At the 2018 International T³ Conference in San Antonio, Jill Gough (@jgough) and I presented the following two hour power session.

Using technology alongside #SlowMath to promote productive struggle

How might we shift classroom culture so that productive struggle is part of the norm? What if this same culture defines and embraces mistakes as opportunities to learn? One of the Mathematics Teaching Practices from the National Council of Teachers of Mathematics’ (NCTM) “Principles to Actions” is to support productive struggle in learning mathematics. We want all learners to make sense of tasks and persevere in solving them. The tasks we select and facilitate must offer opportunities for each learner to develop connections and deepen their conceptual understanding.

Join us to learn more about #SlowMath opportunities that encourage students to persevere through challenging tasks instead of allowing their struggle become destructive. This session will address:

  • How might we provide #SlowMath opportunities for all students to notice and question?
  • How do activities that provide for visualization and conceptual development of mathematics help students think deeply about mathematical ideas and relationships?

Here’s the agenda:

8:30 Introductions
8:40 Intent and Purpose

  • Principles to Actions
  • #SlowMath
  • Norms (SMPs)
8:45 3-2-1 Bridge Visible Thinking Routine
8:50 Using Structure to Solve a Task – Circle-Square Task

9:55 3-2-1 Bridge Visible Thinking Routine

  • 2 questions around Productive Struggle (share one with partner and listen to one of partner)
10:00 Construct a Viable Argument to make your thinking visible:
Does (x+1)²=x²+1?

10:25 3-2-1 Bridge Visible Thinking Routine

  • In the chat, 1 analogy/metaphor/simile for Productive Struggle
10:30 Close

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

Dave Johnston (@Johnston_MSMath) recorded his thinking and learning and shared it with us via Twitter.

And, a little more feedback from Twitter:

Cross-posted on Experiments in Learning by Doing.


Student Voice? Task Selection

We are talking about student voice in one of my graduate classes this semester, and so we’ve been looking out for and paying closer attention to opportunities for students to use their voice in our classrooms and in our school.

One question I have is whether student voice = student choice.
I wonder what student voice in a math class has to do with slow math.

I looked back at a lesson from last year when students had the opportunity to select the task they wanted to work.

We were practicing show your work, and we used Jill’s leveled learning progression to monitor student progress.

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Students looked at the first task (Circles and Squares) and noted what they wonder about how the figures are related to each other.

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We watched Dan’s video for the second task (Some Really Obscure Geometry Problem), and I sent a Quick Poll to collect their best estimates of the area percentage for each region.

The third figure came from the Mathematics Assessment Project, but it is no longer available.

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All of the tasks provided students the opportunity to practice MP7 look for and make use of structure and think about area ratios in figures.

Each team selected the task they wanted to spend more time working.


Students had choice in geometry that day. Did students have voice?

Was that a class period well spent, even if we didn’t synthesize ideas as a whole class? Would it have been better (and worth the time) if students have reviewed the work of those who worked on a different task? What difference does providing #slowmath student voice opportunities make for students?

And so the journey continues …

The Slow Approach

Pearl S. Buck is one of my favorite authors. This Proud Heart is my favorite novel of hers, and I am currently reading The Eternal Wonder. The Eternal Wonder was written in the early 1960s, but then it was stolen and hidden by a former secretary and only recently recovered. I read the highlighted passage more than once when I got to it earlier this week.

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Pearl Buck was before her time on so many issues:

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It doesn’t surprise me that she alluded to The Slow Movement before it had a name.

What connection does “the slow approach” have to how we teach mathematics?

Suppose our destination is “I can write the equation of a circle in the coordinate plane given its center and radius”. If we tell students the connection between the equation, center, and radius, it will only take a few minutes.

But don’t we want our students to know more, see more, much more, before they reach the destination?


And so we choose the slow approach, hoping our students see, in order that our students might know the mathematics.

Buck, Pearl S. The Eternal Wonder: A Novel. New York: Open Road Integrated Media, 2013. 1564. Print.


