Make Sense of Problems and Persevere in Solving Them!

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The Standard

The beautiful thing about the mathematical practices is that they apply to all students, preschool through adult, and the first standard is a great example of that. The first standards of mathematical practice states that students should be able to make sense of problems and persevere in solving them. This means many things but first and foremost, it means that students need to be able to read a question or get a problem and look to find where to begin. They don’t get stuck before starting the question and they make a plan before jumping into the problem and creating what we call “number salad”. Many students see numbers and just start doing math with them without actually determining what they’re supposed to be doing. If they can utilize this mathematical practice, this shouldn’t happen.

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Once your student has found their entry point and made a plan to solve, they should then be checking their progress by relying on the use of concrete representations and changing directions if necessary. A student should be able to begin a problem, get halfway through solving it and realize that what they’re doing isn’t going to work or possibly isn’t the most efficient way they could solve it. They should be constantly asking themselves “Does this make sense?” If it makes sense, they continue on. If it doesn’t, they change course. Students often get an answer at the end that may not fit the question at all but forget to ask themselves that vital question. If they check in throughout their problem solving process as well as at the end, they may need to change course and try again, but they will end up with the correct answer more frequently. 

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The Classroom

So how do you use this in your classroom today? For this mathematical practice, it is important to check in with your students frequently and have them describe their thinking as well as what their next steps are. In a preschool setting, this may look like having students work together and explain to their partner what they’re doing as they do it or by asking them to draw a picture of what they’re thinking. In middle school, it may look like asking your students to find different points of entry to a problem before starting it. No matter what the grade level, it is important that the problems you are asking students to work through and solve have different places they could begin and utilize multiple representations. Teachers should continuously be asking questions while students work together or individually. Picture books are also a great way to introduce the soft skills required in these mathematical practices so that they are relatable to students.

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Question Stems:

• How would you describe the problem in your own words?
• How would you describe what you are trying to find?
• What do you notice about…?
• Describe what you have already tried.

‍Picture Books:

• The Power of Yet by Maryann Cocca-Leffler
• A Thousand No’s by D.J Corchin
• The Dot by Peter H. Reynolds
• Beautiful Oops by Barney Saltzberg
• The Magical Yet by Angela DiTerlizzi
• What Do You Do With A Problem? by Kobi Yamada

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Next Steps:

Now that you’ve got a basic understanding of the first Standard of Mathematical Practice, there are many places that you can dive deeper to learn even more. When it comes to Early Childhood, the NAEYC has developed five ways to support mastery motivation or persistence at mastering challenging tasks.The Charles A. Dana Center out of the University of Texas at Austin has developed video clips that they call “Connections to Classroom Practices” for grades Kindergarten through 12th for each Mathematical Practice. These clips give specific examples of how each standard can be used in the classroom. The global nonprofit Education Development Center (EDC) has developed Illustrations of the Standards for Mathematical Practices for grades 4-12 which give math tasks that encourage the use of specific Mathematical Practices. Explore the hundreds of Mathematic Tasks that have been written by experts for teachers to help build both mathematical understanding of the content as well as the Mathematical Practices.

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Sara VanDerWerf, MDE, will also be hosting a webinar for the first mathematical practice on October 2nd, 2024 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.

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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 

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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

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