Introducing the notion of Proof
In discussing jumping straight into the algebraic method of doing distributive multiplication and collection of like terms, the point is made that "simplifying those expressions would result in stripping the expressions of meaning and connections with geometry."
The capacity for logical thought, reflection, explanation and justification is described as one of five interconnected strands of mathematics learning that are essential for what the editors call mathematical proficiency.
In discussing the importance of all students in the class participating in discussions, she quotes "To the extent that some students are excluded and do not participate, the learning possibilities are diminished for everyone".
Regarding the difficulties of learning through being told, Colin was only able to hear Pam's idea but was unable to learn from it. This was a consequence of a very short discussion time which didn't allow him time to ask questions and discuss Pam's solution.
This is the basic tenet of constructivism: learners need to construct understanding by making connections themselves, not simply by being told things.