Powerful Problem-Solving … For Teachers and Students

Recently, The Math Forum’s Annie Fetter (@MFAnnie) and Max Ray (@MaxMathForum) hosted Elementary Math Chat (#elemmathchat) on Twitter. The focus was Powerful Problem Solving. During the chat, we shared Noticings and Wonderings around a purposefully chosen mathematical image, discussed student responses, reflected on our curriculum’s approach to problem solving, and thought about ways in which we could modify problems to make them scenarios that encourage deeper student reasoning.

The hour-long conversation with my #mtbos (Math Twitter BlogoSphere) colleagues flew by as always, but the next day I was left pondering one of the questions posted the evening before:

solving problems discussion points

During the chat, my focus was on my students. I truly believe that students should solve problems to learn math, rather than learn math to solve problems. As students solve problems in my classroom, I’m able to listen to their conversations and see the mathematical ideas come out through their work. As a class, we then share these ideas, compare them, make connections, and look at larger conjectures and claims.

My focus around this question, however, was slightly different the following day when I was facilitating a teacher professional development session. I began to wonder, do we treat learning with adults the same as with our students?

Mathematical Routines

This particular K-2 professional development session was inspired by Virginia Bastable, Susan Jo Russell, and Deborah Shifter and their book Connecting Arithmetic to Algebra. It’s centered around mathematical routines, and how teachers can structure these routines to allow students the opportunity to articulate “noticings” en route to developing claims. The routine we were discussing that afternoon was “Talking Points,” a quick and timed process that aims to support students in building exploratory thinking and speaking skills. You can read more about Talking Points at this amazing blog.

I started the session with the teachers — acting as students — doing a set of Talking Points I had done with my own students at the beginning of the school year:

Talking Points

(Download the complete Talking Points sheet.)

After they finished, I asked them to discuss how they could imagine Talking Points being used in their classroom to allow for mathematical noticings and claim development. Not only were the conversations about classroom structure and mathematical concepts amazing, teachers got EXCITED about the math they were discussing.

Understanding Student Misconceptions

They discussed misconceptions students frequently had related to content and thought deeply about the bigger ideas surrounding these misconceptions. For example, they moved the conversation from “Students don’t know 2+3=5 is the same as 5=2+3,” to the meaning of the equal sign, and how we as teachers affect student understanding of this concept of equivalence by the way we record student responses on the board, for example. As I listened to their conversations, I reflected on Annie and Max’s question. We were solving a problem to learn math.

That problem was thinking about Talking Points in relation to their students’ needs. And through that process, the teachers learned a lot about not only the bigger ideas in mathematics, but also how our classroom practice can influence these ideas. The teachers were excited because THEY were thinking about how this could work with their students, and THEY were thinking about the mathematical ideas that could emerge through this work. Had I given them the math ideas and classroom practices they were to think about and then apply to Talking Points — learning math to solve problems, in other words — I believe the entire experience would have been wildly disappointing, with teachers leaving feeling like they “did” one more professional development.

Whereas on this day, the teachers owned the experience and walked away having learned more about math and instruction.

Questions About Professional Learning

Reflecting on that chat question in relation to my professional development work, I see powerful connections that leave me with many questions: How often do we give teachers ideas they must implement in their classroom and tools to do so, without offering the opportunity to think about how these tools work for them? How often do we prescribe the problem for teachers, rather than creating a situation where they’re asked to do the noticing and wondering? How much more powerful would it be if teachers were problem solving while at the same time not only learning math, but also learning more about themselves as teachers? How valuable would school/district professional learning communities be if teachers left excited about what they learned because they problem-solved it and owned it?

As teachers, we have so much to think about as we engage our students. But what if what we need to consider is how we learn, as much as how our students learn. As learners, we all — teachers and students — deserve the opportunity to solve problems to learn math, versus learn math to solve problems.

Kristin is a National Board Certified fifth grade math teacher at Richard A. Shields Elementary School in the Cape Henlopen School District in Lewes, Delaware. During her 19 years in education, she has taught 5th–8th grade math, as well as spent two years as a K-5 Math Specialist. She feels fortunate to be involved with Illustrative Mathematics and Teaching Channel on projects developing math tasks, facilitating professional development, and blogging about these experiences. She is always excited to share her love of teaching at conferences such as NCTM, NCSM, ISTE, as well as on her blog. Follow her on Twitter @MathMinds.


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