No Teacher Was in a Hurry

I’ve just finished reading The Classroom Chef, by John Stevens and Matt Vaudrey. The premise has #SlowFood/#SlowMath written all over it, and there are references to slowing down and taking time to listen throughout.


One quote in The Plating – Presentation Is Everything chapter struck me:

Go back through the Entrée stories you just read, and look specifically at the questions each teacher asked the students. Notice how no teacher was in a hurry; they let students discuss a topic or an idea until they were satisfied that the students fully understood it.

How do you make it evident to your students that we (students and teachers) have time to ask questions and learn together?

Steven, John, and Matt Vaudrey. The Classroom Chef: Sharpen Your Lessons, Season Your Classes, and Make Math Meaningful. Dave Burgess Consulting, Inc.: San Diego, CA., 2016. Print. page 109.

What Is Slow Math?

What is slow math? What does it look like in the classroom?

In a recent learning experience with mathematics educators, we used the 3-2-1 Bridge visible thinking routine for viewing and reflecting on my Ignite Talk from NCTM 2016.

Before you watch the talk, what is your initial response to the topic “Slow Math”?

  • 3 words/thoughts/ideas
  • 2 questions
  • 1 analogy/metaphor/simile (How you write this is your choice. You might start your sentence with “Slow Math is like … “)

3 words, before:

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Now watch The Slow Math Movement ignite talk.


What are your new responses to the topic “Slow Math”?

  • 3 words/thoughts/ideas
  • 2 questions
  • 1 analogy/metaphor/simile

3 words, after:

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1 analogy, after:

  • Slow math is like having a personal trainer who makes sure you do every rep the RIGHT way instead of just going to the gym alone and rushing through a workout with bad form just because you can get by.
  • Slow math is like enjoying a Sunday afternoon visit with family.
  • Slow math is like taking the time to let vegetables grow to their full potential.
  • Slow math is like a true friend who takes the time to listen to what you have to say instead of always making the conversation topic about themselves and knowing all the answers!
  • Slow math is like planting a garden. The wait seems forever, but the results are worth the wait.
  • Slow Math is responding with appropriate questions when students ask questions. It is taking the time to find out why something works. And “Slow Math” is taking the time to listen to others.
  • Slow math is like giving a child a lifejacket until you teach them to swim on their own.
  • Slow Math is like eating a nutritious meal – satisfying and useful immediately but continues providing benefits long after.
  • Slow math is like building something; it takes time, effort, support, work, and trial and error.

What is Slow Math for you and your students?

Productive Struggle

One of the Mathematics Teaching Practices from NCTM’s Principles to Actions is to support productive struggle in learning mathematics.

What is productive struggle? What does it look like in the classroom? What does productive struggle have to do with The Slow Math Movement? I’ve written before about what productive struggle sounded like in one class that I observed.

In a recent learning experience with mathematics educators, we used the 3-2-1 Bridge visible thinking routine for viewing and reflecting on Robert Kaplinsky’s Productive Struggle Ignite Talk from CMC-South 2015.

Before you watch the talk, what is your initial response to the topic “Productive Struggle”?

  • 3 words/thoughts/ideas
  • 2 questions
  • 1 analogy/metaphor/simile (How you write this is your choice. You might start your sentence with “Productive Struggle is like … “)

Our team of teachers, in 3 words:

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In 2 questions:

  • How do you make a productive struggle activity/question that could be used for the entire class?
  • How do you avoid “”IDK””?
  • How do we motivate a repeating student to engage in the struggle?
  • What do I need to ask the student in order for the activity to be fun and thought provoking?
  • How do I move a student forward if the struggle becomes unproductive?
  • Can we break the problem down into “”easier”” parts and continue making progress?
  • What are some classroom questions that can be used to produce productive struggle in each standard?
  • What are some indicators that the struggle is no longer productive?
  • Did I create a “”headache”” situation?
  • How long do you allow them to struggle before intervening?
  • How long to allow?
  • How long?
  • How much scaffolding is needed for productive struggle not to become overwhelming for students?
  • How much struggle is too much or too little?
  • How often should students engage in productive struggle?
  • My students have the struggle part down, but how do I get the productive part?
  • What are some ways to encourage our students that “”productive struggle”” is worth the effort?
  • What do I know that I can apply?
  • What is the distinction between productive struggle and frustration?
  • What questions do we ask the students to guide them without giving away too much information?

