Coordinate systems are used as representational tools in the learning and doing of mathematics. However, in many mathematics curricula, coordinate systems are taken for granted and coordinate systems are often unnecessarily restricted to the two-dimensional case. Additionally, researchers rarely address how students might construct coordinate systems or the meanings students impute to coordinate systems. In this study, I investigated how students construct and use coordinate systems in spatial contexts to quantitatively organize perceptual/sensorimotor space into representational space. Specifically, I conducted a constructivist teaching experiment to explore the mental operations and schemes involved in four ninth-grade students construction of spatial coordinate systems. As the teacher-researcher of the teaching experiment, I designed tasks by means of which I asked students to locate objects in two- or three-dimensional perceptual/sensorimotor space and to coordinate units along multiple spatial dimensions. I also constructed second-order models that accounted for the students mathematical activity and shifts in their reasoning through both on-going and retrospective analyses. This dissertation reports results from the teaching experiment. In my analysis, I model the operations and schemesframe of reference coordinating scheme and reversible decomposing schemethat were involved in the students construction and use of spatial coordinate systems. I also identify ways of reasoning that served as productive cognitive resources in the students constructive activities: coordination of multiple images, logical multiplication, and levels of units coordination. The findings have important implications for teaching, curriculum development, and research in regards to students learning and application of coordinate systems.