Tag Archives: Jeff McCalla

A lesson in making use of structure from/with @jmccalla1

Jeff McCalla, Confessions of a Wannabe Super Teacher, published some really good thinking about collaboration vs. competition.  In his post, he describes challenging his learners to investigate the following:

Which of these product rules could be used to quickly expand (x+y+3)(x+y-3)? Now, try expanding the expression.

Product Rules

Jennifer Wilson, Easing the Hurry Syndrome, and I have been tinkering with and drafting #LL2LU learning progressions for the Standards of Mathematical Practice. I have really struggled to get my head wrapped around the meaning of I can look for and make use of structure, SMP-7.  The current draft, to date, looks like this:

What if I tried to apply my understanding of I can look for and make use of structure to Jeff’s challenge?

Scan 1

Note: There is a right parenthesis missing in the figure above.
It should have (x+y)² in the area that represents (x+y)(x+y).

What if we coach our learners to make their thinking visible? What if we use learning progressions for self-assessment, motivation, and connected thinking? I admit that I was quite happy with myself with all that pretty algebra, but then I read the SMP-7 learning progression. Could I integrate geometric and algebraic reasoning to confirm structure? How flexible am I as a mathematical thinker? I lack confidence with geometric representation using algebra tiles, so it is not my go to strategy. However, in the geometric representation, I found what Jeff was seeking for his learners.  I needed to see x+y as a single object.

How might we model making thinking visible in conversation and in writing? How might we encourage productive peer-to-peer discourse around mathematics? How might we facilitate opportunities for in-the-moment self- and peer-assessment that is formative, constructive, and growth-oriented?

Developing a Virtual Learning Community – #T3Learns session

How might we stay connected, offer additional ideas, and share experiences with others? What if we leverage social media tools? How might we continue to lead learning without stretching ourselves too thin? How might we continue to contribute to our learning community when we are apart? How might we be more intentional in PD sessions to foster continued learning? What if we explore effective use of tools to develop and maintain connectedness and build learning communities? Will we learn and share?

Jeff McCalla, @jmccalla1 and Confessions of a Wannabe Super Teacher, and I facilitated a session for T3 instructors on building and maintaining learning communites to learn, share, and support learning.  Our lesson design, strategies, and resources are shared on the Developing a Virtual Learning Community Google doc.  We were charged with the responsibility to lead a session for T³ instructors to  brainstorm and share useful strategies to connect and learn from and with others. At the end of this session, our community should be able to say:

    • I can contribute to learning communities both face-to-face and virtually.
    • I can use social media to connect with fellow T3 instructors before , during, and after PD.
    • I can use social media to connect with participants before, during, and after our PD.

We ran 4 sessions today – all very different.  Jeff is a master of the art of questioning. He guided the discussion and connected to the learning plan while accommodating the learners in the room.  At each session we answered questions concerning the how and why of Twitter and blogging. His blog post What Super-power do you want? offered a grounding story for our discussion.  (Read comments by Bo and Jill to learn more.)

Here are snippets of our conversations, learning, and questions.

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