The research they're referencing includes:
- Conditions of Learning by Brian Cambourne
- Relational/Instrumental Understanding by Richard Skemp
- The Learning Principle by the NCTM
- "Active Learning of Mathematics" by Jim Smith, in the March 1996 Mathematics Teaching or the October 1999 Mathematics Teaching in the Middle School
- Vygotsky's Zone of Proximal Development. (My favorite article about this.)
This is a solar system model - a little hard to see. They had fun developing the metaphor and the extending it. Used the idea of earth, other planets, the sun, constellations to all symbolize different roles.
(Students knew they were being taped for publication, and had a later chance to withdraw.)