#SlowMath – Looking for Structure and Noticing Regularity in Repeated Reasoning from @jwilson828 and @jgough #NCTMAnnual

At the National Council of Teachers of Mathematics conference in Washington D. C., Jill Gough (@jgough) and I presented the following session.

#SlowMath – Looking for Structure and Noticing Regularity in Repeated Reasoning
4:30 PM – 5:30 PM
Walter E. Washington Convention Center, 145 AB

How do we provide opportunities for students to learn to use structure and repeated reasoning? What expressions, equations, and diagrams require making what isn’t pictured visible? Let’s engage in tasks where making use of structure and repeated reasoning can provide an advantage and think about how to provide that same opportunity for students.

Here’s Jill’s sketch note of our plan:

Here’s our slide deck:

Cross posted on Experiments in Learning by Doing


Slow Math Is … Accountable Talk

How many of your students come to you able to say I can construct viable arguments and critique the reasoning of others? How do you provide your students the opportunity to practice MP3? It takes time to listen. It takes time to give feedback. It is faster to tell.

In my Qualitative Research class, we watched Big Fish to think about the difference between perspective seekers and truth seekers. We have been talking about the difference between truth and reality.

How do we teach our students to construct a viable argument and critique the reasoning of others? It takes time to distinguish truth from fiction. It takes time to figure out from whose perspective something might be real. It is faster to refute claims without asking why, when, how.

In “Trial Before Pilate” from Jesus Christ Superstar, Pontius Pilate ponders “But what is truth? Is truth unchanging law? We both have truths. Are mine the same as yours?”

How do we teach our students to construct a viable argument and critique the reasoning of others? It takes time to determine the conditions for truth. It is faster to assert a statement as always or never true than figuring out whether and when it is sometimes true.

Dan Meyer, Shira Helft, Juana de Anda, and Fawn Nguyen presented the CMC North keynote in December 2016. I would encourage you to watch the whole talk. If you are a beginning teacher and/or you support beginning teachers, you might be particularly interested in Shira’s part. I am particularly interested in Dan’s question: How do we help people believe fewer lies?

How do we teach our students to construct a viable argument and critique the reasoning of others? It takes time to distinguish fact from fiction. It is faster to press share without checking primary sources.

In Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning, Hattie et al. assert the importance of expecting students to engage in accountable talk in our classrooms and emphasizes the role that the teacher plays in ensuring that happens. Teachers must consistently exemplify accountable talk. The authors share examples of Accountable Talk Moves for teachers to relentlessly use in conversation with students, with the expectation that students, too, will assimilate into accountable talk in their conversations with others (2017, p. 144).

Screenshot 2018-03-08 10.10.29.png

In a Slow Math classroom, we take time for students to learn to construct a viable argument and critique the reasoning of others. Even though it is faster not to.

Possible Resources for Continuing the Conversation:

Hattie, J. (2017). Visible learning for mathematics, grades K-12: what works best to optimize student learning. Thousand Oaks, CA: Corwin Mathematics.

Interpreting Data: Muddying the Waters

Why Facts Don’t Change Our Minds, from the New Yorker, and referenced in Dylan Kane’s blog post On Changing Minds.

Teaching Why Facts Still Matter, included in the January 31 2017 edition of the NBCT Accomplished Teacher by SmartBrief.

For Ed-Tech Company Newsela, ‘Fake News’ a Big Challenge – and Opportunity, included in the February 2  2017 edition of Education Week Digital Directions.

Slow Math is … thinking about the “right” question to ask

A few years into the journey of teaching through inquiry, I said that my most important work comes before the lesson – planning the questions to ask during the lesson episode.

Dylan Wiliam’s assertion from Embedded Formative Assessment resonated with me and the teachers with whom I work: “Sharing high-quality questions may be the most significant thing we can do to improve the quality of student learning.”


When your team plans together, plan questions to ask. When you find the question that makes a difference in knowing what students are thinking, don’t keep it to yourself – share it.

As I continue to teach, though, I’ve decided that my most important work happens during the lesson – in the moment – making decisions about what to do and ask next based on how students respond.

I’m reading Hattie, Fisher, and Frey’s Visible Learning for Mathematics. I paused when I read the following paragraph.


Slow Math isn’t just for students. It’s for teachers, too.

“Give yourself permission to stop and think about the ‘right’ question to ask at any given point in the lesson.”

I’ve also heard this advice from Elham Kazemi in the form of teacher time outs. Team teaching is such a good opportunity to practice good questioning. Even if you’re alone, though, give yourself permission to take a teacher time out. Slow Math is taking time to think about the “right” question to ask.


Hattie, J. A., Fisher, D. B., & Frey, N. (2016). Visible learning for mathematics, grades K-12: what works best to optimize student learning. (p. 112). SAGE Publications. Kindle Edition.

