Here are some obvious facts to get out of the way...
Most students are physically capable of driving.
Most students are able to learn acceleration, braking, and turning - the basics of vehicle control.
Here is the most important fact that is also easy to forget...
Most students do not understand the serious responsibility of driving and how their driving can alter their lives or someone else's causing lifelong legal, financial, family, and psychological problems.
The solution is not necessarily time. Waiting till a student is older does not guarantee a safer driver, although in my experience the older a student is, more serious they take driver training.
I would look at these things to determine if a student is mature enough to take driving seriously...
Has the student been given a chore or specific task and did they perform that task adequately and on time? This can be feeding the pets, cleaning a room, sweeping the kitchen floor, or bringing in the garbage cans. Does the student need constant reminding?
Has the student experienced a serious responsibility that involves someone else? This can be babysitting a younger sibling, watching a grandparent, or helping someone with special needs. Most students have not experienced real responsibility.
What responsibilities does the student currently have? It could simply be to go to class and keep grades up. If they are in sports ask the coach for feedback on timeliness, work ethic, sportsmanship, and helping their teammates.
Is your student's overall personality goofy. Do they joke around quite a bit. For the most part that is a good quality but it could be a sign that they aren't ready for serious responsibility. As adults we've learned over time there is a time for play and a time for work. Young people sometimes don't realize the difference or they can't compartmentalize there role. Is it a time to be a brother? Is it time to be a daughter? Is it time to be a student? Is it time to be basketball player? Is it time to be a driver? For them it all kind of blends in together - their personalities don't change. So if your student gets put into a position, environment, or conversation that is more serious in nature - and they remain their goofy selves - then they probably aren't ready to take on the serious role of being a driver. This is one of the main reasons why it is best to wait till they are at least 15 1/2 to take driver training. Waiting will also allow them time to see their friends get into accidents or get tickets. Many older students share stories of how their friend's didn't take driving seriously (some are very sad).