High school students' meanings of cartesian coordinate system

The aim of this study was to investigate high school students' reasoning of spatial and quantitative Cartesian coordinate systems, their meanings of a point on a graph, outputs of a function and graphing within spatial and quantitative coordinate systems. The study was conducted at a private high school in Istanbul towards the end of Spring semester in 2021-22 academic year. Participants consisted of 229 high school students from different grade levels who learned different kinds of functions and graphing in Cartesian coordinate system. The instrument with nine open ended questions was developed by the researcher based on the literature. Data were categorized by coded analysis and descriptively analyzed mainly according to framework for reasoning about graphs in spatial and quantitative Cartesian coordinate system and framework for representing a multiplicative object in the context of graphing. Analysis of the results showed that students had critical difficulty in conceiving axes as frame of reference to represent quantities as horizontal and vertical directed distances from origin in describing location of a point and coordinating quantities. Additionally, results showed that significant number of student students viewed x and y-coordinates and output of a function as a point on a graph hence carried non-normative meanings for point in terms of multiplicative object. Besides, students' difficulties with function and function notation found to be an issue in their reasoning about points. Relatedly, results regarding graphing in Cartesian coordinate system pointed to students' difficulties in envisioning a graph as an emergent trace of multiplicative object representing changes in two quantities simultaneously. Students either focused on gross variation of the quantities and sketched a memorized graph, sketched a discrete graph, could not envision how the graph behaves between landmark points or sketched two separate graphs considering time as a secondary variable.