Wiliam, D. (2011). Embedded formative assessment. (p. 104). Bloomington, IN: Solution Tree Press.

#Slow Math is Master Coaching

If you haven’t yet read The Talent Code by Daniel Coyle, you should. Coyle premise is that talent isn’t born – it’s grown. By three important factors: deep practice, ignition, and master coaching. His book has contributed to changing how I look at my role as a teacher.

I ran across Coyle’s blog post recently: There are Two Types of Coaches. Which are You?

Coyle offers a few statements for us to consider to figure out which type. I’ve taken the liberty of replacing the people/workplace/other language with teacher/classroom/student language.

  1. A) I treat all of my students as mostly the same.
  2. B) I treat my students as individuals, with unique motivations, strengths, and weaknesses.


  1. A) In my classroom, I focus on drills and repetition.
  2. B) In my classroom, I focus on awareness and feedback, and helping each student take ownership of the process.


  1. A) In my classroom, I focus on delivering the knowledge to my students to drive improvement.
  2. B) In my classroom, I focus on building partnerships with my students to create the knowledge together.


  1. A) I’m fascinated by designing drills for students to do.
  2. B) I’m fascinated by building plans, tools, and systems for students to use.


  1. A) I’m obsessed with each student’s progress.
  2. B) I’m obsessed with each student’s process.


So what do you think? Is your focus as a teacher on building skill? Or is your focus as a teacher on building students?

Would your students agree with you?


See Coyle’s blog post to find out your official results on his unofficial quiz and check out The Talent Code to read more about becoming a master coach – a builder of people.

Slow Math Takes … Patience

From my husband’s Advent 3 sermon Something on Patience and Joy:

… We might lift up the teacher as an example of patience. A good teacher knows that finally you just can’t impose the answer in a student’s brain as much as you might want to. You have to wait for that student to do that work herself, or not. This is tough, tough work, but finally, there can be no hostile takeover of the mind and will of a student. Learning is voluntary; it’s not mandatory. You have a classroom discussion, and you hear a “wrong-headed answer” (Kenneson). You want to jump in and fix it. But you might kill the thing that is fermenting there if you rush it. You cannot take over that process. You can only make the invitation, and then wait to see if the student will do the work and make her own connections. Teaching takes patience, or it’s not teaching …

Slow Math is … Slow Conversations

At the beginning of our polygons unit, students played a round of hexagons polygraph in Desmos. One student is the picker and another is the guesser. The picker selects a hexagon, and the guesser asks yes or no questions to determine which one was selected.

1 Screen Shot 2016-11-04 at 5.59.42 AM.png

Let’s take a look at a round between SO and SA. SO selected a hexagon. SA asked:

2 Screen Shot 2016-11-16 at 5.55.55 PM.png

SO answered no.

SA eliminated one.

2a Screen Shot 2016-11-16 at 6.00.21 PM.png3 Screen Shot 2016-11-16 at 5.56.08 PM.png

SO answered no.

3a Screen Shot 2016-11-16 at 6.00.30 PM.png

SA eliminated two.

4 Screen Shot 2016-11-16 at 5.56.14 PM.png

SO answered no.

4a Screen Shot 2016-11-16 at 6.00.38 PM.png

SA eliminated three more.

5 Screen Shot 2016-11-04 at 5.52.54 AM.png

SO answered no, and SA eliminated all but one.

5a Screen Shot 2016-11-16 at 6.00.46 PM.png

What a great way for students to learn how to practice MP6: attend to precision. In a whole class discussion, we talked about what it meant for a polygon to be regular. We talked about convex and concave. We talked about symmetry. It turns out that the hexagon SO chose actually does have rotational symmetry – it just didn’t have line symmetry like the rest. My students and I have so many opportunities to learn from each other when we take time to slow down, share our thinking, and listen to other’s thinking.

After a round of Polygraph last year, one student reflected that he learned that he could ask questions to find an answer.

Beautiful Questions.png

Which has me thinking more about Slow Conversations. The Polygraph practice round celebrates the beauty and diversity of all of our students.

Screen Shot 2016-11-14 at 12.31.14 PM.png

How might we teach our students to embrace that diversity by not only asking questions to identify and learn about each other’s uniqueness but also listening to each other’s responses? That’s where Slow Math intersects with Slow Conversations.

Slow Math is … asking questions

I often wonder what we would include in a Slow Math manifesto.

Slow Math is about asking questions. #AskDontTell is one hashtag I regularly use that describes my teaching. But how often does my perspective make me think more about the questions I ask than the questions my students ask?

e e cummings wrote,

always the beautiful answer

who asks a more beautiful question

In “A More Beautiful Question”, Warren Berger tries to figure out why children start school asking hundreds of questions a day but then their questioning “falls off a cliff” as they go through school.

In a Slow Math classroom, questions are not only welcomed – they are sought.