Case Studies

Strengthening Math Instruction

Math Problem Solving: A Thinking Process


For three years beginning in 2014, Washington, D.C.’s Office of the State Superintendent of Education (OSSE) engaged FourPoint to create and implement the Learning Support Network for schools ranking in the lowest five percent (priority schools) and ten percent (focus schools) in student performance. The goal of the network was to provide schools with supports that would lift academic achievement rates. To do that, we knew we needed to focus on classroom instruction.


Because fewer resources were available to support focus schools than priority schools, FourPoint worked with OSSE to get creative about how to provide substantive instructional supports to these school leaders. We know that educators learn better when working with their peers who share similar needs. To that end, focus school teams were divided into Community of Practices[1] (CoP) concentrating on either math or reading, depending on their school’s need. This approach allowed leaders to leverage their collective knowledge about a common problem, share in the development of tools, and participate in rich discussions about solutions. CoP members connected during face-to-face and virtual meetings. Some developed relationships with other leaders that led to peer supports outside of formal meetings.

Most focus schools fell in this category because their students with disabilities and African American students were performing at low levels on the Partnership for Assessment of Readiness for College and Careers (PARCC) mathematics or reading assessments. School leadership teams in the math CoP were led through an abbreviated root cause analysis process to identify a specific math problem of practice to hone in on so that they could boost achievement for all students and accelerate achievement for those falling behind. The math CoP was then segmented further to allow for peer groupings focused on selected math practices.


Most school leadership teams in the math CoP chose to focus on “Understanding and Application of the Mathematical Practices,” specifically, math practice 1 (MP1): Make sense of problems and persevere in solving them.

College and career ready standards require that students go beyond just “doing math” to “thinking mathematically” to build conceptual understanding, a skill that needs to be explicitly taught to students. We worked with school leaders to develop a metacognitive approach to instruction that encourages students to make their thinking visible. Doing so allows educators to monitor, evaluate, and better support students’ knowledge and application of thinking skills as they solve math problems. This approach also got at the heart of the behaviors that students must demonstrate to master MP1:

  • Explain to themselves the meaning of a problem and look for entry points to its solution.
  • Create a plan for solving the problem.
  • Monitor and evaluate their progress and change course if necessary.
  • Check their answers using different methods.
  • Ask themselves. “Does this make sense?”

We also developed several resources to support implementation, including:

  • A series of guiding questions for teacher think-a-louds so they could model the process
  • Graphic organizers that students could use to illustrate their thinking
  • Rubrics that measured MP1 practices that teachers could use—alongside the organizers—to monitor and adjust instruction (i.e., re-teaching or scaffolding)
  • A classroom observation tool that leaders could use to identify changes in both teacher and student behaviors in the use of the practice.



The combination of peer supports and resources paid off. At the end of each year of the Learning Support Network, school leaders reported being well on their way to creating a school-wide problem solving approach to equip students with the knowledge and skills needed to apply mathematical thinking. Classroom observation and PARCC data confirmed changes in teacher practices and improved student learning outcomes.

Classroom observation data revealed changes in teacher practices leading to improved instruction of MP1. Teachers:

  • Modeled the think a-loud process for initial instruction of the practice.
  • Explicitly taught students how to identify multiple pathways to solving problems and compare solutions to those of their classmates.
  • Planned time for students to independently grapple with content and problem solve.
  • Led structured turn and talks to give students opportunities to engage in mathematical discourse about key details and strategies.
  • Charted the number of pathways students took to solve problems and the accuracy of their solutions.

Classroom observation data also revealed changes in student behaviors consistent with MP1 application. Students were observed:

  • Completing problem annotation to explain what they were being asked to do.
  • Authentically creating graphic organizers in notebooks.
  • Using mathematical language when sharing their thinking with peers.
  • Explaining their thinking with multiple representations.
  • Attempting a challenging problem more than once, if needed.

“Four out of ten teachers are consistently using MP1 strategies and language during lesson components. We’ve noticed that all of our students have increased their mathematical discourse with their peers.”

– Lequisha Chavers, Instructional Coach, Whittier Elementary

PARCC data revealed an increase in student learning for schools whose problem of practice area was MP1.


In 2015-16, four of the five focus schools increased student achievement to levels qualifying them to exit focus status.


In 2016-17, two of the three focus schools saw improvements in student learning. Whitter Elementary realized a 38 percent reduction of students in target subgroups performing at levels 1 and 2 in math and Hart Middle School realized an 8 percent reduction.

School leaders credit improvements to the effective design and implementation of a problem solving model and process that empowered students to guide their thinking and that provided information for teachers’ instructional decision making.

“It’s been hard work, but I think we are on our way to building a process that all kids can use in every class. It’s becoming our norm.”

– Collin Hill, Principal Garrison Elementary

[1] Hubert, C., Newhouse, B., & Vestal, W. (2001). Building and sustaining communities of practice in next-generation knowledge management: Enabling business processes. Retrieved 10/15/2010, from

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