Attend to Precision

The sixth standard of mathematical practice, attend to precision, is one that is often thought of in math class but not always for the right reasons. Often, math is thought of as right or wrong, black or white, but that isn’t necessarily the case. The ability to calculate accurately and efficiently is just one of three components to this mathematical practice. Accuracy is often the only part many classrooms have considered in the past. Mathematics is not simply about “answer getting;” mathematics is about having the ability to collaborate and communicate thinking to others, and themselves, with clear and precise language. This means that teachers should not just be the deliverers of content but rather the facilitators of learning. Although educators know the destination and/or purpose of a lesson, students can get there on their own through purposeful questioning rather than directly telling students.

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There are three components to this standard: communicating precisely, using symbols precisely, and being precise in mathematical work. When communicating precisely, students need to be able to select words with clarity and specificity in order to be clear. It is often said that the person in the room that is doing the majority of the talking is also the one doing the majority of the learning. This is why students need to be the ones communicating their learning. Communication is also not just verbal but it can also be done through writing (explaining through words), representations (explaining through pictures, drawings, graphs, etc.), or with numbers and symbols (explaining through equations). A math journal could be implemented to emphasize the importance of the different types of communication. 

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Using symbols precisely means that students need to have built a deep understanding of what mathematical symbols represent. Allowing students multiple opportunities supports their ability to make sense of using symbols. The equal sign, for example, is of particular importance in this mathematical practice. 

Finally, being precise in mathematical work means that students are doing their calculations accurately and efficiently. This is the most familiar area of precision and the one that shouldn’t be overlooked but also not placed above either of the other two areas.

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The Classroom

In the classroom, it is important that emphasis is placed on all three areas of attending to precision, rather than focusing on just one. Educators need to use appropriate vocabulary, explicitly describe their thinking during think alouds, and ask follow up questions to help students become more precise in their communication. Vocabulary is an ever evolving skill; therefore, instruction should connect student language to formal vocabulary. This vocabulary instruction helps bridge the conceptual understanding to the new language because students won’t use the correct vocabulary on their own. Formal vocabulary needs to be taught and encouraged through modeling. The more students talk about math, the better their understanding of precise communication will be.

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In order to help build the precision of symbols in students, teachers can offer practice flexibly and often. Giving students cards with symbols and numbers on them to build equations can be great practice in all grade levels to develop a deep understanding of the mathematical symbols. An example of this could be  putting the total at the beginning rather than the end of an equation can be a lightbulb moment for students to see what the equal sign means. 

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Finally, encouraging students to slow down in their math work can be one simple way to build precision in their mathematical work. Students' brains are often moving faster than their hands and mistakes happen. Mistakes are NOT a bad thing; however, mistakes need to be caught and corrected which is where this standard of mathematical practice comes into place.

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Question Stems

I think that’s a good starting point, but can you be more specific?

Can you say more about that?

Does anyone know what we as mathematicians call __________?

Can you tell me why that seems important?

Does your answer seem reasonable?

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Picture Books

Duck! By Meg McKinlay

Lilly’s Purple Plastic Purse by Kevin Henkes

How to Find Gold by Viviane Schwarz

The Listening Walk by Paul Showers

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Next Steps

Now that you’ve got a basic understanding of the sixth Standard of Mathematical Practice, there are many places that you can dive deeper to learn even more. First, PBS created a video series highlighting the key pieces for this mathematical practice which you can watch here. There are four videos in this series which are all short dives into attending to precision in the classroom. Sadlier™, a curriculum company, created a free tip sheet to utilize the sixth mathematical practice, attend to precision, which can be downloaded here. Finally, EdReports released a Deep Dive into how the 5th and 6th mathematical practices together can build confidence and ownership in students' learning.

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Sara VanDerWerf, MDE, will also be hosting a webinar for the sixth mathematical practice on February 5th, 2025 at 7:00 AM which you can find by registering here.

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If you’d like more information, support, or guidance on developing a better understanding of Mathematical Practice #1, please reach out to our Math Team here at Resource Training and Solutions.

Mindy Strom

Math Lead

Email: mstrom@resourcecoop-mn.gov

Phone: (612) 505-7997

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Megan Klaphake

Math Coach

Email: mklaphake@resourcecoop-mn.gov

Phone: (218) 770-0026

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References:

^{SanGiovanni, J. (2019). Using the mathematical practices effectively in the classroom. https://www.mheducation.com/unitas/school/explore/research/reveal-math-using-mathematical-practices-effectively-classroom.pdf} 

^{Illustrative Mathematics. (2014, February 12). Standards for mathematical practice: Commentary and elaborations for K–5. Tucson, AZ. Retrieved December 29, 2018 from http:// commoncoretools.me/wp-content/uploads/2014/02/Elaborations.pdf}

^{Flynn, M. (2017). Beyond answers: Exploring mathematical practices with young children. Stenhouse.}