Developmentally, most 3Â year olds are a bit young for reward charts to work. And they're far too young for reward charts to work if they have 1/2 a dozen things to keep going for a week. 3 year olds need very immediate feedback for them to be able to link behavior with reward. The other thing is that you need to take a good look at your expectations for your daughter. At 3, according to all the dentists I've talked to (OK, 4), YOU still need to help brush her teeth. They don't have the manual skills to get the teeth as clean as they should be. (You should also floss for her.) Now, if she's refusing to brush when you're helping her, that's a different behavior to work on -- it's called 'cooperating with mommy'.
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For routine kinds of things, it often helped my kids is to establish the routine and then ask them what comes next. They were so proud of themselves for being able to tell me, that it went well. But to be honest, I'm still 'monitoring' the bedtime routine for our 7 and 10 year olds. The routine is: pajamas, snack, read to self, brush teeth, read with mom/dad, go to bed. And I still need to remind them of every bleeping step to get them moving. They'll happily get their pjs on, and then get distracted playing with something (or in ds' case, checking scores on ESPN.com). Writing this out makes me think I need to back off on that a bit for our 10 year old. However, our 7 year old still needs the structure we provide. (She's not very internally structured and so does need firm external structure.)
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For the whining -- that's a big one. While whining drives me nuts, I think it's important to actually turn this into something that she CAN do, rather than something she can't. What does 'not whining' look like? Does your daughter know what it sounds like? Can she do it even when under stress?
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One technique that I've used to some success is to ask my kids to rephrase. It's HARD to keep the emotion out of your voice when you're upset, even for adults. So, when they were 3-4, I'd say something like, "Oh did you mean, "can I please have a glass of water?" Initially, all it took was them saying "yes" and I'd be OK. I figured I had to TEACH them what not whining sounded like. Then once I was pretty sure they understood it and they could use the polite request or polite voice when they weren't under stress, I'd ask them to rephrase a whine. "Hmm.. that sounded rude or whiny, can you say that another way please?" If they needed help, I'd model for them and ask them to repeat (sometimes they would, sometimes not, that's OK). By the time they were 5-6, we were down to: "That sounded rude. Try again." Interestingly enough, dd (who's 7 and my major whiner) can immediately rephrase it into something more polite, but it's very very hard for her to get the whine out of her voice. We're working on it, but I expect it to be a couple of years, quite honestly, before she can rephrase both tone of voice and the sentence. (And then we'll have 2-3 good years until the teenage voice starts to come out).
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If you choose to go with rewards, then as a previous poster noted, you'll have much more success if you work on one behavior at a time. Reward charts work really well for specific behaviors that you want to train (and it is training), but that will eventually become second nature. So, for example, I used reward charts to potty train our ds. I didn't have to use them forever, just about a month. However, I've NEVER used rewards for school work. For school work, I'll sit down with them if they need it, I'll ask them if they've done it. I'll help them in any way I can. But the homework is THEIR work, and if they are not motivated to do it or choose not to do it, then they get to deal with the school on that. (We don't homeschool.)
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Finally, some kids do well with reward charts, others don't. Ds responded beautifully I tried a reward chart for potty training. I tried it with dd last year for doing chores and piano practice without whining. It was a huge failure. After 3 days, she took it, wrote across the top "I HATE CHORES!" and stopped caring. Sigh...