It's a common scenario... The rider tries to send the horse forward while unconsciously blocking them from going forward, or tries to slow down while driving with a tight leg and seat. Learn how to fix this problem here!
The fastest cross-country horses are not necessarily the fastest horses in general, but the ones that are the easiest to set up for the jumps. So work on your horse's adjustability.
Every well ridden corner is a suppling exercise, and should be recognized as such.
A tip for all of the instructors out there... When a student has a lightbulb moment during a riding lesson, ask them to explain it you in their own words. This way it becomes even more cemented in their own mind, and you can more easily help them find it
Always think about the depth of the water when deciding how fast to approach and negotiate a water obstacle. Riding too fast in deep water can easily cause the horse to lose his balance or even fall.