Standards for Mathematical Practice: The Organization of the CCSSM Part III

This is the third post about the organization of the Common Core State Standards for Mathematics (CCSSM).

You might have noticed that when you pull up the CCSSM, the first set of standards (especially if you view the entire document as a pdf instead of on an interactive site) are the "Standards for Mathematical Practice."

The standards we've looked at up to this point have described specific content. (For example, 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.) The Standards for Mathematical Practice, however, do not describe specific mathematical content.  

Rather, these standards describe the way in which students should be practitioners of math. They describe what good math looks and feels like. 

I am fond of pointing out that while these standards describe student behaviors and understandings (because, as we talked about on Day 1, that is the very definition of what learning standards are), these descriptions of "mathematical practice" are true to anyone who really knows their way around math.

So if you lifted these eight descriptions of good math practice out of the standards document, you could also use them to describe how scientists, engineers, accountants, small business owners, CFOs, and ... well, you or I ... do math. Really, anyone who has become competent and fluent with math will be engaging in these practices.

It's worth focusing on the word "practice." The way that this term is used here is not unique to math learning standards. I think specifically of yoga. I'm a fan of yoga, and whether you're in a yoga studio or at home with a borrowed dvd from your library (I fall into the latter category, FYI), your yoga instructor is going to mention your yoga practice. This word means much more than just the repetition of yoga poses. It means everything about the way I engage with yoga ... from my mindset to my breathing to my balance to my physical ability to get into a yoga pose ... all of these things say much about my fluency and knowledge and familiarity with yoga. A yoga instructor, as a very proficient practitioner of yoga, can watch me move through a sequence of poses, and then tell you a lot about my yoga practice--whether I'm breathing right, and isolating the right muscles ... whether I'm focused and meditative as I should be, or distracted and tense.

The same is true with mathematics. The authors of the CCSSM want students to learn math in such a way that they own it for themselves--that their familiarity with it allows them to be the master--to bend the math to their will instead of being a slave to a seemingly incomprehensible and arbitrary set of steps and rules.

This kind of fluency doesn't happen overnight. (Just as I can't expect to go to two yoga classes and be able to do a kickass tree pose.) And it also doesn't look the same at every grade level. What specific actions demonstrate a fluent practitioner in 1st grade might signal a student who is struggling to keep up in 4th grade.

However, there are over-arching ideas that are consistent across grades, even if they are expressed differently at different stages of mathematical development and understanding. Precision (the focus of Practice Standard #6) in primary grades might be as simple as making a clear "T" chart ... whereas in high school, it would be more like writing out clear "let statements" so that it's easy to know what different variables are being used for in a set of equations.

The practice standards are special because of their organizational spot in the CCSSM. In former standards documents (the state standards, or the National Council of Teachers of Mathematics standards document), this type of "process standard" or "logic and reasoning standard" was given it's own domain area. Instead of putting these standards into a domain where it could be said, "Now, we're going to focus on reasoning," the authors of the CCSSM decided to make these standards overarching. The idea is that no matter what content you're teaching in the CCSSM, it should be taught in such a way that the Standards for Mathematical Practice are being encouraged, nurtured, and leveraged.

This is just as it is in my yoga class. No matter what pose I'm in, my breathing is something that needs to be attended to. ( ... as does my mental focus, my balance, and a host of other marks of good yoga practice that I have yet to learn and incorporate :) )

The eight Standards for Mathematical Practice are:

#1. Make sense of problems and persevere in solving them.
#2. Reason abstractly and quantitatively.
#3. Construct viable arguments and critique the reasoning of others.
#4. Model with mathematics.
#5. Use appropriate tools strategically.
#6. Attend to precision.
#7. Look for and make use of structure.
#8. Look for and express regularity in repeated reasoning.      

And while there is certainly overlap between them, Bill McCallum, one of the authors of the CCSSM, put together the following diagram to help us think about how they might be grouped in pairs, with #1 and #6 as overarching, being used when you use the others.

Throughout the rest of our 31 days together, I'm going to try my best to delve deeper into what each of the eight Standards for Mathematical Practice says and means. This is, by far, the most challenging part of the Common Core ... but it's also the meat of the CCSSM, and in my humble opinion, the major contribution of the CCSSM.

I'll put it to you this way: when the CCSSM first came out, and state and district math supervisors weren't sure where to start to move towards implementation of the CCSSM, the recommendation from the major professional organizations for teaching math (the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics) told math leaders in those districts:

"Start with the math practices. If you can be teaching in a way that reflects the practices, the content will be close behind."

Are you enjoying learning about CCSSM? There are more 31 days posts here. And you can join us on facebook and twitter, for conversations between blog posts, and after October! This week's Tuesday night math chat will be on Twitter, at 9p ET--follow along using #CCSSM!