In the earlier years of the internet, most people accessed the web through only one method - a mouse cursor, controlled by either a laptop's touch pad, or a mouse. New ways of interacting with devices and computers continue to arise, though, and these have interesting implications for design on the web.
The most significant new interaction to affect the web in recent years came with the advent of hand-held devices and smart phones: touch screens. Despite the fact that phones have been browsing the internet for a couple years now, the World WIde Web consortium, which defines the 'standard' for websites and browsers, has yet to fully cover all the interactions this introduces - especially since each new kind of device is looking to push the limits of its interfaces even further.
It's easy to think of a 'touch' as a click, but this is too simplistic. One of the most fundamental differences in the way touch screens interact with the web is that somebody with a touch screen cannot 'hover'. Hover effects have become so ubiquitous (particularly in navigation) that some mobile browser vendors have had to introduce interim measures whilst the web catches up. For example, Apple, with it's iOS version of Safari, checks for certain styling tags, and if it finds them, causes the first user touch to trigger the 'hover' effect, and the second touch to trigger the 'click' effect. This was necessary in order to allow users to access much of the already-existing web that utlised hover effects in navigation. For any new website, relying on this feature is both lazy and risky - different devices use a whole range of different browsers, and if you're not using the specific tags these browsers are looking for, your navigation won't work.
For this reason, any site we now develop switches to a touch-based navigation if the screen resolution is below a certain size. Whilst this is the industry standard, though, it won't remain that way for long. There are now tablets whose screen resolution matches that of smaller computer screens, or hybrid laptops that also support touch screens, which cannot be utilised effectively. For this reason, even companies like http://www.google.co.uk/ have elected to have a menu of only one or two items with no hover effect, and a menu that must be opened with a click (or touch), even on large pc screens. Aesthetically, this can seem daunting, but if done right, there's no reason it can't fit into a great design.
The other increasingly common method of interacting with a touch screen is by 'dragging' or 'swiping'. This is only being gradually implemented on the web, but it results in a much more user-friendly mobile experience - electing to utilise more vertical space (i.e. taller pages), for example, reduces the number of times the user needs change page, and putting a simple 'Back to top' button at the foot of the page can save them the annoyance of having to scroll all the way back to the top. Whilst it may seem like a small thing, these kinds of details result in greater user satisfaction with your website, and are a direct result of adapting to the different ways people now access the web.
Whilst touch is obviously the biggest new control method at the moment, and will continue to grow in importance, it is by no means the only alternative to a mouse. There are a few others that, whilst not yet wide-spread enough to be of real note when designing websites, may catch on quite quickly. One such possibility is the increase in voice-controlled technology. Apple, with iOS, Microsoft, with its xbox Kinect hardware (though traditionally a gaming machine, Microsoft is trying to encourage customers to use its new console for far more numerous applications, such as browsing the web), and Google, with its Android operating system, are investing in voice control. Another possibility are devices like Leap Motion (https://www.leapmotion.com), which reads hand and fingure gestures with fine detail straight out of the air.
It's a little to early in their development to know how much these technologies will affect the web, but like touch interfaces, they may become increasingly significant and are therefore worth keeping an eye on. The web will continue to grow and change just at the devices we use to access it do, and growing with it is vital to stop your site (and therefore your school) from appearing outmoded or old-fashioned.