This is probably the number one problem that young teachers have - the student who misbehaves. He gets something out of making poor choices. It works for him! For your entire career, you will have students like this so now is as good a time as any to figure out how to best work with kids who misbehave.
While letting the parents know and getting them is involved is always a good idea, you can't always depend on parents to offer the consequences that will make a difference. First of all, they are sending you the best kid they have. It's not like they are keeping all the good ones at home! Regardless of how this child behaves in your class, they love him dearly and is they could control his behavior in school, they would. They are probably exhausted from doing everything they can just to manage the behaviors at home. What they want is a teacher who understands their child and cares about him anyway! Normally I work toward making all of the reinforcement and consequences self-contained within the school day. You can let Mom and Dad know how his days are going but I usually don't depend on the family to come home after their own exhausting day and be the reinforcer. You can't always depend on their consistency and that will frustrate you and will not help the behavior if the parents are inconsistent. Of course, if you have parents who really want to get involved, their extra reinforcer or consequence will only move the change more quickly.
With the particular child that you describe, it is hard to know what he can control and what he can't but sounds like there might be some of both If he can control it and just chooses to be distracting, that is the easier to distinguish. If he really can't control some of the behavior, you have a different problem. That is where RtI might fit in.
I know you learned all this in school but now is the time to apply what you know. Sounds like you already have a behavior plan for the class that is probably working well for the class, but is not enough for him. I know you have set up class expectations or rules and that the children know exactly what is expected. So... what to do next?
1. Make sure to develop a relationship with this child. If he likes you and wants to please you, your job will be easier. Invite him to spend lunch with you one-on-one or to come in early in the morning or help you in the afternoons. Find out what he likes (this will help as you choose a reinforcer for him) and what makes him tick.
2. You have already gone to the positive (Whoo hoo!), making sure to praise other students for the behavior that you want in him and certainly to praise him specifically when he makes good choices. Keep that up, even when it is hard, and the last thing in the world you want to do is praise him! He is responding to attention so make sure he gets lots of it for positive actions.
3. Ignore as much of the inappropriate behavior as you can. That means that it will increase for a while because he figures he needs to do more if you don't respond at first, but over time if he does not get attention from you or from the class, the behavior will diminish on its own.
4. Chart his behavior for a day or two to get a baseline. What exactly is he doing, how often? This will help you target a single area and will help you know when things are getting better.
5. An individual plan for that child is also the way to go. Figure out what motivates him and offer it as the reinforcer, such as being the line leader or even an extra PE or extra computer time or something that you can arrange in the school day as a pay off for earning a certain amount of points. Make the amount of points attainable, so he can begin to know what it feels like to make good choices. The reinforcer has to be something strong to hold his behavior throughout the day. You might even have to break the day up into smaller pieces and allow a reinforcer after shorter times.
I know that you already know all this and have probably already begun to work on your plan for him, but this is the type of student that every teacher has. Learning to help him use his energy and positive traits in a productive way will make a huge difference in his learning success and the class' peace of mind. Make sure to let us know how it goes!