One of the most important elements that should be considered in graphic education is teaching the basics of visual arts and freehand drawing to graphic students.

Subliminal communication through color and graphics

Universal access- the legibility of colours and particularly of text.

in my opinion, the "cape horn" of graphic design:

orientation systems / signpost

Here's a list of topics that could be included :

Design software

Typography

Web Graphics & Website Design

User Experience

Brand Identity

Book, magazine, and package design

Photography

Illustration

Data Visualization

Design research skills

Professional presentation skills

There are some interesting ideas here, but as a graphic designer/illustrator who now works in film theory, I’d say the primary skill is understanding how diverse humans of different cultures read visual material, whether static or moving. This would include information on the mechanisms of visual perception, how we see, how this affects the things we notice and the things we don’t, and an understanding of how humans read everything as causally structured; ‘I see this because of that, and now that then leads to this...’

In terms of a curriculum this would be applied through any of the disciplines/skills groups mentioned above. Layout/composition, use of colour, understandings of visual literacy, semiotics and aesthetics, as well as the many disciplinary technicalities. For example, in typography it is essential to understand that choice of typeface affects not merely the appearance of text but also how much of it we assimilate, or how the size of type, the leading (space between lines), page architecture such as indents and borders, and character count across a line can all affect our ability, for good or ill, to read the text.

Both of these areas are narrative to their core; they present information that users visually, in different ways, build into understanding. Without comprehending this central theme, no knowledge of software, specialist equipment or access to stock material can make someone a better designer.

Gerard Gibson, that's an excellent observation on what I call interpretative design-being aware of the relationship between the design and the understanding / meaning created by the viewer. My specific interest is the spatial composition of heritage exhibitions.

My opinion is that colour, typography and the basic design elements should be key in the course

You've already received great suggestions. I'd also include some history of how graphic design principles have developed in ways that prompt or capitalise on the emergence of (new) media technologies (including the printing press through to HTML5 and smart technologies). I'd also include something that gets students to think about the same design issue (e.g. website hierarchy) through the perspectives of different types of design experts (e.g. information architecture, web usability, user interface design, marketing).