They are discussing an article by Richard Fulkerson in the journal College Composition and Communication that doesn't appear online (CCC stopped updating their website in 2003, and have also discontinued their JSTOR archive). I haven't read the full article yet, so my ability to comment is somewhat limited.
The main debate is between 'expressivists,' who believe composition should aim to teach students how to write their personal thoughts and ideas, and the 'procedural rhetoric' people, who prefer a more traditional, 'objective' approach. One of the primary names associated with the expressivist school is Maxine Hairston, though there are many others who articulate their own variations of the idea (a good bibliography of much of this criticism is at the bottom of this article).
Intellectually, I prefer the more objective -- one might even say conservative -- approach these days. I want to help my students get prepared for future careers, not simply help them find their own voices. Most college freshman need a great deal of direction with regard to the fundamentals of sentence structure and the forms of argument. On the other hand, if you don't give students opportunities to develop their skills with content that seems relevant to themselves, you are in a world of really bored students, and a dead class. So I'm a little torn (and I haven't even decided how I'm going to approach the class I'm teaching this coming fall... ulp).
There's some other issues here. One of them is the growing digitalization of writing, partly through the Internet, but also in most professional contexts. People increasingly communicate by email, and even send each other formal documents that way. In the old days, those documents were printed out, and the print forms were the ones that were read. But now people read more and more on the computer itself; the experience has become pretty naturalized.
The internet in itself doesn't mean much; if you have to convince the boss to adopt your proposal, you still have to use every persuasive tool at your disposal to do it. The forms and functions of public writing have not changed at all. The changes in the way people write have probably been more secondary, stylistic changes. One of these might be the growing informality of what is considered public rhetorical style. At first, the change was mainly visible in the blogosphere, where the conventions of argument are somewhat different (even in the 'serious,' Crooked Timbery blogosphere) from the conventional print-media. But more and more, the conventions of writing acceptable in blogging are coming to influence conventional journalism. Along these lines, I was struck by a paragraph in George Packer's recent essay on the parent of a soldier who was killed in Iraq:
It was the first blogged war, and the characteristic features of the form--instant response, ad-hominem attack, remoteness from life, the echo chamber of friends and enemies--helped define the tone of the debate about Iraq. One of the leading bloggers, Andrew Sullivan, responded to the news of Saddam's capture, in December 2003, by writing, 'It was a day of joy. Nothing remains to be said right now. Joy.' He had just handed out eleven mock awards to leftists who expressed insufficient happiness or open unhappiness at the news. . . . Sullivan's joy was, in fact vindictive and narcissistic glee. (He has since had second thoughts about the Administration's conduct of the war.) Similarly, as the insurgency sent Iraq into tumult most antiwar pundits and politicians, in spite of the enormous stakes and the awful alternatives, showed no interest in helping Iraq become a stable democracy. When Iraqis risked their lives to vote, Arianna Huffington dismissed the elections as a 'Kodak moment.' It was Bush's war, and, if it failed, it would be Bush's failure.
Packer's characterization of blogging as having acclerated the polarization of political debate in the U.S. seems right to me, especially regarding the Iraq war specifically. Blogging is no longer a subcultural activity. It is mainstream, and it is changing not just the way people argue about politics and war, but the way people argue in public, tout court. Perhaps that's something we should be talking about in comp. classes as well -- though I'm not exactly sure how I would take it on.
(Incidentally, Packer mentions a rather shady involvement in the pro-war campaign by Christopher Hitchens in the article. Hitchens -- always the pugilist -- came back with this piece in Slate. Naturally, in his critique of Packer, he doesn't mention the fact that Packer criticized him in the New Yorker article that he (Hitchens) is now attacking in Slate. Ugh.)