It is common for mathematicians to use counterclockwise (ccw) as positive, and clockwise (cw) as negative. For example, trigonometric functions increase from $0^\circ$ along the positive $x$-axis (East) to $90^\circ$ along the positive $y$-axis (North), sweeping out the first (NE) quadrant of the Cartesian coordinate system. The right-hand-rule rules such coordinate systems.
On the other hand, non-mathematicians are exposed to cw advancement as increasing time in all(?) analog clocks, and so for many of them, cw is the natural sense of positive angular advance. I myself, as a mathematician, view the annual calendar as advancing ccw—summer @$(0,-1)$ South, fall @$(1,0)$ East, Christmas @$(0,1)$ North—but I learned when making a presentation to random people (faculty) that many (most?) view the annual calendar as advancing cw.
My question is:
Q1. Where did the mathematician's ccw convention originate, and where did the clockwise convention originate, and why are they opposite one another?
Q2. Are there data on how we mentally view the annual calendar advancing—linearly: L/R, R/L, circularly: cw, ccw?
Likely the answer to Q2 depends on nationality/culture.
(Although I've wondered this a long time, this posting was triggered by the MESE posting, "Why do we conventionally treat trig functions as going anti-clockwise from the right?.")