One could argue that school is primarily useful for learning to think creatively and problem solving which could be applied to anything that is encountered later on. Many students learn how to utilize the creative process as well as synthesize information into visually engaging forms of communication. That is extremely important.
In order to remain relevant to the design profession, however, designers should know what can be done and what advances have been made to allow things to happen. Similar to being aware of visual trends, designers have to be aware of new code, techniques, and devices that exist. Without this awareness, designers cannot communicate with their developers or use all the weapons available to them in their arsenal. Student designers must be familiar with, let alone embrace the new turns the web has taken and be willing to constantly learn and make adjustments moving forward. Otherwise they're just in a box.
To Students: Become familiar with HTML5, CSS3. Jquery, and what they can do. Learn how and why they are implemented. Better yet, learn how to implement them. Become familiar with responsive design and how it effects the ideal website today. Know both visual and web-based design trends. Learn how UX and Information Architecture works. Predict for the future and try new things. Learn new things. Push your old-school professors to learn new things. Challenge them respectfully (You likely know something web-based they don't. They have years of design experience within the design industry).
To Professors: Be ready to learn new things. Learn what you can about responsive design, HTML5, CSS3, and jQuery among other things. Make your students explore new techniques. You have many connections that can serve as ways to educate students. Invite designers from cutting edge firms to hold a discussion with their class. Utilize the resources on the internet, blogs, and others designer's sites. Know you are laying a foundation for the next generation of designers.