It feels like a dream, but this time two weeks ago, I was sitting in the opening session of the NCTM Annual Meeting in San Diego listening to Gloria Ladson-Billings opening keynote. (I’ll add a link to the video of her talk once it’s posted on the NCTM website.)

It was a whirlwind of a conference. I got to see my friend and former co-worker Meredith, hang out with countless #MTBoS colleagues, and attend so many great sessions! By the time the conference was over, my heart and brain were full to bursting. To get a taste, check out this Twitter Moment I created to capture many of my tweets from the conference.

I also took copious notes throughout the many sessions I attended. I’m not going to bombard you with all of my notes, but I did want to share short summaries and key takeaways from all of the sessions. I know it’s not the same as being there, but I’m happy to share the learning and spark some ideas for those unable to attend.

Here goes!

**The Decision-Making Protocol for Math Coaching: Apply High-Leverage Practices and Advocate Change**

Presenters: Courtney Baker (George Mason University) and Melinda Knapp (Oregon State University-Cascades) See tweets from this talk here.

In this session, the presenters shared the Decision-Making Protocol for Mathematics Coaching (DPMPMC). *“A primary goal of the DMPMC framework is to increase the intentionality of coaching interactions by supporting the user to simultaneously consider mathematics content, coaching and teaching practices, and professional relationship building.”*

If you’d like to learn more, check out the site linked above and specifically check out the two articles they’ve written about this protocol. The first is “Coaches Engage with Principles to Actions” from the September 2018 issue of *Teaching Children Mathematics*. The second is “The Decision-Making Protocol for Mathematics Coaching: Addressing the Complexity of Coaching With Intentionality” and Reflection from the March 2019 issue of *Mathematics Teacher Educator*.

**One Takeaway**: I like the dual-pronged approach to coaching. Whether you follow the protocol or not, I appreciate the challenge of picking just ONE mathematics coaching practice and ONE mathematics teaching practice to focus the work. There’s always so much we *can *do, but if we try to do too much, we decrease the coherence and impact for the teacher being coached.

**Using Lesson Study to Empower All Students**

Presenters: Kyndall Brown (UCLA) and Susie Hakansson (Retired)

In this session, the presenters shared an initiative from the California Action Network for Mathematics Excellence and Equity (CANMEE) to develop and implement a model of lesson study that places an emphasis on equity. The rationale behind this work is twofold. First, they want to make lesson study an integral part of professional learning and continuous improvement. Second, they believe equity and social justice the most urgent goal and challenge for mathematics education. You can access their slides and other materials in this folder.

**One Takeaway**: I really like the idea of using four focal students as a lens throughout the lesson study. *“If we are to focus on equity, who do we select so that we shift our practices to impact positively students’ participation and their increase in mathematical proficiency?”* Not only do you interview the focal students, but you also develop a profile of each one that:

- is asset-based,
- includes students’ prior knowledge (cognitive and affective),
- includes student understandings,
- includes outside of class attributes,
- identifies learning goals, and
- avoids deficit thinking.

**Lesson Study and How to Generate Buy-in that Will Inspire Instructional Shifts and Evolve Teachers**

Presenter: Chase Orton (Independent Consultant) See tweets from this talk here.

While the previous session focused on changes to the lesson study process, Chase focused on steps he takes to build buy-in and set teachers up for brave professional growth before the process even begins. The first step is the passion profile. According to Chase, teaching is a practice of identity. If we are going to ask teachers to undertake the process of lesson study, teachers need to reflect on their own identity – specifically their passions and their why – as well as get to know the identities of the others who will undertake the lesson study journey with them.

The second step is defining the ideal classroom. *“Let’s say you’re teaching or witnessing the best math lesson ever. What does it look like? Be really specific, looking at what the teacher is doing, what students are doing, and what the classroom energy feels like.” *This step creates a powerful pivot to establish focus for the lesson study as participants develop their research question. How does your ideal compare to reality? What forces are restricting your ability to create your ideal math classroom?

**One Takeaway**: I appreciate the effort Chase takes to do the very important work of investing in the people who are going to invest their time and energy into lesson study. How often do teachers feel like something is being imposed on them rather than feel like they are being included and part of a team effort? How often do they get the chance to reflect on their own experiences and beliefs and help set the goals for the work ahead? Chase has written extensively on his blog about his work with lesson. If you’re interested in learning more, check out these posts.

**Minimizing the Matthew Effect**

Presenter: Sara Van Der Werf (Independent Consultant) See tweets from this talk here.

