You know I love you. So in the spirit of collegiality you value, I'll challenge some of the ideas in your post.
There are lots of issues you are describing here, including: collegiality, problem-solving, assessment and curricular consistency. I also recognize the importance of using a common language. That said, I'm a bit uneasy with the appropriation of "debugging" in this context.
First (you can predict what I'm about to say), the richest context for debugging is computer science (programming), a game-changing modern discipline I believe should be experienced in a formal context by every student.
Computer programming not only offers a rich context for developing debugging strategies, but may be the only place where the traditional secondary "math" curriculum has any utility or relevance.
I can't speak to the specific problems being solved by the SLA students, but we know that whatever the thing called "Algebra II" has some serious relevance problems. In 1978, I had a course called "Algebra II with Computer Programming." We used the same crappy Algebra II textbook as the other classes, but solved many of the problems via computer programming.
It would be delightful if such a radical course could exist a quarter century later.
More importantly, I would hope that your use of the term debugging respects what Papert and Turkle call "epistemological pluralism" in a way that coercive curricular tricks like Understanding by Design don't. In other words, people learn in different ways and construct meaning in a personal fashion and style.
"Incremental problem solving" may be appropriate for some learners in some contexts, but it may be overvalued and only represent one debugging strategy. This epistemological stance MAY serve the traditional scientific method, but may be less appropriate in more modern contexts and may seem to some learners as just one more trick to memorize without understanding.
I'm sorry to sound like a broken record, but I find Understanding by Design to be a capitulation that places curricular objectives ahead of learners. It starts with assessment and works backwards. Creativity, individuality and serendipity are incidental to that process or in direct conflict with pre-ordained curricular objectives.
I KNOW that you and your teachers at SLA may be more nuanced than the typical school embracing Understanding By Design as a teacher-proof system presenting the illusion of flexibility, creativity and differentiation. However, as a model school, I truly wish that SLA would move on from Wiggins and McTighe (I won't even mention Wiggins' recent anti-teacher rhetoric).
I'd be happy to suggest some articles and papers that might contribute more widely to this discussion. Or, you can just tell me to take a hike and get back to the work I should be doing.
I couldn't agree more. I think it is a shame that observation often turns into a series of checklists that don't really tell that much about how well a teacher teaches. I empathize with the District walkthrough teams that have such a small amount of time to really assess the quality of a teacher so they have to use them. But I wonder what would happen to our schools/students/communities if they used more statements like you described. I think it would be much better.
I find the classic game "JezzBall" to be a great embodiment of this process and use it sometimes when teaching students debugging strategy. JezzBall's one of those simple 2d games like Snake that's been rebuilt under a thousand different names and styles, most people have encountered it in one form or another. Here's a free Flash-based version: http://www.gamingdelight.com/games/jezzball.php
You have a game board full of little atoms bouncing around. Consider the game board to be the domain of a problem with the atoms representing possible causes or solutions. You win the game by finding opportunities to split the remaining board area, each time eliminating one side of the divide along with any atoms caught in it. Eventually you either eliminate all atoms or narrow down the game board to a small enough area.
I like the talk of common language, and I don't think that it's enough to stop with the connections between math and science. What about the connections between math, science and the humanities?
For instance, do students recognize that we're looking for the same sort of clarity of communication in math and science that we're looking for in students' writing? That the standards for well-crafted arguments are pretty much the same in arguing for an interpretation of a story or of an experiment?
People create the world in their own image, and we need to live in a unified world. We need to return to a world where all human endeavors speak the same core language.