In 1 analogy/simile/metaphor:

  • Productive struggle is like my dad with an iPhone.
  • Productive struggle is like every step on a treadmill.
  • Productive struggle is like finding a tourist attraction using a map instead of GPS; hopefully, you arrive at your location but you learn so much more about the area along the way.
  • Watching successful productive struggle is like watching a caterpillar emerge as a new butterfly
  • Productive Struggle is like potty training a toddler.
  • Productive struggle is like learning to swim
  • Productive struggle is like me trying to keep my cool when the person holding up traffic is on their phone. (major road rage) 🙂
  • Productive struggle is like thinking of similes in math.
  • Productive struggle is like student teaching.
  • Productive struggle is like learning to ride a bike; you have to struggle to learn how to balance before you can ride alone.
  • The teacher is the doctor with the “”magic pill”” to remedy the students’ headache.
  • Productive struggle is like hiking up an extremely steep mountain to get to a magnificent view.
  • Productive Struggle is like trying to find the right combination of flowers for full sun pots in my front yard.
  • Productive struggle is like a road trip with 2 goofy friends and a bad connection to Google Maps.
  • Productive struggle is potty training!
  • Productive Struggle is like me shooting free throws.
  • Bird hatching from an egg. It’s a struggle, but worth it in the end. Without the struggle to break free, the bird can’t survive.
  • S. is what I want my class to be like.
  • Productive struggle is like having a baby. There is a lot of pain in the process, but there are huge rewards in the end!
  • No pain…no gain — for example, in basketball the productive struggle takes place in the form of practice, drills, scrimmages and critique from coach, which all prepare you for the game – success/win!

Now watch Robert’s talk.

What are your new responses to the topic “Productive Struggle”?

  • 3 words/thoughts/ideas
  • 2 questions
  • 1 analogy/metaphor/simile

Learning for a Lifetime

You’ve heard the Chinese proverb: Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime.

You’ve also heard said about someone who gives too much information: Ask her what time it is and she’ll tell you how to build a clock.

(Or maybe you haven’t; my attempts to Google exactly how to say the latter phrase were mostly unsuccessful.)


I recently received an email from a parent.

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What a gift for a student to recognize the value of understanding formulas instead of just memorizing them.


Several years ago, another student wrote “In middle school, I hated math, but having Mrs. Wilson for geometry changed that. She never just tells her students a formula to memorize or a method to apply to problems. Instead, her students discover the mathematic truths for themselves through classroom discussion and individual exploration, making math a story and a compelling one at that.”


I want to think that I’m providing my students the opportunity to learn how to learn for a lifetime: we explore dynamic figures using technology, ask questions, make conjectures, build arguments, prove conjectures.


But how many of them feel like I’m making them “build a clock”?

How many of them prefer “Tell, Don’t Ask” to “Ask, Don’t Tell”?


“Many times I grew extremely frustrated during class and wanted to just give up. Though Mrs. Wilson’s expectations are unwavering, her willingness to help her students in any way made us able to meet her expectations, though not without hard work and a healthy dose of frustration.”


I have some students who love the challenge, others who are willing persevere through it whether they like it or not, and others who roll their eyes, waiting to be told.

So I wonder: How might we provide #SlowMath learning opportunities for our students that sustain them for longer than the next test yet don’t make them feel like they’re being told how to build a clock they don’t care about building?

How might we create and foster a culture of learning in our classrooms, among our students, that will last long after they take our final exam?

We’ve got plenty to work on, as the journey continues …