CSMamma,
I thought I would share a bit from our extended family conversations regarding this issue and others like it.
BACKGROUND: My father-in-law is a retired pastor and a theologian. My mother-in-law is quite a Bible scholar, too. They both read Greek and Hebrew. They rank right up in the top of the Godliest people that I know. In other words, they know their stuff! 
We have had many discussions similar to this and their take is this – when he (father-in-law) was a boy and pastoring churches, there were standards. You know, learn this much information to pass the end of year exam to move on to the next level of Sunday School. They had sword drills and other competitions and there were sometimes prizes awarded. He and his boyhood friends learned & lived out the scriptures as did the children privileged enough to be in his pastorate over the years. They learned Bible stories and memorized scripture because it was expected and God honored that.
Contrast that with today – children move from grade level to grade level in many Sunday School classes just like in many schools without having learned much of anything other than show up, hear a story, eat some cookies and move on. Many of our churches have lost the meaning of discipleship.
There are things that we should do b/c they are good for us even if we are too young to understand or perhaps have poor motivation in the beginning. Showering (not always a boy’s favorite), teeth-brushing, eating vegetables, and yes studying God’s word. Now, I’m not advocating making the Word drudgery, but it is a discipline and not one that we adults always appreciate either, but there is something to be said for being in the habit of study.
I’ve always offered rewards to kids that work hard – sometimes it’s a prize, sometimes pretend $$$ to spend in a store we set up. Yes, the kids like the prizes, but it becomes quite evident that this is not their great motivation. They exhibit what they’ve been learning by choosing prizes for siblings or friends instead of themselves, sharing their $$$ with kids who are visiting and therefore not up to speed on what we’re memorizing. I can honestly say that I’ve had no negative experiences when it comes to rewarding children. There will always be someone whose motivation is wrong, but that is a heart issue of theirs and it need not contaminate what we do with a group as a whole.
Perhaps others have had negative experiences and will chime in, too. I just wanted to share my observations and what I’ve learned regarding this issue.
Many His Word be written upon all of our hearts!
Christie