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Two New Questions

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Math is filled with many different questions. This short video shows the power of two relatively new questions: What do you notice? and What do you wonder? As a teacher leader in a Maryland public school district, I shared the power of these questions with our new educators, showing how open ended questions without one specific answer can be as, or often more, powerful than traditional questions that have only one response. I also showed the power of open ended questions to teachers in Mexico on a recent Fulbright exchange, where teachers often taught in a very traditional manner. Showing educators the power of open ended questions helps open the conversation about mathematics. 

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Kirstin Milks
Kaye Ebelt
Liza Bondurant
Christine Girtain
Jodi Zeis
John Seelke


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Hi John,

I love this reframing of math as "art" with these two important questions! In my work as a high school science teacher, I talk sometimes about how "research" can be bigger, too -- how quantitative data is important, but qualitative data is what often helps us make sense of the numbers, or where to go next.

One thing I've been thinking more about this fall is how to prime students for what they notice and what they wonder, particularly about equity- and access-related data. I'm curious about how where else these two questions have felt particularly powerful in your teaching practice.

Thanks so much for this video -- and for the fun-looking task!

:) Kirstin

Mon, 11/07/2022 - 11:33 AM Permalink

Hello Kristin - So sorry for the delay - I was out of town and just got back into town tonight! First, I love the idea of noticing and wondering things about equity and access data, and well, data in general. For example, I tend to notice that in education we often will talk about percentage gains (or losses) but we rarely look at the n value for stats. 

The task is an amazing one - As I noted, I did it in Mexico and the students, who were not used to these type of activities really loved it!

Thanks for your comments!



Tue, 11/08/2022 - 8:22 PM Permalink
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I loved the idea of color patterns with the math. Could you share the activity with me so I can share it with my math teachers?

Wed, 11/09/2022 - 7:16 AM Permalink
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I agree, John. I've asked these two questions in science with observations and data visualizations (graphs, charts, etc.) and the students' responses always amazes me. It is humbling to see responses that I haven't thought of and to learn from. I've also used these two questions with educators when looking at school data and have found them to be more inquiry-based and "inviting" for educators to digest.

Some things I (think internally) struggle with when posing these two questions:

  • process-time: Should learners come up with 3 notice and wonders? Or should I give 1 minute? But if I give only 1 minute, how would a student feel if they only come with 2 notice & wonderings and others have 5?
  • share-time: How can we ensure the quiet voices are heard? Should all learners share within small groups before sharing out? Should all groups share out?

Do you have these struggles? How do you combat these struggles?

Wed, 11/09/2022 - 7:32 AM Permalink
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In reply to by Elegan Kramer

Hi Elegan - Thanks for the questions. To some of the things:

1. I usually will use 2 minutes of process time - I think that is enough time for students to consider something - I don't think that everyone has to come up with the same number of things - they have to do at least one of them.

2. I often will walk around the room and look at responses, and in particular if there is a quiet child who usually doesn't respond, I will try and encourage that child to share their answer. When I was in Mexico, I had some students ask as a question, "Que es eso" (What is this?). It was a GREAT question to ask, especially if they had never seen anything like it.

I hope that helps.

Wed, 11/09/2022 - 3:12 PM Permalink
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In reply to by Elegan Kramer


I have similar thoughts about how to pose the questions for educators, particularly ensuring the quiet voices are heard! In the remote meeting era of 2020-2021, we used Jamboard to gather see-think-wonders a lot and that helped elevate those voices. Chart paper for chalk talks might be helpful now that we are back in person.

Thu, 11/10/2022 - 11:19 AM Permalink
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I love the idea of asking them questions that they connect to and can reflect on.  How do you guide the questions to be relevant- deeper/analytical questions and not "what is your favorite..."?

By owning the thought process, it sounds like students will definitely be more engaged at the personalized approach.

Wed, 11/09/2022 - 2:49 PM Permalink
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In reply to by Jodi Zeis

Hi Jodi - that's a great question...For example, instead of which is your favorite I have often used Which one doesn't belong, and in ALL cases, ALL of them could not belong, which means that you don't get the idea of one being the favorite. 

Ah, I just realized that you asked about the type of questions the students ask...I actually try and not limit any question, but if I walked by a student who asked "Which is your favorite color?" (from my sheet) - I would try and ask them to find another question that is more focused on the math or the consider what the numbers mean...

Hope that helps!

Wed, 11/09/2022 - 3:28 PM Permalink
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Hi, John! I'd love to know if you have any additional resources for the "best places" for teachers to insert these questions -- certainly they could be asked at any time, but I also anticipate that there are "better" times (such as at the beginning of a new unit, after some kind of demonstration, or perhaps when approaching a particularly difficult problem). I'd love to see if you have additional examples!

Wed, 11/09/2022 - 7:41 PM Permalink

HI Rebecca - thanks for the questions! I can certainly share some other ideas of these types soon. In terms of when to ask these types of questions, I would usually do it at the beginning of a unit or an introduction. What was fascinating is that when I asked that question in Mexico, some saw this as a summary activity. But I see it as a lead into more discussion. For a particular lesson, this could be done as a warm up at the beginning of a lesson...Things like Which One Doesn't Belong are similar types of activities that should be done at the beginning of a lesson or a unit.



Wed, 11/09/2022 - 9:18 PM Permalink
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Thank you for the reminder that everything I am already doing with those two amazing questions can also be applied to Math!  Math is art, and yet a language that is understood around the globe.  Understanding it this way, as a lesson in inquiry, taps into true number sense.

Sun, 11/13/2022 - 10:56 AM Permalink
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This video and concept are simple and powerful.  I love the simplicity of this approach to math, a topic that is so fraught with stress for so many students.  I am curious how you take these questions and convert them into lessons for students ranging from pre-K to 12.  Is this a systemic approach?  Are the teachers well versed in encouraging students to ask and answer these questions as well as moving from the answers to the more complex content.

Thank you for sharing this!

Mon, 11/14/2022 - 12:32 PM Permalink
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Dear John,

This is such a creative way to get kids excited about Math! I apply open-ended questions all the time but never thought of using them for Math with preschoolers and kindergarteners. I will research some more on this approach but I would appreciate so much if you could also lead me to some resources for a younger audience. 

Thanks again!


Tue, 11/15/2022 - 1:28 AM Permalink
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