examine the students’ quantitative reasoning while engaging in the mathematical modeling task, which was designed, for learning the linear function. The participants of the study conducted with a teaching experiment were consisted of ten 10th grade students with three girls and seven boys. The students engaged in the written task in pairs which they decided to work together themselves. The data were each group’s written solutions and the transcriptions of the camera recordings of the process of working on the task. The collected data were analysed in two stages as ongoing analyses and retrospective analyses in the direction of the students' quantitative reasoning. Based on the data analysis, it was seen that students were cognitively more active while they were working on a situation which they had experienced or which was meaningful for them. It could be said that designing the task by considering the students’ quantitative reasoning triggering reflective abstraction was important factor in supporting the students to construct the quantities. In this context, it is suggested to use from mathematical modeling tasks during the teaching concept