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Ever Wonder What They’d Notice?: Annie Fetter

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#NoticeWonder Love – Always Noticing and Wondering

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Before you read anything else, go play Game About Squares. Seriously. Don’t come back here until you’ve gotten to Level 8. But do come back – don’t let it suck you in permanently!

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Noticing and Wondering in High School:  

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Noticing and Wondering in High School:  

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If you've spent any time around the Math Forum folks, you've heard of "I Notice, I Wonder" - two little phrases that we use to start students talking mathematically. We've seen the questions "What do you notice?" and "What do you wonder?" used to launch lessons, get kids doing careful reading during problem solving, help kids give each other constructive feedback, support students to look for patterns after doing an activity, and encourage reflection and extension after a project or activity. They're powerful questions because everyone has something they can notice (note that it's not "what do you know" or "what do you think" - it's a much more fundamental level than that!). And wondering is plain old fun!

A buddy from Twitter Math Camp asked about the value of noticing and wondering for high school. She knew it could be powerful but wondered if colleagues and students would feel it was beneath them. Here are some things I've noticed, and some thoughts about them:

High school students, especially juniors and up, are the shyest noticers and wonderers.

By high school, kids (especially kids who are good at school) are very attuned to what the teacher wants them to notice, so they often say, "I don't notice anything," or "What do you want us to notice?"

Noticing and wondering often starts with "what can I get away with" type noticings like, "I notice the graph is blue," or "I notice your drawing isn't very good."

A good prompt goes a long way with high school students in particular - they have a harder time suspending their disbelief than, say, third graders.

It's harder for high school students to make noticing and wondering a habit - they tend to be more likely to compartmentalize and think of it as an activity someone has to direct them to do rather than a skill.

High school students, like all people, feel valued when their ideas are heard, recorded, and made use of - so they can get a lot of value from noticing and wondering.

Based on my noticing here are some tips for noticing and wondering with high-school students:

Go multi-media. Start with pictures or videos. Some good places to find pictures and videos are:

Make it clear that everyone has something to say and everyone's things are valued, by:

Not commenting at all on students' noticing and wondering, just listening with a welcoming expression.

Writing EVERY noticing or wondering down, whether it's "relevant" or "right" or not.

Asking, at the end, "are there any noticings or wonderings that you're wondering about?" and then encouraging the authors to clarify as needed.

After solving a problem or doing an activity that you launched with noticing and wondering, ask, "How did we use our noticings and wonderings?" and go back through them to value the contribution of each.

When something comes up that a struggling student had noticed, foreground that moment to help give that kid more status. For example sometimes a student notices something "obvious" but then later on that obvious thing turns out to be a key to the solution - value that contribution!

Be explicit about the skill you're teaching. Here are some ways to do that:

Ask students to notice and wonder with different lenses on. Choose a picture and ask "What would a scientist notice? What would an artist notice? What would an athlete notice?" Then ask "What would a mathematician notice?"

After noticing and wondering, once everyone's voice has been heard, ask, "Which of these did you use math to think of?" and "Which of these could we use math to explore more?"

After everyone's voice has been heard, talk about how as a group they're getting better at noticing and wondering.

Look at noticings and wonderings from another class (people share lists on blogs and Twitter a lot and you can compare your list to theirs).

Notice and wonder about an example or image from the text, and then see if you noticed everything that the text pointed out about the image/example.

Use student wonderings to drive lessons to make the class feel more student centered:

Encourage silly, creative, and fun wondering by valuing even off-the-wall wonderings (like when someone wonders "Does Sally have a tapeworm?" when you do a problem about Sally eating a whole pizza, encourage more thinking and discussion about tapeworms and the math behind them).

Choose a student wondering to explore, rather than the question you'd originally intended.

If student wonderings don't make sense to explore that day, come back to them later, support the students to answer them on their own, and/or choose a different scenario where you and the students DO wonder the same things.

Help them remember to use noticing and wondering:

When they're stuck.

When they've got a possible answer.

When someone else is explaining.

When they're reading a textbook.

When they're reading a math problem.

When they're looking at a math image like a table or graph.

All the time!

And as for how to help colleagues experience and appreciate noticing and wondering:

Use your own students as guinea pigs and videotape or record the session. When students notice cool things or wonder something awesome, share that (innocently)!

Math teachers love noticing and wondering about math-y images like this: http://mathforum.org/blogs/pows/free-scenario-filling-glasses-wcydwt/ so get them doing it as a fun exercise, and then thinking about how it can help students.

Send your colleagues to http://101qs.com to get them wondering about math images and videos.