If you ever get the opportunity to see Sara Van Der Werf present, take it! She is one of the most passionate and committed educators I’ve ever met. This session was effectively her throwing down the gauntlet that teachers can and must lead the way to change structures so that *all* students are successful. According to Sara, if we wait on superintendents and administrators, it will never happen. The great thing is that even if you can’t see Sara in person, she does a phenomenal job of writing about her beliefs and advice on her blog. For example, in her session she evangelized Stand and Talks as one of the best things she ever did to get students talking to one another, and for those who couldn’t attend, you can read all about them in this blog post. Be sure to also check out her posts on how she uses name tents to build relationships with her students and her post on why she loves cell phones in math classrooms.

**One Takeaway**: Sara mentioned that using color coding doesn’t get nearly enough attention as it should. She introduced us to the #purposefulcolor hashtag and shared an example of how she’s using color more intentionally to support students. For example, when doing a Which One Doesn’t Belong? she puts each image on a different-color background. Now students can say, *“The red one doesn’t belong because…”* rather than having to generate clunky language such as, *“The one in the upper left corner doesn’t belong because…”*

**Leveraging the Predictable Design of Instructional Routines to Elicit and Use Student Thinking**

Presenter: Danielle Curran (Curriculum Associates) and Grace Kelemanik (Fostering Math Practices) See tweets from this talk here.

It’s masterful how Grace Kelemanik and Amy Lucenta weave intentional and powerful pedagogical moves into instructional routines so they’re baked in from the start. Just take a look at the key teaching moves in the Try-Discuss-Connect routine:

What’s powerful about these teaching moves – individual think time, turn and talk, and the four Rs – is that they were *intentionally* chosen and embedded into the routine because of their alignment with research about how best to support emergent bilingual students and students with learning disabilities.

**One Takeaway**: I love learning about new instructional routines, but I was especially pleased with stepping back and making explicit connections between instructional routines, in general, and the effective mathematics teaching practices from NCTM’s *Principles to Actions*.

**The Hierarchy of Hexagons: An Example of Geometric Inquiry**

Presenter: Christopher Danielson (Desmos) See tweets from this talk here.

By this point in the conference, my brain was already feeling a little full. I chose Christopher’s session primarily to do something fun – exploring hexagons. However, I had previously read about this work on his blog, so I also wanted to experience it firsthand to help me bring this kind of activity back to do with my teachers.

The session did not disappoint! Collectively a room full of educators attempted to name, classify, and sort hexagons in meaningful ways.

- What does it mean to say a hexagon looks like a comet? What are the defining attributes of all hexagons that are comet-like?
- What do you mean when you say a hexagon is boxy? How many right angles are you saying it should have?

**One Takeaway**: During the session, Christopher centered our work around the van Hiele model for geometric understanding.

I’ll be honest that I only first heard about this model a couple of years ago and found it extremely useful when developing a progression of units and lessons across our grade K-5 curriculum. Interestingly, my colleague Edmund Harriss took issue with the van Hiele levels and started a lengthy, but insightful, Twitter conversation around these levels and geometry instruction in general. If you have a chance, I recommend perusing the thread sometime. My takeaway from the conversation mirrors this reflection from Christopher: *“Yup. Not hard and fast developmental rules, but useful structure for describing student thinking and for planning instruction.”*

**More Than Turn and Talk: Supporting Student Engagement in Each Other’s Ideas**

Presenter: Megan Franke (UCLA) See tweets from this talk here.

This was a fascinating session where Megan Franke shared research about the role of student participation in student achievement. A surprising finding in the research is that there isn’t an “ideal” or consistent profile of student participation or teacher support that is best for all students. Rather, the important thing is that teachers create a space where all students are able to participate *in ways that work for them*. For example in a classroom where there are whole class discussions, turns and talks, and collaborative problem solving, students have varied opportunities to participate.

**One Takeaway**: According to the research, student achievement is impacted if the student gets at least one opportunity every class to explain all the way through their ideas. If teachers only lead whole class discussions, this is unlikely to happen for all students but rather a small handful of students. This gives me a goal for next school year to share this research with our coaches, administrators, and teachers so they can evaluate their current classroom structures and adjust as needed to create opportunities in math class for students to find space(s) to participate that work for them.

**Rethinking Mathematics Education (and Mathematics) through Neurodiversity**

Presenter: Rachel Lambert (UC-Santa Barbara), Edmund Harriss (University of Arkansas), and Dylan Lane (Independent Researcher)

In this session, Rachel Lambert challenges the medical/deficit model of disability.

Differences exist, according to Lambert, not as deficits, but as part of natural human diversity. She went on to share research about people with dyslexia and dyscalculia. The medical/deficit model emphasizes the challenges these disabilities pose, but research has shown that people with these disabilities also have a set of strengths. She then ceded the floor to Dylan Lane and Edmund Harris. Dylan grew up with dyscalculia while Edmund grew up with dyslexia. They each shared their story, which emphasized the power of leveraging strengths rather than fixating on deficits.

