A practical point... the slower the spinning, the better your chance to see this illusion. One more tip: try focusing on the left edge of the picture, then slowly pan your eyes to the right.
Looking at the dancer's feet may help her turn anti-clockwise. Concentrating on the shadow may help to switch directions.

History of the Spinning Dancer Illusion
The spinning dancer illusion was born out of a Yale university project to test for 'Left Brain' or 'Right Brain' dominance. The study was started by Roger Sperry who was investigating epilepsy and left / right brain neural connections.

Left Brain Functions
Perhaps speech is the most important left brain function. This left side also processes maths and logic.

Right Brain Functions
The right brain is the locus for spatial awareness, imagination, fantasy also risk taking.