Share Annie Fetter's Ignite talk about noticing and wondering: http://www.youtube.com/watch?v=WFvYZDR4OeY

Share some of these blog posts about noticing and wondering or with examples of noticing and wondering:

So, Math Twitter Blog o Sphere - if you've noticed and wondered with high school students, what have you noticed and wondered about them? What's unique about the high school experience, and what helps high school students and their teachers value noticing and wondering?

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If you've spent any time around the Math Forum folks, you've heard of "I Notice, I Wonder" - two little phrases that we use to start students talking mathematically. We've seen the questions "What do you notice?" and "What do you wonder?"

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Noticing and Wondering in Elementary School

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Noticing and Wondering in Elementary School

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My colleague Max recently blogged about noticing and wondering in high school, Noticing and Wondering in High School and I thought it would be fun to blog about using it at the elementary level. The essence of our "I Notice, I Wonder" activity is that you give students a mathematical situation or picture or story, without asking any specific questions, and ask them to list everything that they about it, and everything that it makes them about.

I've written about it in the past, including in one of our Teaching with the Problems of the Week documents, How to Start Problem Solving in Your Classroom [PDF]. In that, I tell the story of the first time I explicitly asked students (who were "low-level" eighth graders) to tell me everything they "noticed" about a picture. The short version is that the students were awesome and their teacher was amazed at how much math they came up with.

Just as I started composing my post, I got email from my friend Debbie, who teaches at an elementary school school in the district I live in. She described the first lesson she did with a new class she's co-teaching, in which she asked the students to notice and wonder. I asked her if I could use her story as a "guest post" on my blog, since I think it's as compelling as anything I could have written. She agreed, so here goes.
Debbie's Story
I taught an amazing lesson today. It was the first day of math class for the year. Our whole district is starting a new math program. Our fifth grade is grouping homogenously for math. Instead of teaching the highest ability students as I usually do as "Teacher of the Gifted," I'm co-teaching the lowest two classes with two other teachers, a regular education teacher and a special educator. Together we have 22 struggling math students.

Predictably, the topic for lesson 1.1 was place value. But my goals were to engage the students, to create a safe space for learning, to get them thinking and asking questions, and to evaluate their understanding of place value. Instead of using the lessons from the book, which used place value charts with the places labeled, I started by handing out blank, unlabeled place value charts and asking pairs of students to talk about them. I suggested that they notice and wonder. And the three teachers got to wander and listen in. It was amazing.

First, they had to decide the orientation of the paper. Some kids held it vertically and saw it as a thermometer or list. Most held it horizontally. Many recognized it as a chart to use with money or decimals or place value. It was gratifying to see that they recognized the format. When we reconvened to share ideas as a group, our conversation was directed by their noticings and wonderings. I was able to review concepts of place value, numbers vs. digits, etc. not by following the book, but by following the comments from the kids. I praised their questions, asked them to respond to each other's comments, and kept the discussion flowing.

At one point the kids parroted the places: ones, tens, hundreds, thousands... and I wrote them on the board. They got to millions, ten millions, hundred millions and then got stuck. Some thought that next comes thousand millions and others thought next comes billions. It was a perfect teachable moment; all I did was draw the lines between hundreds, thousands, millions and point out that there were three columns in each, and there was a collective "ah-ha!"

Eventually, I asked the kids to put the place labels into their charts. It was fascinating. About a third of them labeled left to right. That certainly told us a lot about their level of understanding of place value! We have a lot of work to do. But that meant that about two-thirds of them were able to label the places correctly, which is good. I used one of the incorrectly labeled charts and we started talking about it. I asked if putting a 7 in different places changed the number of M&Ms the digit represented. I covered up parts of the chart and asked them to read the number, then revealed the next column. Again, we had "ah-has." I'm not sure who was more excited, the kids or me.

I had been worried that the other two teachers were going to object to my non-traditional approach, especially on the first day of using a new program. I was pleasantly surprised; they saw the value. During the lesson, the regular education teacher kept flipping through the teacher's manual. She realized that I had covered material from the first THREE lessons, although I'd not completely finished any of the lessons. So while my approach was non-traditional, I was covering the curriculum and we weren't "behind." More importantly, both of them recognized and valued the high level of student engagement. In fact, one pointed out that one boy who struggles with attention had been totally attentive and even participative. They saw the excitement among the students, they noticed that even reluctant students participated, and they recognized the significance of the multiplicity of "ah-ha moments."

It took me at least another hour to come off the "high" from the lesson.

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Noticing and Wondering in Elementary School

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My colleague Max recently blogged about noticing and wondering in high school, Noticing and Wondering in High School and I thought it would be fun to blog about using it at the elementary level.

