I think cartesian coordinates may start with (0, 0). To move left and top by 1 px it's (1, 1).
While in array it's (1, -1).
I don't know what you think you mean by "in array it's (1, -1)". (0,0) is the origin, and that's where you start. To get to the fourth quadrant, you would turn right, move forward, then turn left again (which is now down), and move forward and there you are at (1,-1). (Or if you mean internally, then the origin is probably , but that's not relevant at all from the teaching Cartesian coordinates thing, because the 10-year-olds aren't learning about how the system works.)