Every curriculum can be viewed at several different levels of granularity. Let’s look at what’s important when we’re teaching math. At one level the curriculum is obvious: Algebra I, Geometry, Algebra II, etc. But of course that’s much too broad, so we introduce a more granular description, mentioning units, like quadratic functions or fractals. And then within the units are topics, like quadratic equations or the Mandelbrot Set. And then within each topic are skills and concepts, like using the quadratic formula or iterating a complex function.
With these four levels of granularity we tend to lose sight of the forest (to switch natural science metaphors), so we introduce other curricular concepts, like Big Ideas and Standards. For an example, see the Quadratic Functions unit in Weston’s Algebra II course, which lists eight Big Ideas spread out among four of our Standards. (Unlike concepts and skills, these terms require Capital Letters.)
But no matter what the level of granularity, all of this falls merely within what we might call Curriculum B. Math is what we know how to teach, and math is what we’ve been hired to teach, so math is what we do teach. In the old days math might have just been a laundry list of skills, but then we moved to higher and higher ways of thinking about it, from concepts through Big Ideas. Nevertheless, it’s just math. And if you pinned us down to analyzing what’s truly important, we would have to admit that there’s a hidden Curriculum A that’s more important than any particular mathematical skills or concepts or even Big Ideas. Why do we care so much about getting students to cite sources honestly, treat their classmates and teachers with respect, think creatively, question authority, work together cooperatively, and generally act like responsible adults? Because we know that in the long run those are what’s important. It sounds so fuzzy to claim that what we’re really teaching is honesty, respect for others, independent thinking, skepticism, cooperation, and responsibility, but surely there’s no doubt that those are more important than the quadratic formula.