The Cartesian coordinate system is a fundamental necessity to mathematics. Anyone beyond elementary school knows this. However, when a student first encounters the system, it can be overwhelming. Two number lines- one horizontal and one vertical- at the same time? Negative numbers? This can be a difficult system to master for many students.
Helpings students recognize the usefulness of a mathematical concept or system, before they are introduced to the technical terms and procedures, can be very helpful. Surely students could learn about the Cartesian coordinate system by having the teacher stand in the front of class and lecture on about the origin, x-axis, y-axis, procedure for graphing, etc. However, in the case, students do not fully recognize the utility of the system. Additionally, all the terms, definitions, and procedures can scare students away. Admittedly, this is how I taught it last year, resulting in low engagement and effectiveness. Instead, having students discover the Cartesian system layer by layer would allow them to realize its beauty, before learning the ins-and-outs.
To do this, I had two students volunteer come to my interactive white board (IWB), which was simply a white screen. I had Student A face the board, while Student B turned the other direction. With student A watching, I marked the board in the upper-left hand corner.
I then created the same exact page, before I had marked the board, which in this case was simply another blank white page. Student A would now give directions to Student B on where to mark the board, trying to get as close as possible to where I had marked it before. However, Student A now had to turn around and face away from the board. This forced Student A to only give verbal clues. Student B would use these clues to make their best guess, resulting something similar to this:
Most cases resulted in the the students getting vaguely close, but never spot on. As a class, we reflected and discussed how difficult this was.
I then had the students repeat the process, though this time I added an x-axis and y-axis (explained to them as a horizontal and vertical line). Again, I marked the board with Student A watching, and Student B facing away: