It seems to be a quality parents want to instill in their children, as well as i.e.- teenagers bragging about having music playing, texting, video chatting, all while doing homework, they claim is the best possible atmosphere; for getting their school work done....
"Trying to do two things at once is usually a recipe for doing both badly, according to a long line of research. We’re slower and less accurate when we try to juggle two things."
Generally, it is thought that multi-tasking is just the brain rapidly shifting its focus from one matter to another instead of doing both (or several) things simultaneously. This is very straining and distracting for the brain, and so it ends up doing less well on both tasks than it would if the tasks were done separately.https://www.apa.org/research/action/multitask.aspx
However, there is an interesting article that says there might be more going on that that. The article explains 2 studies done that seem to indicate that our ability to perform a task might depend on the context in which we learnt to perform the task. E.g. " If you’re typing while listening to a conference call, maybe you’re less likely to make mistakes if you were equally distracted when you originally learned to type." https://hbr.org/2015/01/the-curious-science-of-when-multitasking-works
People have a tendency to get distracted during mundane tasks that are not immediately rewarding. They counteract this by doing things that are immediately rewarding, such as answering a text, listening to music, or checking Facebook notifications. We tend to repeat behaviors that feed the pleasure center of our brain, and thus we learn associate certain behaviors with pleasure (and feel encouraged to continue repeating them once they are determined as 'pleasurable' behaviors). For this reason, we may keep coming back to things that have been pleasurable in the past, and all the more better if that thing can retrieve the pleasure in a relatively quick period of time (i.e. music, Facebook, versus exercise or reading a good novel). There is evidence for this in the phenomenon known as 'conditioned place preference', which is a person's conditioned preference for places that they associate with high reward, and an aversion to places that remind them of negative or traumatizing events. In those who take stimulant medication (medications that tackle the 'reward' center of the brain), there appears to be a developed conditioned place preference for the area(s) where the medication is taken. 
That being said, it may be that children need these distractions in order to increase their intrinsic motivation to focus on tasks that are not immediately rewarding. In that sense, this form of multitasking can be seen as helpful. The problem steps in when you have people who are intolerant to unpleasant stimuli (i.e. people who naturally have low activity in their pleasure centers). These people may find it difficult to multitask because they may struggle to focus on one thing long enough to understand it. They may also demonstrate impulsive behaviors due to lack of control over their reward center (and, by proxy, their motivation). 
The optimal learning state is considered to be that of flow, colloquially known as being 'in the zone'. This occurs when
a person performing an activity is fully immersed in a feeling of energized focus, full involvement, and enjoyment in the process of the activity. In essence, flow is characterized by complete absorption in what one does.
The suggestion behind such a mental state is that the person is singularly focused on the task at hand. Therefore, it may be less that multi-tasking increases one's ability to perform well in school; rather, it may be that the ability to achieve a sense of singular-minded focus on one task at a time may put you in a better position to accomplish more in a shorter amount of time. In this sense, it isn't how much the student can do at once, but how much the student can accomplish in a set time period that may determine their success in school.
 Tzschentke, T.(2007). Measuring reward with the conditioned place preference(CPP) paradigm: update of the last decade. Addiction Biology. 12, 227-462.
 Grant JE, Potenza MN (2004). "Impulse Control Disorders: Clinical Characteristics and Pharmacological Management". Annals of Clinical Psychiatry 16 (1): 27–34.