Based on interviews during parent-teacher night, it's clear that the more traditionally-minded Portland Public Schools are still somewhat under the thumb of Euclidean metaphysicians preaching as "self evident" "axiomatic" these beliefs we might not always agree with, but that's not a serious source of frustration for me.
It's a beautiful system, and even if full of logical holes and a source of some awkwardness in later thought patterns. Systems have holes, tiz in their nature. Even arithmetic is incomplete, from a "prove me true" standpoint.
Traditional schooling isn't the only source of learning, so we're able to counter-balance the overly mired stuck- in-the-mud traditionalists through other venues in our culture, e.g. via Internet and television.
Those signing up for self schooling after school, or otherwise lurking, get our different approach, starting with spatial experience, walking through buildings and so on, the architects' CAD system (animation of interiors and exteriors). This gets them thinking in terms of Google SketchUp, other affordable tools, leading to job relevant skills in several directions.
Our shoptalk is likewise deliberately "hybrid" in that we don't believe in overly specializing under the thumb of this or that cultish discipleship (e.g. the Euclidean and/or Pythagorean semi-visible colleges); we draw from a wealth of resources (URLs), including from many non Indo-European. That's almost a hallmark of our shared North American culture: its multi-cultural basis in federation among states, territories, and semi-sovereign interior nations. No way is our USA a strictly top-down control system -- a difference many of Euro heritage get confused about, especially monarchists.
Anyway, in keeping with are starting with spatial, many students self school using Zome aka ZomeTool. If unfamiliar with this artifact, you might want to do some background reading here:
What gnu math guy David Koski is finding, and publishing about through my studio, is this cool sequence of ratios, twist surface and total rhombs in all the Baer cells.
Now of course this is all very specialized and not necessarily a corner stone in any curriculum, but you see how we've got a strong associational network going, between hands-on tools (such as Zome and vZome), and some state of the art geometrical studies that are both easy to grok and spatial, i.e. not purely planar, in harmony with our 'Beyond Flatland' marketing campaign (goes back to at least 1997).**
A primary means for sharing these geometric studies, based around focal points we've discussed quite a bit in this archive, is through YouTubes, Google Videos and such. Even at relatively low resolutions, you're getting the benefits of rotation, translation, scaling, the transformations we study in class. Plus you're getting hands on experience with the various file formats and video clip editing techniques (audio too).
For an example of the kind of geometry clip I'm talking about, check out my own contribution to the literature, focusing on our discovery awhile back regarding a volume relationship between rhombic dodecahedra and tria- contahedra of certain radius: