Really interesting tweet and replies today:
For passers-by, the SMPs are the Standards for Mathematical Practice in the Common Core math standards. From the standards themselves:
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Seeing all this got me thinking. Here’s an opinion I have that other math teachers might disagree with:
I don’t think that the SMPs are describing something that a student, or any human, can become “proficient” in. I don’t think they are skills that can be developed and employed regardless of content.
Instead, I think of the SMPs as ways of learning content more deeply, and learning content in ways that help students to transfer that knowledge in the future. When I teach my students about conic sections, I want them to construct viable arguments and critique the reasoning of others while trying to better understand the multiple meanings of eccentricity. I want them to model with mathematics to better understand how conic sections are related to planetary motion. I want them to use appropriate tools strategically to visualize and better understand the relationships between different types of conic sections. I want them to look for and make use of structure to better understand the big ideas of conic sections, and see them as one interconnected whole rather than a set of procedures to memorize.
I think that, if my students successfully use the SMPs to engage more deeply with the content they are learning, they learn that content in a way that helps them to apply what they know more flexibly in the future. And the more math students know, and the deeper they understand that math, the better position they are in to be quantitatively literate in the world, and be able to solve new problems by connecting and applying what they already know.
On a fundamental level, I teach math because I hope that what I teach helps students to solve new problems and reason in the world beyond my classroom. But I try to do that by teaching content first, and I use the mathematical practices as a lens through which to help my students learn that content. My goals on a daily basis are for students to learn math and to come to believe that they are people who can be good at math and use math in their lives. The practice standards are a means of meeting those goals, not goals in and of themselves.
Five Twelve Thirteen 
“Mathematically proficient students start/ make sense/ understand/ …..”
These are the first lines of the SMP’s.
What about the rest of the students??????
Interesting! Never noticed that before. It would be interesting to try to frame that around what it looks like for students to learn, rather than setting up a dichotomy. Though I do see value in painting a portrait of what we want as a part of writing standards.