The 8 Mathematical Practices: New Roles for Teachers and Students

By Shannon Samulski

Given the importance of the 8 Mathematical Practices in understanding and implementing the Common Core math standards, every educator must have a firm knowledge of these practices. Unfortunately, that’s not the case. Many teachers don’t understand the practices, the relationships between them, or how to weave them into their curriculum.

If they are to use the Mathematical Practices to improve math instruction and student learning, educators need to know what these practices look like in action. In this article, we’ll take a peek into a classroom to see how the Mathematical Practices play out and to show educators how they can transform the vision into their own classrooms.

Teachers: Engaging, questioning, guiding

Math teachers know how to teach. The question is how to go a mile deep like the new standards expect. That requires a dramatic change in how instruction is approached. No longer is there a need for teachers who tell, explain, follow the text book, or give answers. No longer do teachers need to instruct students to “do this” or “do that.” Rather, they need to release control to the students so the students can figure things out on their own—that way, they are much more likely to retain it. They need to encourage, facilitate, and guide. They need to turn inquiry into their primary instructional tool which leads to students independently solving problems.

That requires creating a student-driven and student-led classroom where the children can make connections, collaborate, question, and discover on their own. What does such instruction look like? In classrooms where this transformation is unfolding, you’ll see and hear teachers who:

  • Engage students using investigations and discovery learning
  • Question to get students to think at a higher-level and explain, justify, and elaborate
  • Build on previous knowledge to make connections
  • Assess students in many different ways—from portfolios and tests to demonstrations and projects
  • Guide their instruction through the results of assessments

Students: Collaborating, listening, communicating

The 8 Mathematical Practices will also impact student learning—in a big way. Students will become the source of mathematical ideas. They will take responsibility for their learning. They will form new habits of mind, thinking processes, and attitudes. They will become problem-solvers who see math in the world around them and have a math mindset. No longer will students work in isolation, sit and listen to the teacher talk, memorize procedures, answer teacher questions, or use technology only for calculations. An observer of a classroom where the 8 Mathematical Practices are in full swing would see students who:

  • Work together to solve problems that have applications in the real world
  • Use technology to explore and gain deeper insight
  • Listen to and question each other
  • Communicate mathematical concepts to each other
  • Learn through games, journaling, math salad bars, and other fun techniques

The 8 Mathematical Practices are not new names for old ways of doing things. They are different. They require systematic change. And that takes time. It’s a worthwhile investment—teachers who understand and properly use the 8 Mathematical Practices can successfully make the paradigm shift now required in the math classroom.

Take a closer look at the 8 Mathematical Practices and how to transform your math culture. Check out SDE’s webinar 8 Mathematical Practices: Addressing the Higher Standards (Grades 3–5) by author and intervention expert Shannon Samulski.

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