While I disagree with life not being a competition, I agree with it too. Ha! Sometimes competition is a good thing, others a bad. When we learn to compete against ourselves, we are challenging ourselves to be better at whatever the process or job at hand is (I do this often to prevent boredom). When we compete against others, we are learning to win AND lose. Life itself is not a competition, but life is full of competitions.
As for math, I was a math whiz... until I got to my junior year in high school. I allowed myself to step down from the accelerated path/the competition to be the big fish in the small pond. Only it backfired on me. Instead of bringing home A's in hard classes, I was barely making C's in the easy ones. I needed the challenge. I needed the competition - whether that was from within or with my peers.
So you don't want to not push her, but at the same time, you don't want to push her too hard. The thing I love to do with my DS5.5 is to challenge him to the math (and grammar) lessons while playing or having normal conversations about things not necessarily related to a lesson. With math, it gets harder as they get older, but it still can be done. I would start there... if you're talking about her favorite hobby, let's say it's taking pictures, you can talk about figuring out how many pictures can be taken in so many seconds on a certain setting (if you dive into aperature settings, etc...). Or, the total pictures taken when changing the size). If it's making jewelry, you can ask how many 1/2 inch beads can be placed on a 10 inch string (adding other sized beads or leaving room for the "clasp").
I don't know what is actually taught in 4th grade math, so my examples may be WAY off, but I know that working math and grammar "problems" into every day conversations is really exciting to DS.
Also, have you talked to the school/teacher? Maybe now that she's exceeded what they are learning by what she's done over the summer, they can give her more challenging questions with the regular course of study????
