Not all negative actions have positive replacements.

* Please don't lick your knife.

* Please stop asking for X as I've already told you we can't afford it (I sometimes do offer to help them find a job though, or suggest an entrepreneurial idea; depends if it's a short term demand or a long-term or capital item.)

You could create a dummy action (distraction/redirection), which I see often -- it seems needlessly passive to me.

One could say "please take care with your knife" but that assumes the child knows what "care" means which is often a bad assumption with a child. One could also give the child a rubbish knife to remove the risk (I'd rather they have usable tools).

With commands like "don't run" by using the more passive "please walk" one is limiting unnecessarily. "Please skip, or jog, or walk, crawl, roll, sidle, shuffle, hop, shimmy, or ..." sometimes it's better to be direct (but maybe not always).

FWIW, you're getting your psych terminology mixed up AFAICT: "Please walk!" is a negative reinforcement, it's an admonishment to increase an action. "Thank you for walking" would be a positive reinforcement (only if they're already walking). In contrast "Don't run!" is a positive punishment, an admonishment to reduce an action. For completeness, a negative punishment would be taking away something to reduce an activity, maybe stopping smiling at a child when they misbehave.

I do agree it's good to reinforce desirable behaviour. One of the things that's difficult about being poor is finding no-cost pleasant stimulii for reinforcement. One can easily use food, which I think is possibly one of the factors in the obesity crisis.

Well, its hard to give positive reinforcement right at the instant where bad behavior is happening. I think what he meant was something like

* You were behaving really well ("like a grown up", which some kids love) when you were using your knife to cut the food only before

I see how this might take some practice to do on a regular basis. I think it should be easier if the positive/negative feedback is verbal only (that's good/that's bad and not much more), which relates to your point about no-cost reinforcement

Yeah I read a similar piece of advice recently to the effect "toddlers hear a lot of No. Limit the No and when possible offer them a qualified yes instead."

Something like:

* Can I eat another banana?

* After we go for a walk, you can eat another banana.

Apparently another important part of the parenting process is consistency -- if you promise "after X, we will Y" you should do it or explain why not / what changed.

I think promises to children should generally be rare and meaningful, not just thrown around.

The conditions always change with children. If you already promise ice cream and then the kids start behaving badly, what can you do? You either get into threatening mode ("no ice cream for you then!") or break your promise or you put up with it.

Furthermore the kids don't even enjoy it unless it's unexpected. As soon as they feel entitled to the ice cream, they are more likely to argue about who has more than to just smile and eat it.

I have anecdotally found this true as well. Toddlers and small children have a terrible working memory. It really is what's limiting their ability to count, speak coherently etc.

Promises often needs to be repeated to stick. Therefore they need to be made meaningful. Making promises about a banana when working memory have purged that information five minutes later just makes promising stuff pretty empty (for really small children, that is).