The Pomodoro Technique & Scrum/Agile
I recommend checking out the Pomodoro Technique. It's a super simple productivity technique that is designed to improve your focus and your own productivity by eliminating distractions, and maintain concentration by taking breaks at optimal times.
The best part is that there is no book to buy, and you can get started in minutes. The Pomodoro website can get you up and running quickly. Basically, you're focusing on a single task for 25 minutes, and then you take a 5 minute break before starting the next Pomodoro. After 4 Pomodoros, take a longer break.
Lifehacker users voted it the #1 productivity method, and I find that it's compatible with the Getting Things Done methodology (a book I personally recommend). Will it cure world hunger? No. In fact, you can't even eat the timer even though it looks like a tomato.
It works a lot like scrum. You create your list of tasks, and then estimate them based on the number of Pomodoros they will take to complete. Each day is like a sprint, and each Pomodoro is like a story. As you get better at the technique, you perform daily retrospectives to improve the process and the estimation. If you don't like their pencil and paper approach, you can use Trello.
I'm definitely not an expert, but I've already realized some of the benefits. It's amazing how many little distractions occur in a 25 minute period, killing productivity. Unlike a computer, we humans are absolutely terrible at switching tasks.
With an entire team, the challenge would be coordinating everyone to minimize potential interruptions. I did find some teams using it with limited success. For example, here is a detailed analysis of Pomodoro combined with Scrum:
Some interesting quotes from that article:
"I think expanding the Pomodoro Technique® to a whole team can prove very difficult. Probably it's not even desirable."
"How you work most efficient is very individual, but to be productive I think you have to feel comfortable about, and like, the way you work."
Give it a try. Couldn't hurt.