Visual: Encouraging mathematical flexibility #LL2LU

From Jo Boaler’s How to Learn Math: for Students:

People see mathematics in very different ways. And they can be very creative in solving problems. It is important to keep math creativity alive.


When you learn math in school, if a teacher shows you a method, think to yourself, what are the other ways of solving this? There are always others. Discuss them with your teacher or friends or parents. This will help you learn deeply.

I keep thinking about mathematical flexibility.  If serious about flexibility, how do we communicate to learners actions that they can take to practice?

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How might we narrow what separates high achievers from low achievers? If number flexibility is a gateway to success, what actions are we willing to take to encourage, build confidence, and illuminate multiple pathways to success?




  1. Jill,
    You are speaking my language!!!! I really like the levels you have described here and the fact that finding a solution in one way is the baseline, if you will. I wonder how teachers will work with students on mathematical flexibility. I worry that teachers– especially elementary base teachers who haven’t had as much training or passion about math– are not as comfortable and confident in their own mathematical flexibility. Will they teach the different methods but yet fall back on the traditional method in either assessments or their own explanations? How might they “live” the flexibility in their classroom, celebrating each method/solution that children use in such a way that the teacher truly understands it, too?


    • The question raised here about teachers living flexibly in their math classrooms is a good one! It’s all about being willing to take risks and potentially fail publicly. I plan on using “Number Talks” to build flexibility and number sense. I also plan to make more student work public and available for feedback from peers. My hope is that this will encourage and celebrate flexibility, for me, other teachers, and students.


      • Sounds like a plan, Kato! The more math talk you have with the students, the more their comfort level and confidence will increase- and yours, too! I am proud that you are serving as such a strong model for your fellow teachers at Trinity!


    • Angél, This connects to one of our summer reading choices, 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret Schwan Smith Mary Kay Stein. The first of the 5 practices is anticipating what learners might do, think, try. How we might anticipate what another might do requires flexibility in our own thinking. This leads to the necessity of teaming. If I share what I think with you, and you with me, I add to my toolkit of ideas. It takes practice and sharing for sure.


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