Math Practices vs. Habits of Mind vs. Positive Norms

The term "math habits of mind" was first used by Cuoco, Goldenburg and Mark in a great 1996 article (linked here).  The habits of mind that they envisioned are process and disposition standards rather than content standards.  The general idea was that the content of mathematics will evolve, so we want to give students "a set of tools that they'll need to use, understand and make mathematics that doesn't yet exist" (Cuoco, Goldenburg, & Mark, p. 2).  The habits of mind are the tools they proposed.

The Common Core Standards for Mathematical Practice (also know as the 8 Math Practices) were influenced by the habits of mind as well as the NCTM problem solving standards and the National Research Council's 2001 Report "Adding it up" (linked here)  Like the habits of mind, the Math Practices address thinking processes, and dispositions that help students develop "deep, flexible, and enduring understanding of mathematics" (Briars, Mills, & Mitchell, 2011, p. 20).

Recently, Professor Jo Boaler published a set of "Positive Norms in Math Class" (linked here) that focus on developing processes and dispositions that provide a fertile environment for math growth.

I have spent more time than I would like to admit combing through these process standards and norms looking for commonalities.  I used a table to map the habits of mind and the positive norms to the Math Practices (linked here).  

This helps me to see how they are interrelated.  By using the positive norms you can address the Math Practices and habits of mind.  The math practices are streamlined versions of the habits of mind.  The habits of mind help you understand what the Math Practices really mean ("make use of structure" much?).

I prefer to use the norms to talk about disposition and the Math Practices to talk about process, but in reality, they all one and the same.  And they all support deep and transferable conceptual growth.  They are all pulling in the same direction.  What a relief!

Additional food for thought...

Another very helpful way of looking at the Math Practices (and indirectly the habits of mind), came to me from a WCSU colleague this summer.  It lists student and teacher "look fors" by Math Practice.  It's a pretty helpful document, and I would suggest checking it out if your looking to get a better handle on these process standards (linked here).

Talk about pulling in the same direction... For those not specializing in math, the venn diagram below shows intersections between the Math, Science and ELA practices that I find helpful (linked here).

To recap, there need not be a debate about which of these approaches is "best."  They are all part and parcel of the same thing.  The important thing is that we teach processes and foster dispositions that support rigor in mathematics for all students. 

What are your takeaways?  What are your questions?  Please comment below...