My Favorite Math Practice
Common Core Standards for Mathematical Practice:
- 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.
When I was first learning about the Common Core Standards for Mathematical Practice, I gravitated toward Math Practice 1 – Make sense of problems and persevere in solving them and Math Practice 3 – Construct a viable argument and persevere in solving them. These two practices seemed clearly understandable to both me and my students, and they made sense from a practical, everyday point of view. Who wouldn’t want to learn to make sense of things, persevere in the face of challenge and to be able to engage in well reasoned conversations built around evidence? As I worked with my students, we talked about these two math practices a lot, along with paying attention to the math practices that were already, to some degree, a part of my regular classroom instruction: MP 4 – Model with mathematics, and MP 5 – Use appropriate tools strategically and MP 6 – Attend to precision.
I gave myself permission to not engage in Math Practice 7 – Look for and make use of structure and Math Practice 8 – Look for and express regularity in reasoning. I didn’t readily know what this thing called “structure” was, let alone how you might see it or use it. When I made an attempt at defining structure, my ideas came out more like repeated reasoning. As I continued to improve my understanding of all of the math practices, MP 7 and MP 8 became clearer. And then, just recently, I heard someone speak at a math conference. What the speaker said made so much sense that many of the separate pieces of information that I had come to understand shifted to create a more cohesive understanding of the math practices as a whole.
The speaker was Grace Kelemanik and her talk was on the math routine “Contemplate then Calculate” (#CthenC) from the book Routines for Reasoning (#4RforR). What she presented helped me understand that:
- Not all math practices are created equally. Each math practice plays a different role as students become mathematicians, yet they all work together.
- Math practices should be seen as an opportunity, not a hurdle for students that struggle with mathematics. Many of the types of learning experiences that engage students in the math practices are similar to the types of learning that support students with learning disabilities and English learners.
- The three math practices that I left until last to understand are vital avenues for thinking that can be taught through specific instructional routines. Check out this visual of the math practices that describe the avenues of thinking.
So, what is my favorite math practice today? Math Practice 7: Look for and make use of structure. For me, seeing structure is the ability to see complicated mathematical representations in chunks that can be worked with or rearranged to make problem solving easier.
For example, seeing and using structure can be found when you look at the problem 8 x 15. If you can “see” this as 4 x 2 x 15, which can change into 4 x 30 then you are using mathematical structure. (By the way, this example is begging for a graphical representation to go along with it but that is not going to happen right now.)
MP 1 and 3 used to be my favorites, but for 2017 I have a new favorite… MP 7 Look for and make use of structure. I still like you MP 1 and 3, but I am adding a new favorite to my list. As long as I am calling out favorites, for those of you that are familiar with NCTM’s Principles to Action, the Mathematics Teaching Practice Use and connect mathematical representations is one of my favorite teaching practices because these two favorites work so well together.