- Episode Highlights
- Transcript
In this episode, we take a closer look at Math Practice 6: Attend to precision, and explore how it goes far beyond correctness. You’ll hear how precision in language, symbols, and structure supports deeper understanding, and why developing this skill is just as important for life as it is for math class.
We’ll also unpack how to help students refine their thinking out loud, use vocabulary in context (not just memorize it), and make thoughtful decisions about when precision really matters. Whether you’re introducing new math language or helping students rethink the equal sign, this episode will challenge what you thought you knew about “being precise.”
Links mentioned in this episode:
Math Practice 6: Attend to Precision
Hello, Meaning-Makers! Welcome to this next episode of the Meaningful Math Podcast.
After covering the first five Math Practices in previous episodes, I’m happy to be back to discuss Math Practice 6, and the meaning of this practice might not be what you think it means. Let’s get started!
What Does It Really Mean to Attend to Precision in Math?
When you hear the word “precision”, what comes to mind? If you’re like most, you probably think of correctness and accuracy. And while those terms are associated with precision and thus Math Practice 6, they are not the complete picture. A large focus of Math Practice 6 is actually precision in communication.
Now, I know what you’re thinking, “We already covered communication – that was Math Practice 3!” And you’re right – we did and it is! These two practices are strongly connected, and we will explore that connection throughout this episode.
Supporting Students in Explaining Their Thinking Clearly
As we’ve discussed in previous episodes, math is no longer solely about getting the right answers. It’s about the process students go through to arrive at their answers and how they make sense of mathematical ideas.
With this in mind, Math Practice 6 focuses on students precisely communicating these processes and ideas. This means they are able to explain their thinking and ideas concisely and clearly.
Have you ever had a student who, when asked to explain their thinking, simply says, “I just knew it” or “I just did the math”? We want our students to be able to go deeper and say more than this. We want them to share HOW they knew it and WHAT math they did.
Why is it important that students are able to do this? Well, here are a few reasons to keep in mind:
- As students communicate their thinking, they are simultaneously reconsidering and refining their ideas. This helps push them in their own learning and understanding.
- Students learn and expand their own thinking as they listen to the reasoning of others. They are able to critique and challenge each other’s thinking, which helps develop their own conceptual understanding.
- The ability to communicate precisely is something that will benefit students in all areas of their lives – throughout their years in school, in relationships with others, and in their careers. It’s truly an invaluable skill.
When students communicate with precision, they are specific about their thinking and the steps they took, and they can explain each step – specifically WHAT they did and WHY they did it. They do this concisely by saying enough to be able to get their point across, but not so much that they are rambling and giving unnecessary details.
It is HARD to find the right balance between saying too much and not enough. This is something that’s even difficult for adults to do! Therefore, the process of helping students attend to precision should be gradual and intentional.
Prompts to Help Students Communicate with Precision
Here are some prompts that might help you support your students to communicate with precision:
- Can you tell me more about that?
- Talk me through your thinking, step by step. What is the first step you took… then what did you do next?
- Why did you choose to solve the problem this way?
- What label or unit would make sense with this answer?
Teaching Math Vocabulary Through Context, Not Memorization
When students communicate precisely, they are able to use appropriate math vocabulary. This requires the teacher to intentionally model the use of math vocabulary, and this happens best when it comes up organically.
For example, in a lesson where students are analyzing a painting with the intention of learning about intersecting and parallel lines, instead of frontloading the lesson and telling students what these terms mean, have students make observations and describe what they see. Then, you can explain to students that there are terms that help us identify lines that have these characteristics, and you can name those terms.
It’s best that students not learn math vocabulary by memorizing definitions. Instead, math vocabulary is learned best when students experience it in context, like the lines in the painting.
When students are younger, their understanding of math vocabulary is based on fewer experiences compared to older students. As they have more experiences, they refine their understanding of math vocabulary.
This is similar to how a baby might call anything that is furry a dog because that is the furry animal most familiar to them. Over time, as they experience and interact with more animals, they develop more precise vocabulary to identify other furry animals.
Similarly in math, a student in preschool or kindergarten might call any shape with four sides a square. Then, as they gain more experience with shapes in context, they develop more precise vocabulary to name various shapes.
Using Symbols and Equations to Communicate Clearly
In addition to math vocabulary, the use of math symbols helps students communicate with precision. Students connect math vocabulary to the correct symbols as they communicate the steps they took to solve a problem and why they took those steps.
Similarly, when students show their work and write out the steps they took to solve a problem, they attend to precision through the use of the correct symbols. You can help support students in developing these skills by modeling what it looks like to explain your thinking aloud, recording the steps you took.
It is very common for students to record their steps horizontally. For example, in the problem 24 + 28, students might solve it using expanded form and write “24 + 28 = 20 + 20 = 4 + 8 = 52”.
But this is not true. 24 + 28 is not the same as 20 + 20, and that is not the same as 4 + 8, which is not the same as 52. The equal sign does not necessarily mean an answer is coming. It’s important to help students understand that the equal sign means “the same as”.
Additionally, the equal sign shouldn’t be used to show relationships. For example, saying 3 dogs = 12 paws is not true. While 3 dogs might have 12 paws total, the two terms are not equal to one another.
It’s a small nuance, but it makes a big difference! It’s crucial that we model precise use of math vocabulary and symbols so that we can help our students develop their understanding of these terms.
Knowing When Precision Is Necessary
Another component of Math Practice 6 is helping students understand that certain situations require more precision than others.
For example, imagine you are measuring the length and width of your windows to get the measurements for curtains. Now, imagine you are measuring ribbon to tie on a present. Which situation requires more precision?
Unless you’re a professional gift wrapper, I’m guessing you would say the curtain measurements need more precision. After all, an inch can make a big difference when it comes to the curtains hitting the right spot that you want them to! The ribbon measurement is something I can estimate, or “eyeball”. I don’t need to get out a ruler and measure it to the nearest inch.
We want our students to attend to precision by knowing WHEN precision is necessary and to what level it is needed. As students develop their ability to do this, they are simultaneously strengthening their number sense and their innate understanding of mathematical ideas.
When students attend to precision, they also learn how to siphon out unimportant details so they can focus on the details that matter. Focusing on every detail can be super overwhelming and unnecessary, and can lead to anxiety and nervousness around math. Filtering out unimportant details so you can attend to the important ones is a great life skill, too!
Reflecting on Math Practice 6
Meaning-makers, I can’t wait to hear your thoughts about Math Practice 6. What are some ways you can be more precise in your usage of math vocabulary and symbols? What experiences can you give your students that will help them experience attending to precision? What are your big takeaways from this episode? What questions do you still have?
This is a lot to take in, and you’re doing great! Thank you for being so open to thinking deeply about these math practices with us. We have two more math practices to dive into, and I can’t wait! Until then, meaning-makers, have a great one!
