Tips & Tricks for Applying the Standards for Mathematical Practice to Drive Instruction

I loved teaching math. Throughout my 13 years in education, I’ve served as a high school math teacher, an instructional coach at the middle school level, a math consultant at the state level and a Director of Math for a K-8 network supporting 5 different schools.

 As a teacher I would always tell my students, “Math is the most creative subject because there is always more than one way to solve a problem.” This statement was the driving force behind how I asked questions and delivered instruction on a daily basis.  Before I knew about the 8 Standards for Mathematical Practice, I was living them out in my classroom, and based on the data, my students made major gains because of it.

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The 8 Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

While it might seem like a heavy lift to incorporate any one of the 8 Standards of Mathematical Practice into one class period, I’d like to highlight a few and give some practice ways you can start implementing them in your classroom if you aren’t already.

Based on the way I loved to learn and incorporate student voice in my classroom, my favorite practices are 1, 3 and 4. 

#1 Make Sense of Problems and Persevere in Solving Them

Students have several different learning styles and ways of thinking asking questions like “Why do you think that’s the answer?” or “Are you sure?” students feel pushed in their thinking which can help develop strong problem solving skills. The “microwave generation” (an era accustomed to instant results)  wants to get things done quick, fast and in a hurry. Students are often in a similar mindset when solving math problems, but could benefit from slowing down and being challenged to really “know that they know.” Soon after, they’re able to start making connections, build confidence, and grow an understanding for the math problems they’re solving. Asking these questions can reinforce students' ability to ”make sense of problems.” 

Pro Tip: Save the questions below to help elicit student thinking:

• Why do you think that’s the answer?
• Are you sure?
• What would happen if…?
• Why did you…
• Is there another way to (draw, explain or say) that?
• Is there a more efficient strategy?

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#3 Construct viable arguments and critique the reasoning of others

Finding the right answer to a math problem is always a satisfying feeling, but it’s not enough to verify a student's understanding. It’s important for students to be able to explain their reasoning as it can help foster ownership in mathematics. An easy way to do this is by allowing students to show and share their work in front of the class.. My favorite method was to invite students to the board and share/show their answers and work. Once they’ve finished sharing, I’d do the quick “Raise your hand if you agree/disagree.” Regardless if the entire class agreed I’d ask, “Did anyone do anything different but got the same answer?” 

This shows students that there can be more than one way to solve a problem (my favorite part about math!). This also gets students to explain their thought process while being able to respectfully agree or disagree. 

Pro Tip: This can also be applied to group work.  Students can complete problems on their own and then connect with their table or partner to share and compare answers. If they found different answers, the students should be challenged to convince their partner to change their answer, or create a viable argument for what the final answer should be.

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#4 Model with mathematics

Modeling with math not only allows for students to see problems in different ways, it also creates a guide for students to be able to solve problems and explain their reasoning. Gone are the days where procedural practices are the only ways of solving problems. As we support conceptual understanding or math, students also need to be able to show what they know and be able to apply it in real world situations. 

One of the ways I would model math in my classroom was to give my students the answer and say, “Ok we know where we are going, how do you think we get there?” I’d have students solve the problem and if they found one way quickly I’d challenge them to find another way to solve the problem. Using my student as a teacher method, I’d have a student show their work and then ask, “Who did it a different way?” Modeling isn’t just about showing the steps, but encouraging students to think like mathematicians.

Pro Tip: It’s important that students understand math both procedurally and conceptually. Be sure to give students opportunities to use mathematical tools, manipulatives and tasks that require them to model their understanding of math beyond the procedural tasks.

As the school year begins to wind down and testing begins to ramp up, why not challenge yourself and your students to utilize the Standards for Mathematical Practice. If you’re already familiar with them and using them on a regular basis, great! If not, try starting with one or two and see how it goes. 

If you are looking for some practical ways to incorporate them in your classroom, check out these best practices from achievethecore.org. This resource also shares how to use ASSISTments to foster the use of the Standards for Mathematical Practice in your classroom.

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