Here are a few observations that came up when working with L today:
- When working on solving a mathematical problem, aspects of the problem shift in and out of focus, much like viewing the 'Necker cube' (above). Doing mathematics can require attention on one thing for prolonged periods, which is difficult.
- Sometimes when less seems to have happened, whether that is in the eye of the learner or the teacher, more has been learned.
- The process of re-membering is a gathering together of fragments, through re-living a previous event, re-visiting mental/physical records.
- It often seems as though insights come out of nowhere. But with careful re-construction, they might be traced back to something, a seed, that happened earlier.
- Leaving a problem, and returning to it at a later time, brings fresh insights.
- It may be difficult (for a learner) to differentiate between what is conjecture, and what is fact.
- Someone who views themselves as a 'non-mathematician' might not consider what they are doing as 'proper' mathematics, as this is something that only mathematicians do. It might be tempting for the teacher to perpetuate the roles of Sorcerer and Sorcerer's Apprentice.
- A period of working un-systematically may be required before it becomes possible to work systematically.