Jason Zimba is working on a technical manual that will describe higher order structures in the Common Core standards, such as flows, streams, and ties. Here is an example of what is meant by a flow. What I like about this diagram is that it illustrates the way mathematical ideas are unified as the subject progresses. For example, the disparate ideas of whole number, fraction, decimal, integer, and rational number are unified in an understanding of the number system. Mathematics doesn’t branch out and get more complicated, it collates and compacts ideas into more powerful and denser ideas.
Visually documenting the deep structures and flow in Common Core is really important. I wonder if this work could be used in PD working on “curriculum vision” for the CCSS, or even if it would benefit students to do some of the work. I’ll check back here often for progress updates…
In the meantime, here’s my beginnings of an attempt to align the Mathematical Practices with problem-solving strategies and activities and thinking about developing problem-solving strategies. I hope it’s useful to someone. http://mathforum.org/blogs/max/2011/01/31/problem-solving-strategies-and-the-common-core-practice-standards/
I am in the middle of a workshop for middle and high school math teachers. While most of the time I have been doing math with them, today we did a session introducing those who were interested to the Common Core. The participants found this flow especially helpful and asked to see more like it.
My understanding is that Jason Zimba has prepared a document describing structures like this and it should be getting some sort of distribution … I’ll update when I know more.