I’m Not Procedural, I’m Divergent


Recently I began reading Jo Boaler’s amazing book Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (Boaler, 2016).  At this point I have read about half of the book and even when I have set the book aside for a while, my mind keeps contemplating the ideas shared.  The research and ideals are fueling my teacher’s soul.  Each page and new concept serves to reaffirm my own pedagogical practices and beliefs. I can’t contain myself, and find I am yelling out “Yes, yes, yes!” with every encouraging page.

As a teacher for students with disabilities, I have been educated to teach with a closed mindset, and to educate my students likewise.  For example, Saunders, Bethune, Spooner, and Browder (2013), contend children with moderate to severe developmental disabilities are frequently deficient in their rudimentary mathematical abilities.  These researchers assert that students are capable of learning content required of grade level standards if educators utilize a systematic, procedural approach in their teaching.  At the core of these procedures is the use of prompting.  Prompting begins with ensuring the student gets the right answer followed by a series of prompts that are scaffolded to reduce support.  The student is trained to follow procedures that lead to the correct answer while eliminating instructor support.   This approach is supported by the final report of the National Mathematics Advisory Panel.  Educators are advised that students with learning disabilities should receive some, but not all, systematic instruction that has teachers lecturing, exhibiting exact strategies, or using prescriptive teaching methods (2008).  According to Witzel and Riccomini (2007), once teachers optimize their mathematics curriculum, they must model and guide students through the educational resources they have chosen.  While the National Mathematics Advisory Panel supports that these strategies are successful with students with moderate to severe learning disabilities, the practice of rote, procedural teaching is in direct conflict with the philosophies of other great mathematical philosophers such as Vygotsky, Bruner, and now, Jo Boaler.

As I am reading Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (Boaler, 2016), I keep wondering if Boaler would consider creating a student friendly version of this book.  I believe my students would find the information liberating and empowering!  I know I can continue to hone my open mindset teaching skills while encouraging students to develop their open mindset, but I want more.  Just as we strive for students to conceptually understand mathematics, I also want them to have a conceptual understanding of the teaching approaches utilized and the practices I ask them to employ in my mathematics classroom.  In the whisperings of my mind an idea has emerged, but right now it has no backbone, it has no form, only a name; I Am Not Procedural, I Am Divergent.   I find myself wondering, how to take the ideas from the Divergent series and utilize them in a math classroom.   My mind is whirling with ways to compare and contrast the factions to the practice of rote, procedural learning. The possibilities are endless: “Faction vs. Algorithm, What’s the Connection?”  “Tradition vs. Innovation, What’s the Risk?”  “Conformist vs Divergent, How do I Break the Mold?”

At this point these are only ideas in my mind.  However, these ideas keep tickling my brain, and I can’t let them go.   Therefore, I feel the need to put my thoughts in writing for others to consider.  I have discovered in order to have a true mathematical mindset, joint construction of knowledge is paramount.  Operating in a vacuum, believing that what we have going on is the end all, is a death sentence to innovation and growth.  We need to share notions with one another, collaborate and challenge each other’s thinking.  Just as our students need to engage in constructive dialog, we also do.  It is with this belief that I am leaving my pondering here, hoping that they will spark a conversation, generate ideas, and challenge my thinking, so that I may continue on my journey to cultivate a mathematical mindset.

Works Cited

Boaler, J. (2016). Mathematical mindsets: unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco: Jossey-Bass.

National Mathematics Advisory Panel. (2008). The final report of the national mathematics advisory panel. Washington DC: US Department of Education.

Saunders, A. F., Bethune, K. S., Spooner, F., & Browder, D. (2013). Solving the common core equation teaching mathematics CCSS to students with moderate and severe disabilities. Teaching Exceptional Children, 24-33.

Witzel, B. S., & Riccomini, P. J. (2007). Optimizing math curriculum to meet the learning needs of students. Preventing school failure, 13-18.





2 thoughts on “I’m Not Procedural, I’m Divergent

  1. Andrew Sommer

    Hey Jo Boaler has created a student friendly MOOC version of her course. There is a paid one for teachers and parents, which closely mirrors and expands on the ideas in the Mathematical Mindsets book, and a student version available at youcubed.org


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