This may not be too relevant for your needs as it goes back to the early 1980s, but I'll lay out what my design education was:
I took a three year full-time diploma course in what was called 'Visual Communication and Design', I also did one-year part-time post-graduate courses in photography and video production, while teaching.
Bearing in mind there was no such thing as a Mac in 1983, during the three years in design school, most of the work was taught using traditional methods, a focus that I still believe is more than capable of teaching the fundamentals of design. In the first year, classes included:
One full day of drawing, split into general drawing and life drawing. Life drawing was the real deal, nude models, plaster casts, field trips etc. General drawing was hours of drawing things like egg-beaters, cubes, household objects with a perfectionist and technical approach taught by a drawing teacher who had been taught by someone who taught at the Bauhaus. It was one of the most difficult classes I've ever had to do, but it taught me how to see.
3D design, working in materials like metal, plastics and moulding of different materials.
2D design which included silk-screen printing and illustrative work using gouache and acrylics.
Typography classes, starting out with hand-lettering and constructing traditional Roman letter-forms, working our way up to designing typefaces by hand with drafting instruments. We also worked with letterpress, setting type by hand and studied the history of typography and had to sit exams on it.
Full day of photography. Huge darkrooms and studios, shooting work we'd done in other classes, as well as portraiture and field work.
Projects that involved giving presentations to the entire design school, all years... this helped tremendously down the line with client presentations and even brief-taking.
Repro: where we studied how ink gets on a page. Sounds simple, but these classes were the fundamentals of knowing how to work as a print designer. Lots of field trips.
But the second and third years were even more involved, extending into packaging, campaigns, full-scale typesetting, book illustration etc with outplacements in the third year. Looking back over 25 years ago, our first early projects in 2D design were done with cutting out and collaging techniques using only coloured paper. Using these simple techniques trains you by focusing only on matters of balance, proportion, scale and hue.
The fundamentals of design are not to be found in knowing how to use software, they're in much simpler methods that build up to a rounded overview of the entire field. I don't usually comment on work in this forum, but often I see work that shows capability in software technique, with little understanding of sound principles, particularly where type is concerned.
In my last job, I also had to coordinate the work of some freelancers, a couple of whom would send me work in RGB, for instance, or without bleeds. They didn't last long. So, regardless of whether it's print or web, 3D or 2D, packaging or illustration, my advice would be to look for a course that isn't purely about the software. Having a look at any student shows or graduating portfolios from any particular course will give you insight into what can be expected, as well as closely studying the details of any course.
I wish you all the best. It's a highly-competitive field where talent doesn't always win out; you have to know how to effectively communicate as well, so don't spend too much time in the early stages looking at the nuts and bolts of specific software packages, and give some serious thought as to where it is you want to end up. Good luck, but make your own luck as well.
