There has been some interesting research published recently about children eating their vegetables. Check out http://www.nutritionsociety.org/blog/paper-month-nudge-children-eat-more-vegetables (now unavailable – edit Sept 2022) for more details.
It goes to show that if you don’t offer a variety of vegetables, children will not have the chance to try them. I meet lots of parents who say their children won’t eat vegetables. What they often mean is that their children won’t eat some of the vegetables they are giving them. Broccoli and cabbage are common culprits. I recommend trying other vegetables, trying offering raw vegetables for a different texture and not making vegetables a big deal. The worst thing to do is offer a treat for eating vegetables as this makes them sound like they are not nice and you need a treat to cope with them.
Don’t get me wrong, I know how frustrating it is when vegetables are refused – often with loud protests!