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.

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

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SO answered no.

SA eliminated one.

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SO answered no.

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SA eliminated two.

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SO answered no.

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SA eliminated three more.

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SO answered no, and SA eliminated all but one.

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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.

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

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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.

Talk Less

I saw Julie’s tweet a few days ago with the hashtag #talklessam (started from one of the sessions at Twitter Math Camp).

My family and I have been listening to Hamilton nonstop for the past 3 weeks, so when I saw talk less, I immediately heard (in tune) Aaron Burr’s advice to Alexander Hamilton when they first met:

Talk less

Smile more

Don’t let them know what you’re against or what you’re for

Although Burr’s advice is a sign of his weakness, I wonder whether it a sign of strength for teachers in a Slow Math classroom. I’ve seen and learned from so many teachers with a great poker face during class discussions. With practice, I have gotten better at not giving away who is correct and who is incorrect. I’ve gotten better at asking “are you sure” to both correct and incorrect responses so that students have to discuss why they are answering what they are answering.

How might you implement Burr’s advice in your next lesson?

I think of Tim Kanold’s blog post Leaving the Front of the Classroom Behind, in which he urges us to look at how much time we are leading from the front and how much time students have the opportunity for peer to peer discourse.

Robert Kaplinsky recently issued a call to action to post a sign on your door, welcoming observers to your classroom to give feedback on what you’re working on. Maybe you want to combine Tim’s advice with Aaron Burr’s and ask someone to time the interactions in your classroom. How many minutes are you talking compared to your students?

I’ll look forward to reading about your experience over at #ObserveMe and #talklessam.

#SlowMath First Day Message

What do you make sure your students take away from the first day of your class?

Our learning intention for the day: I can apply mathematical flexibility to show what I know using more than one method.

We used Jill’s learning progression so that students could self-assess where they were throughout the lesson.

Flexibility #LL2LU Gough

We started with Which One Doesn’t Belong.

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Students moved to the designated side of the room for their answer. Can you find more than one reason yours doesn’t belong? Can you find a reason top left doesn’t belong? Why can you say bottom left doesn’t belong?

We continued with a sequence for which there is more than one way to think about your response.

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I asked several students to discuss their responses with the class. After one student explained her rule, I asked other students to give the next number in the sequence using the first student’s rule. When I asked NA what the next number in a particular sequence was, she hesitated for just a moment. She looked at her calculator and then she looked back at me. I could tell she didn’t want to use the calculator, but I could also tell she wanted a second to think about her response. I stopped the whole class, looked at NA, and said, “We are not in a hurry. Take as long as you need to think before you answer.”

Every time I teach I have to Ease the Hurry Syndrome. Of course we could “do more” if we could go faster. But doing more and going faster isn’t what my students need. My students need me to carefully select which learning episodes (tasks, questions, interactions) will maximize learning. My students need me to give them time to think and time to learn and time to share.

Our students responded to two prompts after class.

During the first day of class, I learned …

  • I learned that I can solve problems in many different ways. I also learned that I need to have an open mind this year during math.
  • I learned the importance of thinking outside the box and how their could be multiple ways to answer a question. For example with the question that asked which shaped didn’t belong. All of the answer choices had reasons as to why they didn’t necessary belong.
  • I learned that math is a much bigger subject than I thought, and that anyone could be good at math.

This year in geometry I will …

  • do my best to not be discouraged when it’s hard but instead work hard with an open mind set to learn the material.
  • I will do my very best to succeed in Geometry and form a better explanation for my answers.
  • Learn how to make my math skills better and see things that I wouldn’t usually discover.

Our message seems to have been heard: We want to show what we know using more than one method, and we can often add to what we know by listening to and learning from each other.

I look forward to a good year enjoying lots of #SlowMath lessons.

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?

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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.

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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.

Math … in One Word

How do your students feel about math coming into your classroom?

We asked our Algebra 1, Geometry, and Calculus students that question on the first day of class last year.

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How do your students feel about math after spending a year in your classroom? Can a Slow Math classroom change students impressions of what math is and how they feel about doing it?

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What word do you want your students to think of when they hear math?

What will you do this year to make that happen?

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?