Making sense of making sense

As you've surely surmised, given my incessant ballyhooing about my Newton v. Leibniz analysis coupled with the continued absence of said analysis from this blog, it's proving to be a helluva chore to extract the essence of my students' reflections on the project and distill it into anything simultaneously meaningful and manageable.

I really do hope to have a nice post on the project up before the REU starts (June 8th!) and my life becomes decidedly busier once again.

For now, I've started to catalogue my notes on the students' reflections according to several rough headings, as follows:

The nature of discovery. Reflections on this topic center on the ideas of discovery and invention: is there a difference between the two, and how can one tell one from the other? Who is entitled to discover or invent, and how does one go about doing these things?

The nature of mathematics as a discipline. Reflections in this category include comments on the way in which math is made and the way in which it's communicated. The deepest such comments were purely epistemological, striking at the very heart of knowledge itself.

Personal reflections. What did the students gain from the project personally? What did they learn about themselves as people, and as learners?

Suggestions. How might the project be modified in the future in order to make it more effective? The suggestions I received ranged from minor comments on the process to major structural overhauls.

Given the depth of these ideas (and the prolixity with which my students produced them), I hope you'll agree it's no surprise I've been prevented as yet from digesting them and writing on them.

This week, an abstract; next week, a post. I promise!