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Heinemann is a publisher of professional resources and a provider of educational services for teachers and educators from kindergarten through college.

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Max Ray-Riek on the Teacher Who Changed His Life

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Sense Making: It isn’t Just for Literacy Anymore: Annie Fetter

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What's Going On in This Graph?

_________

Rihanna or Justin Bieber? The Weeknd or Migos? If you live in the U.S., what's the most popular musician or band in your area? Take a look at this set of 50 fan maps, based on YouTube's geocoded streaming data, and see what you discover.

The maps come from The New York Times's Upshot, which emphasizes data and graphics in its analysis of politics, policy and everyday life. There you can find charts, graphs and interactives of all kinds on everything from cultural phenomena, like music preferences or "Game of Thrones" characters, to breaking news events, such as North Korea's missile launches, to the important issues of our day, like affirmative action and the opioid crisis.

Teachers tell us these data visualizations are rich texts for classrooms across the curriculum, not just in the math or statistics class. Whether in a literature class analyzing Jane Austen's language, a science class considering climate data, or a civics class studying gerrymandering, teaching students how to read, interpret and question graphs, maps and charts is a key 21st-century skill.

As Judith Hante, a math instructor at San Diego's Miramar College, recently wrote to us, "So much data comes flying right at teens and young adults these days, and so many of them don't have the tools to know how to understand it, what questions to ask, or when it is just plain misleading in the way it is graphed. I'd like to see them be skeptical and be better consumers of information."

Well, we've developed a way to do just that. This year, we're delighted to announce that we'll be partnering with the American Statistical Association (A.S.A.) for a new monthly feature, "What's Going On in This Graph?", or "WGOITGraph?" The A.S.A. educates the public about using data to understand our world and believes that statistical literacy is important for everyone.

If you're familiar with our popular " What's Going On in This Picture?" series, you'll have some idea already of how "WGOITGraph?" will work. In that feature, we partner every Monday with Visual Thinking Strategies to publish an intriguing Times photo stripped of its caption, and to invite students to come to our site and discuss what they see. On Fridays, we reveal the original caption along with related information. Teachers tell us that the exercise helps students practice their visual thinking skills and their use of evidence to support claims, across subjects and grade levels. And - just as important - they tell us it's fun.

In this experiment with the A.S.A., we're going to do the same with The Times's rich trove of graphic visualizations - graphs, maps and charts.

Here's how it will work.
Starting on Sept. 19 and then afterward on the second Tuesday of every month from October to May, we'll publish a Times graphic on a topic that is suitable for subjects across the curriculum.

The content and statistical concepts will be suitable for most middle and high school students. Often, we'll strip it of some key information, then ask students three question - inspired by Visual Thinking Strategies, but anchored in math and statistics thinking:

* What do you notice?
* What do you wonder?
* What's going on in this graph?

The first two questions might be familiar to many math teachers. The National Council of Teachers of Mathematics' Math Forum advances these simple questions to encourage students to become active and curious critical thinkers rather than passive consumers of mathematics. Here's why:

The process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking What do you notice? What do you wonder? we give students opportunities to see problems in big-picture ways and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems.

Here's a written explanation about how the strategy works during the different steps in problem solving. In this video, embedded below, Annie Fetter, a math educator at the Math Forum, explains how she uses the notice-wonder strategy with students.

The last question we pose - What's going on in this graph? - invites students to think critically about what they have already noticed and wondered. Their answers will reveal their interpretations of what they have discovered.

Teachers from A.S.A. will help select the graphs we use each month, moderate the live online discussion and, equally important, provide a "reveal" at the end of the week. The reveal will include whatever information is missing and also provide related statistical concepts and academic vocabulary to help students increase their depth of quantitative literacy.
We will publish our first "WGOITGraph?" on Tuesday, Sept. 19, and then we'll continue on every second Tuesday from October to May - Oct. 10, Nov. 14, Dec. 12, Jan. 9, Feb. 13, March 13, April 10 and May 8 - so mark your calendar. You'll be able to find all our "WGOITGraph?" posts in this column.
And, just like with our sister feature, "WGOITP?", we'll provide live moderation on the first day of publication. So, from 9 a.m. to 2 p.m. Eastern time on the Tuesdays that we run this feature, moderators from A.S.A. will help push students to look closely at the graph and think deeply about what it might mean.

Since the graphs themselves will remain online at the top of each post, teachers can continue to use them for discussion with future classes without the "answers" - whatever information we have omitted - being obvious. Teachers can use any week's graph, and students can post comments, whenever it is convenient. We will leave each post up and open to comment indefinitely.

Please let us know what you think of this new feature. And if you're as excited about it as we are, please help us spread the word.