**One Takeaway:** Often we oversimplify kids, especially when we see them struggling. There’s a false deficit binary of being high or low at math, but it’s not that easy or simplistic to categorize children that way. We are all a combination of strengths and challenges. If we can see *all* of each other, we can get past deficit thinking. We need to complicate the way we think about our kids, but also how we think about learning mathematics. Math has to have more ways for students to develop and demonstrate understanding – more linguistic for some, more visual for others.

**Collaborative Coaching: How Can We Learn as a Team?**

Presenter: Nicora Placa (Hunter College) See tweets from this talk here.

In this session, Nicora Placa talked about the important role of collaborative coaching as a different type of learning opportunity that allows all members of a team to learn together and take risks. When selecting coaching strategies to use in collaborative coaching, Nicora looks for tools that focus on foregrounding student learning and student thinking. In this session, she shared the plan for how she uses clinical interviews during collaborative coaching:

- Background reading / Book study
- Watch videos of interviews
- Select tasks and anticipate misconceptions
- Practice interviews with each other
- Conduct and record interviews in team meetings / PD
- Analyze interviews
- Summarize and share what we learned

She also gave us an opportunity to practice conducting an interview in trios. One person acted as a “student” working on a math task, one person acted as the interviewer, and the third person recorded what the “student” and interviewer said. Afterward we reflected on the kinds of questions asked and alternatives that could have been asked to elicit more student thinking.

**One Takeaway**: I appreciate that Nicora shared the challenges of listening to student thinking:

- Listening only for the right answer or particular solution path
- Thinking about next instructional move instead of listening
- Assuming students are thinking the way you are thinking
- Not listening for what students know
- Not trying to make sense of what students are doing

The sample questions as well as list of questions to avoid were extremely helpful.

**The Whole-School Agreement: Aligning Across and Within Grades to Build Student Success**

Presenters: Sarah Bush (University of Central Florida), Karen Karp (John Hopkins University)

The Whole School Agreement process aligns models, language, and notation across and within grades to that students see the regularity and familiarity in a cohesive approach to teaching mathematics. The presenters encourage centering this work around their articles:

**One Takeaway**: I’m excited to use this framework and these resources to support coaches and campuses. I was familiar with these articles, but I’ve never used them to center the work of creating whole school agreements. The presenters shared resources in these handouts that can help with the work:

**Coaching Toward Common Ground: Creating a Shared Vision and Growing Professionally as a Team**

Presenters: Delise Andrews (Lincoln Public Schools) and Beth Kobett (Stevenson University)

The presenters took us through a sped up version of a process they use to help teams create a shared vision and find common ground. First, we worked together to illustrate a picture of the “ideal” math classroom. Then we used our pictures to list qualities of our ideal math classroom. The presenters then posed a question to us, “If this quality isn’t there, what’s the opposite of that?” This led us to develop opposites for each one of our statements. Then we drew lines between them to create a spectrum, because often we’re not at one or the other. Rather, we’re somewhere in the middle.

Next, everyone in the group got to put a mark on each line to show where they are in their practice. This is very eye opening because patterns emerge. Perhaps as a team we are all doing really well on Thing #1, but Thing #3 is an area where we struggle. This can help us develop goals.

After picking one thing to focus on, we went through another exercise called 20 Reasons Why. Basically we had to come up with 20 reasons why that thing is the way it is right now. This is more challenging than it looks! It’s easy to come up with the first 5 or 6 reasons, but getting to 20 requires thinking beyond the usual suspects. Finally, if we had time, we would have sorted our 20 reasons and talked through the reasons for our sorting. For example, we could have sorted them into categories, “Things I can control” and “Things I can’t control.”

**One Takeaway**: I liked the idea of reversing assumptions. According to the presenters, breakthrough ideas happen when we challenge our original ideas and even reverse our thinking. What if the opposite is true? For example, if our team’s original reason was, “We don’t have time to plan these kinds of lessons,” we could turn it on its head and said, “What if we did have the time? How would we plan differently?”

Another example would be, “Our students who are struggling with 5th grade math don’t know basic math facts.” If we reverse our assumption, we come up with, “What if our students who are struggling do know some basic math facts?” (What? They don’t know any? Oh, they do know some. Good. We have a place to start.)

## The End

Whew! Just going through all that makes my brain feel full all over again. If you attended NCTM what were your big takeaways? If you didn’t attend, but read through my tweets, this post, or other tweets, what piqued your interest or resonated with you?