DD6 is a perfectionist, who is very afraid of trying new activities or taking to the next level with existing activities.
1. I agree that we do try to remind her of her previous fear of trying (for example) gymnastics and how much fun she is having now.
2. We often sit with her while she observes the new activity and/or situation. Ask her what are her concerns and questions, and address them accordingly. This seems to ease her mind, but not always change her mind.
3. Sometimes, we show her video clips (found on web, mostly youtube) or read books about the new activity/situation.
4. For the activities she loves and enjoys already, we try to praise her for trying rather than the end-result. We also try to drill the concept of "strive for excellence and not perfection." I must admit, this is easier said than done/understand by the child.
5. We see if DD's best friend(s) can join the same activity... having a good buddy sometimes work wonders.
6. For games like Chess and Scribble or puzzles, we just leave the game open in our family room (or wherever DC spent most amount of time). Sooner or later, DC would either start playing or be curious. One down side though: One time DC took 6 wooden puzzles apart and mixed all the piece, and promptly hid a couple of pieces for treasure hunt. Unfortunately, this set of puzzles did not come with solutions and the treasure hunt did not have a map. LOL!
Hope these tips helps...
Mag