Look For and Express Regularity in Repeated Reasoning

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The Standard

The eighth and final standard of mathematical practice, look for and express regularity in repeated reasoning, allows students to create more efficient and generalizable strategies to solve problems. Students love to discover patterns to see why something works. This mathematical practice capitalizes on this by having students look for things that happen consistently in the problems that they solve, describe it and then justify it. In layman's terms, students take an educated guess, check to see if their guess worked and then generalize their strategy to explain to others. 

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Just like the seventh mathematical practice (look for and make use of structure), students develop the ability to look for and express regularity in repeated reasoning on a continuum. Some students will see the reasoning quickly without playing around with a problem or task while other students will need multiple concrete examples to understand it. No matter how fast a student understands the repeated reasoning, they are developing shortcuts from exploration and they need to develop that understanding themselves rather than be told the shortcut and why it works. Students will be able to develop rules for solving problems based on their own discoveries with repeated reasoning and the patterns that they recognize.

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The Classroom

In the classroom, teachers should be intentional about setting up mathematical tasks that lend themselves to the discovery of patterns. Students should be allowed to discover a pattern through exploration, developing their understanding of the pattern through time and practice, and supporting them through proving that it works consistently. This all takes time and needs to be revisited often in order for students to develop a deep understanding of the patterns in mathematics.

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Question Stems

What do you see happening?

Will that always work?

What would happen if … ?

How do you know?

Could you create a rule for …?

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Picture Books

Beep Beep, Vroom Vroom by Stuart Murphy

Pattern Fish by Trudy Harris

Amazing Art Adventures by Yolanda Zappaterra

I See A Pattern Here by Bruce Goldstone

Simon Sock by Sue Hendra and Paul Linnet

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Next Steps

Now that you’ve got a basic understanding of the eighth Standard of Mathematical Practice, there are many places that you can dive deeper to learn even more. The West Virginia Standards for Mathematics includes Mathematical Habits of Mind which includes the eighth mathematical practice, look for and express regularity in reasoning. They’ve created a short overview, a rubric for implementation and a vertical progression from Kindergarten through high school which you can find here. Illustrative Mathematics, a curriculum company, has created vignettes and a few videos that give a good example of what the eighth mathematical practice can look like at different grade levels. Finally, in an issue of Mathematics Teacher, there is an article titled “What is “Repeated Reasoning” in MP 8?” that dives deep into what repeated reasoning is in algebra and gives examples.

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Sara VanDerWerf, MDE, will also be hosting a webinar for the eighth mathematical practice on March 12th, 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.}