I finished reading Gee's excellent book (2003) a few days ago and I must say I really enjoyed it. One thing that's fascinated me is that it's like a course on cognition seen from the perspective of video games and therefore, it made me revisit most of the important concepts explored in the Understanding Learning in the Online Environment course.

A few weeks ago, I started a thread about Gee's key principles of good learning design because while reading his book, I felt that some principles lead to or were redundant with others. Other students' views reminded me that all principles are very important. Nevertheless, by reading some sections of the book again (especially the definition of each principle), I still believe that understanding properly the core ones can help reduce the list:

That's very obvious for the first principle:

Active, Critical Learning Principle is very complex and, according to pp. 39-40, encompasses Situated Meaning Principle, Affinity Group Principle, Design Principle and Metalevel Thinking about Semiotic Domain Principle.

It is also linked to Identity Principle (see pp. 43-44) and strongly related to Semiotic Principle and Semiotic Domains Principle

Similar relationships may be drawn for other principles:

• Semiotic Principle => Multimodal Principle
• Subset Principle => “Psychosocial Moratorium” Principle
• Committed Learning Principle => Practice Principle which leads to Intuitive Knowledge Principle
• Subset Principle in addition to Practice Principle => Bottom-up Basic Skills Principle
• “Regime of Competence” Principle => Ongoing Learning Principle
  It's also related to Incremental Principle
• Probing Principle => Discovery Principle
• Situated Meaning Principle => Text Principle
• Distributed Principle => “Material Intelligence” Principle

On the other hand, I find the following principles are more independant:

• Identity Principle
• Self-Knowledge Principle
• Amplification of Input Principle
• Achievement Principle
• Multiple Routes Principle
• Intertextual Principle
• Concentrated Sample Principle
• Explicit Information On-Demand and Just-in-Time Principle
• Transfer Principle
• Cultural Models about the World Principle
• Cultural Models about the Learning Principle
• Cultural Models about the Semiotic Domains Principle
• Dispersed Principle
• Insider Principle

I hope this need to summarize them hasn't lead me to make false associations. I'd be happy to know what you think and to be corrected as appropriate...

References:

Gee, J. P. (2003). What video games have to teach us about learning and literacy. New York, Palgrave Macmillan