It is not uncommon to find the ability to multitask in the project managers' jobs requirements. What is actually "multitasking" and are project managers really doing different things at the same time? Say, for example, as these two performers unicycle and juggle at Exeter Bike Week Event 2006?
I looked at the research on the topic. It shows that we overrate our ability to multitask. See, for example, what neuroscientist Earl Miller at MIT says: "People can't multitask very well, and when people say they can, they're deluding themselves. The brain is very good at deluding itself. What we can do, he said, is shift our focus from one thing to the next with astonishing speed."
With the technology in hand, we tend to delude ourselves even more. Especially, if you find yourself, as I sometimes do, among high-tech jugglers. Research conducted at Stanford University found that multitasking is less productive than doing a single thing at a time. For multitask believers, researches have (sort of) good news: multitasking is possible, but it comes with a cost to efficiency and productivity, while also raising risks. See the research done by the American Psychological Association http://www.apa.org/research/action/multitask.aspx.
I can do some salsa moves, flip crepes with my right hand and wipe clean the excess of butter on the pan with my left hand, all at the same time. But I cannot type a final project report with my right hand and write down the plan for a new project, while getting updates on a running project over the phone. What I can is to master the tasks. And say good buy to the illusion of multitasking.
To master the tasks, I apply the 'urgency vs importance' test. From the list above, the plan for a new project will get priority as the launch of activities depends on its approval. I'll focus then my attention to the running project's updates and the final report will be my priority nr.3. I'll commit to the order of priorities and make sure the team members share the same understanding. Depending on circumstances, tests of 'task's value for the job' and/or 'estimated effort per task' can apply.
Next time, at a job interview for a project manager or project assistant position, when you are asked about how good you are at multitasking, you may want to clarify with the interviewer what they understand by multitasking. If they believe in the myth of multitasking, let them. Just make sure you show how you can manage tasks. It can be examples from your experience. Or the interviewer can offer you an in-tray test. And make sure you do not multi-task at the interview, if possible :).