Uncommon Core

My title probably makes the most sense if you were tracking the Math Wars from an angle similar to mine, wherein Common Core was a buzz word, and stood for “what we should be covering” at some minimum level of competence.

In the case of mathematics, bleeping over bases other than 10 was OK if you wanted to meet minimum standards. Local governments could not require a school to shut down because it withheld sharing about binary and/or hexadecimal numbers, and skipped Unicode as a topic. Community standards protected vestigial curricula.

I was not one of those pushing draconian measures, nor interfering with the political process, by sponsoring foundations. I was no Rockefeller, Carnegie or Ford.

Oregon Curriculum Network was just that: a font of curriculum development ideas, very low key.

I was no Bill and Melinda Gates Foundation, not by a long shot.

I held my own on math-teach, Forum 206 at the Math Forum, for over a decade.

When big foundations are in play, they usually get more turns at bat and teachers get more marching orders from those corners.

I was not a source of teacher marching orders.

Uncommon Core was meant to spread by diffusion, by osmosis. Great ideas have their own motive power.

Having Polyhedrons become paradigm Objects in the Object Oriented sense was one of our pillars. A tetrahedron might be special-case instanced by giving four coordinates, in either XYZ or IVM coordinates.

I mention IVM (“isotropic vector matrix”) in particular, as that abbreviation would not be used outside Uncommon Core, for the most part.

You’ll recognize whether your school was left out based on such criteria.

Did you come all the way to America and never get even an iota of American Transcendentalism?

As we learned from Santa Fe Institute, which did its own research in this area, scale matters and follows rules.

When we resize a Polyhedron (say a tetrahedron) the surface area and volume both change as a 2nd and 3rd power of the change in linear dimensions.

In other words, double the six edges of a tetrahedron, and see area increase four-fold, volume eight-fold.

Shrink edges to one half their former size, and watch area and volume change by factors of 1/4 and 1/8 respectively.

Coding such a Polyhedron in Python is quite straightforward. The subclasses of said Polyhedron (e.g. Tetrahedron, Octahedron, Cube and so on) all start out with canonical volumes, based on how they’re concentrically arranged.

Again, Uncommon Core suggests volume numbers you will not have heard of if your school was not involved.

A question you might now be asking yourself centers around “compatibility” i.e. how well do uncommon and common core co-mingle? That’s a big question and results are ongoing. Ideas sharpen when set against one another and made to compare and contrast.

We better understand what is meant by “base 10” when we’ve looked at the other bases. The New Math of the 1960s was built from the ground up around this insight, which Common Core considers extraneous.

For this reason alone, expecting positive synergy makes plenty of sense. Going back and forth between two standards of unit volume (like two bases), as we do in “Martian Math”, awakens a sense of novelty and possibility.

What might an “alien mathematics” look like? We encourage an exploration of the literature, with movies to boot. Have you seen some of them?

In sum, Uncommon Core connected coding to polyhedrons and polyhedrons to an alternative paradigm in part just to give a sense of what “alternative paradigm” actually means. What’s a “paradigm”?

Anthropology opens up, to the extent we’re able to get philosophical about our own assumptions. Students getting bases 2 and 16, also get tetravolumes, all in the context of learning to code.

The philosophical content of Uncommon Core is robust in that we tackle the concept of “dimension” head on, providing more perspicuity than usual.

We know the importance of “multi-dimensional spaces” in Machine Learning, which inherits from linear algebra. We also recognize how Extended Euclideanism pushes us to think in terms of perpendiculars (orthogonals), each linearly independent of the others.

The injection of yet another namespace using “4D” as a meme (R. B. Fuller’s), is not about adding confusion so much as nuance. Our abilities as diplomats (those with diplomas) likewise increases with our appreciation for “namespaces” as a concept. Cultures, i.e. forms of life, differ.

Meaning depends on context. Mathematics is not about establishing a single context for all naming. We learn better how to share the road, given the multiplicity we have to deal with.