Spontaneous
Pursuit.
Idiosyncratic
foci
1) Work in opposite direction but insufficient
information to solve by substitution.
2)‘Unusual twist’: more than one solution.
3) Discover complexity: For example, how does
the specific link with the physical and the
algebraic? How can findings be checked or what
mathematical arguments exist?
4) Successive discovery of complexity:
progressive links between various complexities.
5) Task triggers to more complex thinking: Why
was more than one rectangle possible?
The nested nature of
autonomy within
spontaneity accounts for
lack of evidence of
spontaneous questions.
Several insightful
comments (not questions)
occurred:
[0,19] will be a straight
line; and
Use of [9, 10] to get 9.4.