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.

Advertisements

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.

Slow Math is … valuing why

One of our math teachers, Shera Higbee, sent the following to our math department over the weekend.

Screen Shot 2016-11-14 at 10.19.20 AM.png

Slow Math is not just about how to do math … it’s about valuing why the math works. I am grateful to work with teachers who agree. And I am grateful for students who recognize and appreciate that why is valued.

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.

1 Screen Shot 2016-09-20 at 8.57.31 AM.png

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

2 Screen Shot 2016-09-20 at 8.57.22 AM.png

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.

5 IMG_0929.JPG

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 …

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.

Screenshot 2016-08-09 10.03.04.png

Screenshot 2016-08-09 10.02.58.png

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.

Screen Shot 2016-08-17 at 5.20.19 PM.png

Screenshot 2016-08-09 10.03.27.png

Screenshot 2016-08-09 10.05.43.png

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.

Screen Shot 2016-08-11 at 9.00.30 PM.png

Pearl Buck was before her time on so many issues:

Screen Shot 2016-08-11 at 9.39.43 PM.png

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?

3-screen-shot-2016-03-04-at-9-47-46-am.png

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.