In an effort to generate some interesting discussions, I thought it might be interesting to discuss different learning environments.  In my research, I've noticed there are a few different approaches to teaching gifted children in particular.

1) "Enrichment" - in our school system, "enrichment" is really popular.  Apparently enrichments means to provide more worksheets or assignments to the same concept being taught so the child spends the appropriate amount of time on a subject.  The additional works is at the same cognitive level as the regular classroom work (i.e. not the same concept but a greater challenge). 

2) Accelerated pace - same subject material.  Same amount of work.  Faster pace. 

3) Expansion - My understanding is that this one takes the same concept and presents the concept in a variety of different ways.  For example, 3*7 is taught as rote, then taught as 3+3+3+3+3+3+3, then taught with a manipulative in groups of 3 7 times, then shown as 3 squares next to each other in 7 rows, etc.

4) Deep dive - A concept is taught once.  Work is provided until the concept is learned, then the complexity of the concept is explored to the child's ability regardless of grade level.

Am I missing anything?  In what types of environments have you found the different styles?  Pros/cons?  Other thoughts?