Blogs 
When teachers read professional books, the majority of interaction around the content is based solely on our interpretation and its application to our work. While we know discussing the content with others would allow us to gain a new perspective on the material, finding time for a book study seems nearly impossible; and particularly with this subject, finding someone who would love to read and engage in discussions around a math book is often difficult.
Enter Twitter, the social media outlet that has changed the landscape of my professional learning.
Since last year, the book Connecting Arithmetic to Algebra by Susan Jo Russell, Deborah Schifter, and Virginia Bastable, has been the focus of my professional learning. Ideas from this book greatly influenced my planning, instruction, and reflections on student work, as I wrote about here.
While my thoughts and reflections about this book have been valuable, my application has been based solely on my own interpretation of the material. That is, until I started tweeting about how the book was positively affecting my instruction.
Through Twitter, I was fortunate to “meet” Mike Flynn, who works closely with Virginia Bastable, one of the book’s authors, at Mt. Holyoke College in Massachusetts. Through my Twitter interactions with Mike related to this work, others began engaging in the conversation as well. As a community of learners, we posed interesting questions and used the space to post student work samples. These examples showcased students building upon their understanding of numbers and operations en route to formulating conjectures and claims.
This simple tweet from Kassia sparked an amazing Twitter conversation that continued weeks after its initial posting:
This difference between claim and conjecture was important to establish before continuing our conversation. Up to this point, the two words had been used interchangeably, leaving any distinction up to the reader’s interpretation. While we felt a stringent definition wasn’t necessary, being precise in our language gave us a referent for future thoughts and examples.
As the discussion moved forward, we began working with the understanding that a conjecture is formed as students notice patterns they think to be true. As this conjecture is further explored and becomes more generalizable with support, it is a claim.
Now the question became, how do students prove a claim and what justifies substantial support? At this point, Elham joined the conversation with a reference back to Virginia’s book:
This piece of the discussion hit home for both Simon and me as we reflected and shared samples of students writing and proving their claims in our classrooms.
As weeks went by, the discussion about conjectures and claims continued. Each of us offered varying perspectives on how we engage our students in this work, and questioned the process both teachers and students go through in developing this cycle within the classroom. There were so many interesting thoughts and unanswered questions at every turn. Fortunately, we had an invaluable resource just within our reach. Mike organized and offered the opportunity for us to chat with Virginia, one of the book’s authors, about all these ideas.
Approximately two months after Kassia’s initial tweet, we had the opportunity to “meet” face to face with Virginia Bastable in a video conference call.
We spent over an hour asking questions, bouncing around ideas, offering thoughts, discussing research, and most importantly, attempting to understand how we can improve our classroom practice to best support our students’ mathematical reasoning. It was an amazing opportunity that expanded beyond the Twitterverse, and allowed me to move beyond simply reading the book to truly experiencing it. The feeling was mutual and of course, we had to tweet about it:
The most amazing part of this entire learning experience is it didn’t end after the video conference. We each left with excitement, thoughts, and possibly even more questions related to the work of connecting arithmetic to algebra. We expressed our lingering thoughts and reflections on Twitter:
To extend the learning beyond Twitter, Simon followed up the conversation with a quick blog post to share with others.
After this experience, I’m left not only thinking about the book’s content and ideas, but also about how professional learning experiences similar to this could be used to enable others to move beyond their singular reflections and applications to deeper collaborative work.
To that end, I’ve engaged in an online book study with fellow Teaching Channel Laureate Crystal Morey, which will take place on TeachingChannel.org and on Twitter. Check out my blog for more info.
A special thank you to Mike Flynn and Virginia Bastable of Mt. Holyoke College for organizing such a wonderful conversation, and to all of my tweeps involved: @TracyZager, @ekazemi, @wendymh1231, @Craig_Schneider, and @Simon_Gregg.
