Implementing the Standards for Mathematical Practice

June Mark has over 20 years of experience in R&D focused on mathematics professional development, instructional design, and curriculum implementation. She is the project director and author of EDC’s new Transition to Algebra curriculum, which launched at the 2014 National Council of Supervisors of Mathematics (NCSM) Conference. At NCSM and the National Council of Teachers of Mathematics (NCTM) Research Conferences, she shared findings from a four-year study of school districts’ implementation of elementary mathematics instructional materials and, with Victor Mateas and Johannah Nikula, discussed professional development that draws on an innovative online resource: Implementing the Mathematical Practice Standards. In this post, June describes this resource and related professional development. 

When the Common Core’s Standards for Mathematical Practice (SMP) came along, our team at EDC asked ourselves, “How can we help teachers learn about and better understand the SMP, and better support students in developing these practices?” We were already familiar with many of the ideas underlying the SMP because they are very similar to our own “Mathematical Habits of Mind” (MHoM) approach.

For over 20 years, we have sought to build students’ and teachers’ use of MHoM—ways of thinking, mental habits, and research techniques that mathematicians draw upon—to deepen their understanding and enjoyment of mathematics. The MHoM lie at the core of our curriculum and professional development efforts and, nationwide, we have collaborated with mathematics teachers to cultivate students’ development of the MHoM. From this work with teachers, we knew that it was not enough to just offer strategies to support students in developing the SMP. Instead, a group of us—Al Cuoco, Mark Driscoll, Paul Goldenberg, Deborah Spencer, and I—envisioned a resource that would help teachers gain a deep understanding of the SMP, to see how these mathematical practices would be evidenced in students’ mathematical thinking, as well as how to support students in using the SMP. This resource, the free Implementing the Mathematical Practice Standards website is now “live” and available.

Exemplifying the Practices

Launched with support from the National Science Foundation, the website’s 20+ Illustrations engage Grade 5–10 teachers in using—and envisioning students thinking about and using—the SMP. Each illustration has six elements:

  1. Mathematics Task: Presents a problem or question that encourages use of at least one SMP.
  2. Student Dialogue: Allows users to “eavesdrop” on a conversation among a group of students who share their thinking as they work on the task. Dialogues highlight students’ use of the SMP, as well as the range of responses they might have to the task.
  3. Grade Level and Standards: Lists the highlighted SMP, related Common Core content standard(s), and grade range.
  4. Teacher Reflection Questions: Engage teachers in thinking about and reflecting on the SMP and Common Core content spotlighted in the student dialogue.
  5. Mathematical Overview: Offers a detailed discussion of the SMP illustrated in the student dialogue and explores the mathematical ideas that underlie the dialogue.
  6. Student Materials: Provides teachers with related mathematics tasks and discussion questions they can use to engage students in using the SMP.

For each illustration, we ask teachers to work through the mathematics task and reflect on the SMP they use. Then, we ask them to read the student dialogue, ponder the reflection questions, and dig into the Mathematical Overview for more information. Visitors have the option of leaving comments to share their thoughts about each illustration. In addition to the project’s principal investigators noted above, a talented group of EDC staff—including Johannah Nikula, Katherine Schwinden, Victor Mateas, Mary Fries, Jane Kang, Matt McLeod, and Mari Halladay—helped bring the site to life.

In spring 2014, our team will add another 11 illustrations—including a little more on statistics, a broader range of mathematical tasks, as well as SMPs that many people find challenging, such as SMP 2 (reason abstractly and quantitatively). Since the launch of the site, we have had over 49,000 visits from visitors from all 50 states. To date, our most popular illustrations are Rectangles with the Same Numerical Area and Perimeter, Sum of Rational and Irrational is Irrational, and Finding Parallelogram Vertices.

Piloting Practice-Focused Learning Communities

In addition to the site’s self-guided learning, we have designed and piloted a 20-hour professional development (PD) course that features the illustrations. Currently, we are field-testing the course at district sites in Colorado, Illinois, and Massachusetts and gathering participant feedback to help us refine the course. We have also designed a facilitator institute that prepares mathematics directors, coaches, and teacher leaders to offer the course in their districts.  

During the course, teachers engage in a cycle of doing the site’s mathematics tasks, thinking about the practices they use, talking to peers about how they approach tasks, and analyzing the dialogues and real student work samples for evidence of the SMP. We are finding that participants appreciate the opportunity to do the mathematics and think about the reasoning they use, as well as to hear other teachers’ reasoning. The process offers teachers a useful window into students’ thinking and reasoning and hones their ability to recognize the SMP in action. Participants have told us that after tackling the tasks, and seeing peers approach the tasks, they realize how much it benefits students to struggle with tasks, think deeply about them, and come up with their own solution plans.

Curriculum planning is a key part of the course and engages teachers in thinking about how they will apply what they have learned in their classrooms. Teachers define learning goals for students and decide how they will support students in engaging with mathematical tasks and choosing paths to complete tasks. In response to feedback from the pilot test, we added a new dimension to the curriculum planning activities. Pilot participants told us that while they love the rich, open-ended tasks, many of their districts use mathematics curricula that include more straightforward, typical tasks. So, in a new activity, participants bring in tasks from their own curricula and, with support from peers and instructors, decide how they will structure these tasks to encourage students’ use and development of one or more SMP. In the field tests, this activity has been very successful.

Looking to the horizon, we hope to continue to expand the website and the PD course. In addition to providing more Grade 5–10 illustrations, we would like to extend the work to support K–5 teachers. In 2014–2015, we will conduct another field test using revised materials that respond to field test feedback. And, we are exploring options to modify the course to incorporate blended learning strategies.