The SMPs: Part 1
Overview
The Standards for Mathematical Practice (SMP) describe the habits of mind that all K-12 students should be developing as mathematicians. The SMPs were developed from two previous documents - the NCTM Process Standards and mathematical proficiencies describe in the National Research Council’s report Adding it Up.
The 8 math practice standards are:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Insights from the Teaching Channel Blog
Check out the Teaching Channel Blog where Ben Curran takes time to write a 3 part series to describe specific examples of how some of the math practices can be seen in the classroom.
SMP #1 Make sense of problems and persevere in solving them.
Blog Post #1: The Key to Unlocking the Common Core Standards in Mathematics, he addresses the challenge of teaching students how to persevere in their problem solving. Curran writes:
“In math class, how often do we ask our students to persevere? We all tell our students not to give up, but this practice standard calls for us to go beyond telling to teaching students how to persevere. How often do we teach them to try different approaches, test ideas and revise their thinking?
This won’t happen in one lesson of course. So how do we do it?
One idea is to commit to presenting students with regular mathematical challenges that have multiple steps and that require close reading.”
Continue reading his blog post for ideas to support students in learning to persevere in their problem solving, click here.
SMP #3 Construct viable arguments and critique the reasoning of others
Blog Post #2: 3 Strategies for Bringing Argument and Critique in the Common Core Class, Curran examines the challenges of getting students to communicate through argument and critiquing. Curran provides 3 practical examples of including this SMP in our classrooms: (1) Be wrong more often, (2) Examine student work, and (3) Ask Why?
SMP #4 Modeling with Mathematics.
Blog Post #3: Curran writes regarding the Standards for Mathematical Practice #4 Modeling with Mathematics. His post, 3 Keys to Modeling in Mathematics in the K-8 Classroom, he challenges teachers to give it context, go deeper, and tap into resources.
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Standards for Mathematical Practice Resources
There are so many resources out there addressing the CCSSM content standards and the SMPs. When searching the vast amount of resources, I try and look for sources that are reputable. If the resource is connected to one of the writers of the Common Core, or by a state or national math organization then it most likely will have resources that truly align to the vision and purpose of the CCSSM.
Progressions
The Institute for Mathematics & Education is publishing learning progression documents for the CCSSM’s various domains and grade spans. The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.
Check out the Progression documents for SMPs:
Illustrative Mathematics
Illustrative Mathematics has many resources, with a main focus on mathematical tasks aligned to the standards. Teachers can search by grade level, domain, and /or standard to locate tasks specific to their needs. The website is constantly being updated and more tasks and commentaries of tasks are being added all of the time. One of lead writers of the CCSSM, William McCullum, is a founder of the website.
Illustrative Mathematics™ was originally developed at the University of Arizona. It was started in 2011 as an initiative of the Institute for Mathematics & Education funded by the Bill & Melinda Gates Foundation and has operated since 2013 as a 501(c)(3) nonprofit corporation.
Check out:
- Standards for Mathematical Practice section has examples at various grade levels of what that SMP could look like in the classroom.
Inside the Mathematics
Inside the Mathematics has many great resources around the CCSSM - both the content standards and mathematical practices. This initiative grew out of the Noyce Foundation’s Silicon Valley Mathematics Initiative. SVMI is based on high performance expectations, ongoing professional development, examining student work, and improved math instruction. The initiative includes a formative and summative performance assessment system, pedagogical content coaching, and leadership training and networks. Coaches in SVMI learn strategies of re-engagement with students around mathematics assessments, and Public Lessons on re-engagement are featured here.
Check out:
- Common Core Resources: Mathematical Practice Standards and Mentors of Mathematical Practices
By no means is this an exhaustive list of resources. Please take a look at a couple of these links (or all of these links) and learn more about the Standards for Mathematical Practice. Check back for Part 2 where I will share more about the SMPs.
