Dear Teacher: An Expanded explanation of work from my new favorite book

I have recently read, then created some professional development for teachers in my district based on the book, Powerful Problem Solving, by Max Ray.

As soon as I finished the first chapter, I knew I would have to turn it into some action learning.  I had to TRY it myself.   

I love math, and I am always looking for ways to improve my teaching practice, and now my coaching practice.

The strategies here, not only improved my practice, but they forced me to CHANGE my practice.   Yep, it was uncomfortable.  No, I didn’t think it would work.   Yep, I thought it would be too hard.  The reality, is when I unsilenced my students’ voices, and gave them choice in what they would do, we both learned a great deal–my students about math, and I learned about them.

We tried the same “I notice, I wonder” activity in 9 different classrooms, grades 3-5. In trying out strategy from the book, we found that we needed to make several refinements to meet the needs of our students.   This is important because anytime you are trying something new, it is challenging, and you have to stay with it.  Eventually, you will work out exactly how to talk less and get your students talking more.

One of the refinements was to have the students categorize their wonderings by three different types:   Type 1, a little math, maybe one step/operation.  Type 2: more challenging, maybe 2 or more steps/operations.  Type 3:   a reasoning problem, no math yet.   

Our original types inadvertently imposed a teacher judgement on the student work, and we wanted them to categorize, not judge, their questions.  Here is the final, student generated category list:  

student category

The red edits were student suggested edits.

We made a conscious effort to call the work “categorizing” not ranking.

From our final, 9th, session, 4th grade.  


pp noticings


pp wonder 1  pp wonder


Round 1:  Pink         Round 2:  Green      Round 3:  Blue

We noticed that the more we asked them to go back and wonder, the deeper and more complex their questions became.  

An interesting observation is that more than half the students chose a more complex question when given the opportunity. When asked why they said they wanted their brains to grow, they liked the challenge, or just that they thought it would be more fun!   There was a lot of laughter in the rooms!    

Several students did state that they chose “easy questions”.    We accepted that-  I’m confident that over the course of a year, these few students will still have a lot of opportunities to choose more challenging questions for deeper problem solving.  

This work required the students to use many different math skills and standards.   In Texas, we also have process standards, which are the tools students “use to acquire and demonstrate mathematical understanding.”   (From the Texas Essential Knowledge and Skill, or TEKS, introduction to the Process Standards.)  Our task as teachers this year is to use the process standards as a lens to identify the mathematical tasks and experiences that will help our students mathematize their world.  

Things I learned from this series of lessons:

  • I need to talk less, and give students time to think, time to talk, and time to listen to    each other and learn.  
  • Interventions could happen in the moment. When I uncovered a misconception, it was easy to step in, ask some guiding questions, and help them clarify their own thinking before it became a solid misunderstanding.   
  • The English Language Learners had support from their peers, as well as from the charts.
  • It was constant formative assessment-I was constantly getting information about what my students knew as well as where they were confused.  
  • Students love choice, and given the chance, will choose more problematic questions over “easy questions”.
  • Student choice gives every student an entry point.
  • When students have fun and there is laughter in the math class, great learning occurs by students AND teachers!

My new wondering is “What would happen if students experienced this type of problem solving and opportunities for choice the entire year?   What would happen to their level of questioning?  Would they continue to work at a challenging level?  Would their work go in cycles, sometimes easy, sometimes rigorous?”  
Many thanks to my partners, Linda Hicks-Green and Michelle Vogl-we were all involved in the entire process and learning together!

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