Written By: Suzanne Hood, Instructional Coach, and Exemplars Math Consultant
I’ve always believed in the power of students to use their own childlike curiosity to problem solve. These problem-solving experiences happen for our students naturally, through the math they use in cooking, playing games and playing with toys, among other things. Problem solving is a life-long skill all mathematicians use. The true power of a mathematician is the ability to see math in all situations and solve problems using a toolbox of proven strategies.
While I believe that students are innate problem solvers, I also believe that learned algorithmic thinking corrupts a child’s natural ability to problem solve and discourages perseverance. Although I have met many teachers who share my belief that problem solving should be the focus of the math, many struggle to create this culture in their classroom.
This is becoming more apparent—and the stakes of ignoring problem solving much higher—as we approach testing season. The classrooms that will likely fall behind in this new era are those who insist on teaching math through algorithmic thinking. Conversely, I am convinced that teachers who use problem solving to teach math, supported by materials like Exemplars, will have students who score proficiently on the state assessment and are more prepared for success beyond the classroom.
So how can teachers help their classrooms make this critical transition to problem solving? My personal story of transformation, which began after participating in one of Exemplars’ Summer Institutes, offers a path forward. This was when I realized two important things: first, I needed to work on my own personal proficiency in teaching problem solving. And second, I wasn’t alone; veteran teachers confessed their frustration in teaching problem solving, and many admitted their backgrounds did not include support in how to instruct students through the problem-solving process. Here are seven things I’ve learned on my journey to becoming an educator fully committed to teaching mathematics through a problem-solving approach.
1. Nurture a community of trust.
Based on my experience as a Mathematical Instructional Coach in Georgia, I believe it is essential to nurture relationships and establish a community of trust between teachers, so that discussions are authentic and all voices are included. Trust is a prerequisite for being able to assess the strengths, weaknesses and gaps of teacher readiness in the classroom. Only when teachers feel they are in an environment where they can share their knowledge, their doubts and their pedagogical weaknesses, will they be able to feel comfortable.
2. Establish a baseline of teacher readiness.
Evaluating teacher readiness and needs and getting them on the same page is an important first step. How can you get teacher teams to have collegial conversations when everyone has a totally different math background? Do all teachers even want a problem-solving classroom? Do they know what that means? Asking these questions can be illuminating, albeit tough. As such, using universally agreed-upon protocols such as those from the National School Reform Facility can establish a baseline to work from, encourage collaboration, and support an atmosphere of trust.
3. Assess student work so you can see where the gaps are.
One way to assess teacher acuity and readiness in teaching problem solving is by assessing student work using an Exemplars task. Here’s how it worked for me: At the first Professional Learning session, I asked teachers to bring classroom samples from their most recent classroom Exemplars task. As a community, we agreed to facilitate the discussion with the protocol Atlas – Learning From Student Work. As I observed teachers at the meeting, I noticed that while some teachers were proud to display their samples, others pretended to forget their samples or chose to stick their student work in their tote bag. As we used the Exemplars standards-based rubric to score our samples, it became clear that our understanding of the skills needed to meet the standards did not align. The journey began; teachers began to talk about problem solving.
4. As a team, align your mathematical beliefs towards problem solving.
When we began, we knew we shared some foundational mathematical beliefs. We also knew that we needed to solidify a shared understanding of how a mathematics culture transfers knowledge from the teacher to the student. We used the Math Framework (a document listing all the mathematical beliefs of the faculty) as a tool to target instructional strengths and weaknesses. As a team, we revised the document to build cohesion and a shared understanding of our beliefs. Next, I had the team read a book rooted in Vygotsky’s constructivist theory to increase our group’s understanding of the problem-solving trajectory. Because we had been working hard to build an atmosphere of trust, teachers felt safe sharing their struggles and personal hardships with teaching problem solving. We discovered that we shared similar experiences, and that we all believed our students would be successful at any problem if we just taught them the necessary skill set. The student samples, however, told a different story.
5. Create simple tools to help teachers and students internalize the standards and assess their progress.
At our next meeting, we reviewed Exemplars student work samples and discovered a misconception: we thought we knew how to teach problem solving, but we were actually teaching skills in isolation. Why? Quite simply, it turns out that many teachers lacked background knowledge about the Standards of Problem Solving. To facilitate the understanding of the standards, I created posters with clear icons for each standard (Problem Solving, Reasoning and Proof, Communication, Connections, and Representation). These anchor charts would support teachers and students. It worked. Now, teachers could explain each standard. Each classroom in our building displayed the posters. It was a great reference for both students and teachers. We made a replica of the posters into a small book that students put in folders for their own reference. Students used the folders as portfolios to track their problem-solving progress, and created data notebooks to reflect on their growth and set goals for their next Exemplars task. Using data notebooks empowered kids to self-reflect on their own progress.
6. Hold individual meetings with students to track progress and set goals.
Currently, I am encouraging teachers to hold one-on-one Exemplars conferences with their students. Individual conferences support differentiated instruction, meet students where they are, and set goals for the next problem-solving task. Although this approach makes some teachers uneasy at first, they become more confident over time. Allowing other teachers or coaches to observe and co-teach the process can lead to greater transparency and effect change in teacher practice.
7. You may not get the teacher of the year award, but you’ll still be changing students’ lives.
At the beginning of my career, I thought Oprah would call me to announce my Disney Teacher of the Year Award. While this hasn’t happened yet, I do have countless memories of the sparkle in a child’s eye when he or she announces, “I get it!” I believe I have the responsibility to show up every day prepared to change the lives of children and equip them with the skills to be life-long mathematicians. Exemplars provides the problem-solving tools necessary to guide teaching and build capacity for each child’s mathematical journey.