Getting comfortable with the Common Core standards for mathematical practice can make a big difference in your classroom.
Imagine your curriculum as a cross-country road trip: sights to see, viewpoints to photograph, restaurants to try. These are the content standards, the “what” for students to learn. You (and your curriculum) have planned everything out as little dots across a map.
Now, picture the “how” of all the little details: What vehicle you’re taking. The tunes playing. The car snacks. Route A or B.
The “how” matters. I am not going to care about a beautiful overlook if I’m hangry and I need a rest stop! Our students are exactly the same. It matters how we invite them to interact with the what. Are there times we have lost the joy in our mathematical road trips because we forgot that the journey is as important as the destination?Probably. I invite you to focus on that joy a bit more this year. Our newly released quick reference guide and lesson planning tool can help you on your journey.
The CCSS standards for mathematical practice: A reminder
We teachers are familiar with our content standards. We know if our students need to be able to calculate the area of a circle or demonstrate the mean. However, that “need to be able to” holds hands with a “how they are able to.” Can their skill be repeated beyond tomorrow’s test? How deep does that knowledge go?
This emphasis for thinking deeply rather than just answering correctly is what my colleague Ted Coe refers to as “habits of mind” that lead to “ways of thinking rather than ways of doing.” Luckily, we have the standards for mathematical practice to help students access all the wonders of mathematics by helping them sense-make, represent, explain, and talk about mathematics. Here they are, in case it’s been a while since you looked at them all together:
- 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.
I’ll be honest. The eight standards sometimes sound like math salad. How can you find an answer without “attending to precision?” When are students ever not “making sense of and persevering with problems?” At times, the standards can feel like a cross between “Huh?” and “Duh.”
The standards, simplified
Karen Fuson, math educator, CCSS author, and all-around math advocate, recently suggested a recategorization of the standards to help teachers group them so they can better focus on four different skills:
- Sense-making. With sense-making, students encounter a problem, wrestle with it, and care about solving it correctly. They demystify problems.
- Structure. Structure in math helps students notice patterns, see and use math as a “language” (with correct syntax and grammar), and remember “if it worked for that, could it work for this?” It helps them continuously remember and apply what they’ve learned.
- Drawings. Visual representations help students communicate math visually, selecting the correct tools. Drawings help them externally demonstrate the math.
- Explaining. When students can explain math, both in general and specific terms, they are better equipped tolisten and respond to others, and they can compare and expand on arguments, too. They can talk about the math.
Here’s how these align with the eight CCSS standards for mathematical practice:
- Sense-making = #1. Make sense of problems and persevere in solving them. #6. Attend to precision.
- Structure = #7. Look for and make use of structure. #8. Look for and express regularity in repeated reasoning.
- Drawings = #4. Model with mathematics. #5. Use appropriate tools strategically.
- Explaining = #2. Reason abstractly and quantitatively. #3. Construct viable arguments and critique the reasoning of others.
How to apply the standards
Our quick reference guide and lesson planning tool build on Fuson’s work with the goal of making it easier for you to apply the standards in your classroom. They can help you expand on the necessary skills and behaviors we already find in the most engaging math classroom. Designed to be digestible for novice and experienced teachers, they include objectives that can be seamlessly incorporated into already-planned lessons.
Teachers, we want the road trip to go well. Every year, we fill up the gas, check that the A/C is working, and get the mango slices at Trader Joe’s. Yet sometimes, we get so focused on the destination, we forget we are probably spending more time in the car than out of it. Of course it matters how much attention we give to the content standards for our specific grade level. But there’s also a reason the first standards in the CCSS are the eight standards for mathematical practice.
This year, I encourage you to focus a bit more on the how, trusting that the what will come.