I keep detailed notebooks of thoughts gathered from PD, readings, and meetings, ideas for future problems, lessons, and units, and reflections of small victories, detours, or interactions. I’ve used this system since before I’ve taught and it works well for me to process in the moment or look back on my thoughts.

I am in the process of rewriting/rethinking my course standards for next year and I reviewed my pie-in-the-sky thinking and goal setting. And I stumbled upon my hopes and dreams of class discussions from July 10, 2009. Here’s what I came up with back in the day.

My non-linear notes:

And the more traditional notes:

**Use sentence starters** – How can I scaffold students to being good mathematical conversations? How can we talk about the *process* and not just the *solution*?

- Our approach was like ______’s work in that we both ______.
- Our approach builds on _______’s work in that we _______.
- Our approach was different from ______’s approach because ______.
- I know this works because ______.
- When I see ____, I infer ____.
- I think this was _____ when I saw/heard
*<evidence>* because *<explanation>*.
- This work is similar to what we did before because …

**Leading Questions** (always connect to the objectives AND think about is the question to orient, assess, or advance student thinking – questions don’t always need to come from the “teacher”):

- How were you thinking about it?
- What stayed the same?
- What changed?
- Where did you start?
- What seems significant?
- How does this representation show your thinking?
- Where are we able to generalize?
- What is different between these two problems?
- How do we capture that thinking onto paper?
- What does you agree/disagree with from this group?
- Think and digest this thought and rephrase their thinking.
- Are you able to come up and explain/walk through your thinking?
- What’s s/he doing?
- What is the story of your work?
- How could you show it another way?
- How could you explain this in context?

I think this flash back is a bit exciting. I know SL has been thinking about this a bit deeper than I have more recently, but my beginning thoughts from four years ago may persuade me to think a bit more about how to incorporate more sustainable discussion routines into classes.

Other awesome things I should think about/remind myself about for math discussions?

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*Related*

I like these questions. I’d like to add a few of them to a list I’ve been working on for a book I’m putting together. May I discuss this with you by email? I’m at mathanthologyeditor on gmail.

Sure! I’ll send you an email tonight! Does the book focus on math discussions?

The book is

Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers. I think you’ll like it. Here’s a preliminary web site. My list comes from Bob Kaplan, who runs some great math circles in the Boston area.I don’t know your email. Would you email me, please?