They shouldn't be allowed because the world is full of distractions and using phones will only create more. Sure, using phones would help unlock new learning techniques, but some kids would text, play games, and mess around instead of actually using their phones for a good scholastic use. Calculators, books, and websites can be used but that's what there physical calculators and books are for. Websites can be printed, but I can see your point. But I still strongly go towards my side.
The thing is, if kids want to learn then they will learn. A phone can be used as a distraction, but so can thousands of things. If a kid wants to pay attention in class and get good grades then they will; however, if they don't then they will find some way to distract themselves. Many kids in class, draw, day dream, or talk amongst themselves. It is the student's own will and self control that will get them good grades. If they don't have that then they won't get good grades. Period.
So, while phones can be used as a distraction, students who want to be distracted will be and those who don't will not. Students also need to develop this sense of self control on their own. If they can't handle the temptation of a cell phone or a computer game then they will never be able to keep a real job. Also, cell phones can be used to make calls to parents for forgotten things, money, medications, or even emergencies.