What Do the Standards for Mathematical Practice Mean to You?

  • What Do the Standards for Mathematical Practice Mean to You?

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    By Kitty Rutherford, Posted April 13, 2015 – 

    The Common Core’s Standards for Mathematical Practice (SMPs) focus on what it means for students to be mathematically proficient. I have heard many people say that the SMPs are the heart and soul of the Common Core State Standards for Mathematics (CCSSM). These standards describe student behaviors, ensure an understanding of math, and focus on developing reasoning and building mathematical communication. Each standard has a unique focus, but each also interweaves with the others as we put them into practice. These practices empower students to use math and to think mathematically. Our job as teachers is to help students develop these practices to become effective mathematicians.

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    The SMPs describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM Process Standards of Problem Solving, Reasoning and Proof, Communication, Representation, and Connections. Second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

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    The SMPs are a significant focus of CCSSM. These eight practices describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics.

    One way to build a deep understanding of the SMPs is to read one practice at a time and reflect on the following questions:

    1.   Why is this practice important?

    2.   What does this practice look like when students are doing it?

    3.   How can a teacher model this practice?

    4.   What could a teacher do within a lesson to encourage students in this practice?

    5.   How can you assess proficiency in this practice?

    Before CCSSM was implemented, I visited a few fourth-grade mathematics classrooms. I presented a cognitively demanding mathematical task, and students worked collaboratively together to solve it. I then introduced the SMPs by explaining to students that these are standards that mathematicians practice to help them excel in mathematical thinking. I asked students to think about the task they had just solved: If they were to explain to someone what that practice meant or looked like, how would they do it? After some discussion, students created posters to represent their thinking about the SMPs. In this task, students explored prime or composite by building possible rectangular arrays for the numbers 1–25. After the task and much discussion, students created posters.

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    In another fourth-grade classroom, students were given the task of finding the perimeter of a figure. These are some of the posters of the SMPs that these students created.

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    I noticed a blond, blue-eyed little boy sitting alone as he worked diligently on a simplistic drawing. As I approached, he looked up, and in a sincere, heartfelt tone he informed me that this was a picture of his friend persevering not only in math but in his everyday life. Pointing to the empty desk next to his, he whispered, “My friend has cancer. He is not in school today because he just received a cancer treatment a few days ago.”His comments shook me to the very core. We do many of these practices every day, not just in mathematics!

    Now it is your turn. Have a conversation with your students about one of the Standards for Mathematical Practice. Have them illustrate what they think it means.

    2015-04-13 Ruherford AU PicKitty Rutherford serves as the North Carolina Elementary Mathematics Consultant for the Department of Public Instruction in Raleigh. She is an experienced leader, collaborator, and licensed educator with a master’s degree in elementary education coupled with more than twenty-seven years’ experience in teaching elementary school students, training educators, collaborating with multiple stake-holders, and implementing effective programs. She has received such honors as the Presidential Award for Excellence in Mathematics and Science Teaching, NCCTM Outstanding Elementary Mathematic Teacher, Alpha Delta Kappa State Excellence in Education Award, and Teacher of the Year Finalist. She currently serves as the State Coordinator for NC Presidential Award for Excellence in Mathematics Teaching and on the board of North Carolina Council of Teachers of Mathematics.

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    Karen Decker - 7/23/2020 1:34:48 PM

    Thank you for sharing that the standards of mathematical practice are not only valuable for math, but great for any discipline. It was so touching to read about the child applying perseverance as an attribute he saw in his friend with cancer. Seeing the student as a whole person is beautiful. We are not teaching math, we are teaching students about math. 

    "Throughout history, and in cultures all over the world, education rightly conceived has had two great goals: to help students become smart and to help them become good.” Thomas Lickona & Matthew Davidson, Smart & Good High Schools. 

    Tanaga Hannah-Rodgers - 5/18/2020 7:31:05 AM

    I appreciated the student depictions of the Practices because it gives a lens into their perception of what it means to think mathematically.