Peer Group Networking

Of course there is any number of ways to resequence topics in a logical progression, especially since maths form a network, not a linear stairway, so it's really a matter of deepening over time, by retracing a lot of the same ground over and over, adding in new topics as they arise (this is of course an organic ideal rarely attained without caveats).

However, there's a comfort zone that goes with one's ethnicity as a math teacher that prevents resequencing too deeply and disruptively, which expresses itself with this clinging to physical hardcopy textbooks as the embodiment of any serious-minded approach to math teaching.

More emphemeral digital alternatives, including hard media such as CD and DVD, get shunted into a holding pattern (mañana syndrome) while in practice each year is much like the last, for at least a half generation (a decade or so), again because of the comfort zone of the math teaching ethnicity.

In competition with the math teachers, we now have the emergence of self-teaching peer groups who forsake the more traditional textbooks in favor of cyber-curricula of one flavor or another.

Traditionally, these peer groups have formed in the adult world as teams within companies, in order to share inhouse proprietary knowledge and trade secrets related to the business. However, with the emergence of social networking software such as MySpace (Orkut an early pioneer in the genre), college and grade school aged kids in the K16 pipeline are finding increasing opportunities to do more than just socialize.

They're colluding to form study groups, other intelligence gathering machinery for the purpose of practicing the social skills they'll need to survive in tomorrow's cyberspatially aware business networking environments.

Multiuser online gaming is another vehicle for this kind of personal development, and I'm not just talking about first person shooters and their limited appeal among girlz, Lara Croft notwithstanding (CBS News correspondents Lara Logan and Kimberly Dozier more define the archetype -- intelligent and compassionate, not unabomber gun-toting thugs).

In any case, marvels and superheros abound in this cartoon world of shared imagination, resulting in an explosion of new ethnicities and subcultures, many of them shared internationally i.e. across the political lines drawn by earlier generations of world game player.