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What I Hope To Accomplish
#Becomingmath is a book I will have around and delve into forever. So for this book study I gave myself a goal: see if I could unify Tracy’s philosophy in #Becomingmath with Daniel Willingham’s philosophy, based in cognitive science and represented in his book Why Don’t Students Like School? with my teaching experience. (Discolsure: I have a strong bias towards Tracy’s philosophy that I need to be aware of and check to give others a fair shake).
So it’s:
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A Bit of My Experience Teaching Students As Young Mathematicians
In my 4th grade Math Laboratory we talked a lot about how we were thinking, acting, and working as young mathematicians. A few of my early inspirations for doing so were drawing on the Writer’s Workshop idea from Lucy Calkins that other teachers in my school used where they intentionally refer to students as “writers.” I had also read parts of Cathy Fosnot’s Young Mathematicians At Work series. In addition, the way I understand the Standards for Mathematical Practice is that they are practices that a mathematical mind can engage in from kindergarten into perpetuity. So why not start referring to students as “mathematicians”, guiding them to practice as such, and reinforcing the ways in which they were doing so? CAVEAT, when I started doing this I had NO IDEA what grown mathematicians such as Terry Tao or Sara Billey actually do.
Why is Chapter 3 So Special?
An excerpt:
p. 31 CHAPTER 3 Mathematicians Take Risks
What a passage! It speaks to me. I can clearly see how for our students whether in kindergarten, 4th grade, or high school so much of mathematics FOR THEM is unsolved and open. Why not use this to our advantage?
The concept of using the identity property to multiply a fraction to get a common denominator so you can perform an operation is decidedly solved, but my 4th graders don’t know that. What fertile ground to create opportunities for them to explore and discover what to them is unsolved and wide open. A few examples from my classroom are here and here.
What About Willingham
There’s a lot from Willingham’s work that I need to square with #Becomingmath and my experience, but to scale down the scope I’ll look at two things to start from Why Don’t students Like School?
#1 Chapter 6: What’s the secret to getting students to think like real scientists, mathematicians, and historians?
The short answer: Don’t.
*Ouch*
With subheadings in the chapter under “Implications for the Classroom” such as:
- Students are ready to comprehend but not to create knowledge
- Activities that are appropriate for experts may at times be appropriate for students, but not because they will do much for students cognitively
- Don’t expect novices to learn by doing what experts do
It’s a bit hard to see how I’m going to square this circle.
#2 Use Discovery Learning with Care (from chapter 3 pp. 82-83)
“An important downside, however, is that what students will think about is less predictable. If students are left to explore ideas on their own, they may well explore mental paths that are not profitable. If memory is the residue of thought, then students will remember incorrect ‘discoveries’ as much as they will remember the correct ones.”
Hmm, now this passage and pages give me some things to think about as I do believe that “memory is the residue of thought” and fully understand that discovery/invention requires mistakes/incorrect discoveries.
What next?
I have my cognitive work cut out for me (and what I outlined above is just a small subset of each philosophy).
But I’d also like to supercharge those cognitive capabilities by seeing if others have considered Willingham’s work or that of other cognitive scientists. Do YOU have thoughts on anything I brought up here or how Willingham’s work integrates with Tracy’s? If so, I’d love to get a conversation going that’s more than me talking to myself :p
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I am leading a group of teachers in grades 1 – 8 with this book.
How do I respond to teachers who tell me their math curriculum, as defined by our text books, is not open. It is about learning how to do the procedures. It is not exploratory. Yes, it is about problem solving, which can be done different ways, but there’s only one answer.
If they take time out of the book, to do some open mathematics and explore, they won’t finish the book.
How can I encourage them?
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This is not a very helpful answer for the near term, but, they should figure out the textbook adoption process, insert all of their voices into it, loudly, and ensure their school chooses a better book next time.
Near term, it’s tough because teachers generally don’t have unspoken for time for extra planning. It might work to figure out what’s the minimum they feel they must do from their book and spend any leftover time on better tasks. Deciding what to cut from their book could be a project for a PLC or vertical alignment team that is already established and already has time set aside. So can finding, curating, and writing better tasks. It would likely take admin support to free them up from doing something else in order to spend time on that.
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Is it possible for the teachers to think of the textbook as a resource rather than the curriculum? The adopted textbook might be outstanding when it comes to providing independent practice with procedural problems, but is not rich in tasks and adequately framing the eight mathematical practices. Perhaps find something positive to say about the textbook and how it fills that need, but other resources should be used to supplement the procedural problems.
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For me, this question leads directly to the section of the book inspired by Dan Meyer regarding the idea that Math Class Needs a Makeover. Tracy does a great job of demonstrating how a procedural problem can be transformed into a rich task, as long as the teacher had the content and pedagogical knowledge to orchestrate the transformation. I would encourage your teachers to “makeover” an existing problem with a keen eye on the math standards and the specific learning target. This will provide not only a powerful learning opportunity for the students, but it will build the content and pedagogical knowledge of the teachers you support, all while still utilizing the text books they have been provided.
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I will get back to you soon with an update. Looking forward to discussing this with you 🙂
P.S. this is a test to see if I can post w/out an error
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Can I post a new reply and have that work as well?
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