For more teacher and student statistics resources, go to the A.S.A. K-12 website, which includes is Statistics, resources, professional development, student competitions, curriculum, courses and careers.

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Announcing a New Monthly Feature: What's Going On in This Graph? (Published 2017)

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What's Going On in This Graph? _________ Rihanna or Justin Bieber? The Weeknd or Migos? If you live in the U.S., what's the most popular musician or band in your area? Take a look at this set of 50 fan maps, based on YouTube's geocoded streaming data, and see what you discover.

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Look, Mom! I'm a Mathematician!: Max Ray-Riek

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Teaching Isn't Rocket Science. It's Harder.: Max Ray-Riek

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Here are Max's (@maxmathforum) slides! Click to advance slides. Notice and Wonder Instruction Routine

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Big idea: Two little words that have been making a pretty big difference in how teachers get students talking math: Notice and Wonder .

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The Thinking Teachers Do So ThatStudents Do All the Thinking

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The Thinking Teachers Do So ThatStudents Do All the Thinking

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Steve

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Chapter 4

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Recently NCTM created a new page on their website that you now reach if you type in http://mathforum.org. From that page they've linked to:

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originally posted August 9th, 2014
During our recent EnCoMPASS Summer Institute (#ESI14) Fawn Nguyen's comment that she'll have 140 students this year, started me reminiscing. I, like Fawn does now, taught in southern California and having at least 140 students was normal. I usually taught 5 of our 6 class periods (at times I could have "sold" my sixth period but resisted it!) and classes could be as large as 36 students. That could mean 180 students but usually my load hovered around 150. It's my normal mindset to think in terms of those numbers.

During #ESI14 we were talking about giving written feedback on the Problems of the Week (PoWs) either using the My PoW Work as a Teacher option of the PoWs or the EnCoMPASS software option and both of them can be daunting experiences if you are faced with 140 expectant students. Why didn't I get feedback? When are you going to look at my work? Why did you write to her and not to me? Those are a few of the questions I can imagine students asking between the time they submit their work and when I promised they would have feedback ... and, of course, the worst are the sad faces!

Here are some ideas I have for keeping sane!
Feedback Buddies
[During the Institute we talked about Revision Buddies (page 175 in Max's book, Powerful Problem Solving) and this idea can be built on it.] If you're doing problem-solving activities in pairs, for any given problem give feedback to Student 1 of the pair. This cuts the amount of feedback in half for any given problem [70].

Group Buddies
If 70 is too great a number to handle, consider grouping pairs of Feedback Buddies and having groups of 4. Give feedback to Student 1 of the group. This cuts the amount of feedback in quarter for any given problem [35].

With either of the ideas for Feedback Buddies or Group Buddies, you would give feedback to Student 1 for Problem 1 and then Student 2 for Problem 2, etc.

Random 7
I'm thinking that if Fawn has 140 students and she has 5 class periods then she as 28 students in each class. I'm also thinking that she might use groups of 4. So, what if she used a Fast Random Number Generator app to come up with 7 students who would be receiving feedback on the PoW. She would give those seven students feedback and that's how the groups would form to have conversations about her feedback and how they should use it to revise/improve their work. [If she happens to prefer groups of 3, then that would be Random 9 instead!) [35]

Random 3
This might be a way to start just because it's VERY manageable for the teacher and it can be used to introduce the idea that you'll be giving feedback and it might lead to conversations about what the process is and what the expectations are. Once the students have submitted, randomly choose 3 students' work from any one class. (I wouldn't pick a low, medium, high submission - I would do it randomly ... or ... I might not even pick one of my students' solutions but instead lift a solution from the Teacher Packet and use it to generate your feedback!). [3] or up to [15] if each class is different.

In April, 2017, I joined Max Ray-Riek to talk about effective forms of written feedback. "We want [the students] to think more about the problem," says Max. "That's our goal in giving feedback: to say something to the student that makes them want to return to the problem and think again." You can view a short video on Heinemann's site: https://blog.heinemann.com/giving-feedback-to-students

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originally posted August 9th, 2014 During our recent EnCoMPASS Summer Institute (#ESI14) Fawn Nguyen's comment that she'll have 140 students this year, started me reminiscing. I, like Fawn does now, taught in southern California and having at least 140 students was normal.

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Beginning to Problem Solve with“I Notice, I Wonder”TM

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Beginning to Problem Solve with“I Notice, I Wonder”TM

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Noticing & Wondering: Unlocking Sense-Making

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Noticing & Wondering: Unlocking Sense-Making

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Melynee Naegele

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Noticing & Wondering: Unlocking Sense-Making