Noticing and wondering is a powerful tool. My favorite part about noticing and wondering is that every single student can participate mathematically. Everyone can notice something, and everyone has something they can wonder about. It’s a great way to get students thinking about a problem. No matter what your background, language, gender, or family, everyone has something to wonder and notice.

**What is noticing and Wondering?**

Noticing and wondering is a routine that encourages students to make careful observations while clarifying a problem or situation. It also helps stimulate curiosity and sets the stage for inquiry.

**Why notice and wonder?**

- It levels the playing field.
- It gets students thinking and talking early in the lesson.
- There is no wrong answer so teachers can affirm ideas their students share.
- It directs students’ attention to the things that are mathematically important in the question or picture.
- It gives students time to make sense of the problem without any pressure to solve it.
- Teachers can build on what students have shared– often borrowing their exact language– to ease into the next part of the lesson and building confidence at the same time.
- It’s a life skill.

**How can this help students? **

- Students can identify important information in a story problem.
- It connects their own thinking to the math they are doing.
- It helps students notice the details in their math problem.
- It helps students feel safe.
- It helps students think about the problem before they start solving it.
- It encourages the process of thinking about math and connecting ideas and wondering about it.

**How to Implement Notice and Wondering**

There are many ways to implement, but this is what I like to do:

**Step 1**: Put up a story problem or a picture and ask students what they notice.

**Step 2**:Students think then pair share their noticing with their team.

The group’s recorder writes down **all** noticing of group members. Groups pick favorite noticing to share out to the class.

**Step 3: **I make a public record of noticing and keep them on display throughout the problem-solving process. Collect additional noticing that students would like represented but aren’t on the class poster. Students should add noticing they like to their own recording sheets.

**Step 4: **Repeat the same process with wondering.

**Step 5:** Reflect. Looking over our list I give students a chance to reflect on their noticing and wondering. What leads to mathematical discoveries?

**Step 6**: Proceed with the problem.

**Step 7: **Check back on your noticing and wondering when you are stuck during a problem. ( If students have noticed and wondered their way into a problem, those noticing and wondering can serve as reminders for different ideas that can help students get unstuck).

**Question Stems ** “Look at your work and your partner’s work. Is there anything that jumps out at you that looks different?”

“What would be worth a try?”

“What would happen if …?”

”Would it help to …?”

“ Would ___ work?”

As I guide my students in noticing and wondering their problem solving abilities increase. They are better able to noticing and wondering mathematically. This begins as a practice strategy, then a skill , that soon becomes natural to them. Students are also fulfilling mathematical practice #1 which states-*Make sense of problems and persevere in solving them. *And who doesn’t need this skill in their life?

**Beginning to Problem Solve with “I Notice, I Wonder”from NCTM**

### Patty Reed

#### Latest posts by Patty Reed (see all)

- What Do You Notice? What Do You Wonder? - December 5, 2016
- Reciprocal Math Teaching - November 26, 2016
- 5 Steps Toward Equity - October 30, 2016

Deb Webb says

Not only is this great for math and science, but it’s a natural for ELA as well! I can’t wait to try this with my short story unit and also apply it during revision of student writing. This would also be a great activity to do when discussing stereotypes and bias during my advisory class. Can’t wait to try this! Thank you!

Douglas Ferguson says

This is a great activity. I’ve definitely come across the concept via current science circles, but I like this approach. Thank you for sharing and I’ve already made a note to try it out in January!

Patricia Gustin says

Science uses noticing and wondering a lot. I am going to appropriate the protocol you shared. As Tom noted, this is an effective way to get students to write as they record their thinking.

Francis Jequinto says

This definitely sounds like Science to me – many publishers are a big fan of the 5E model. The first E (engage) is all about these kind of things – what are some phenomena you can make observations on? What are some questions these phenomena lead you to? Are any of these questions testable? That process leads naturally to scientific investigation, and it’s great to hear another department (especially one so closely intertwined) using the same kind of starter.

Now it’s just about aligning with common language between departments, right?

Patty Reed says

That would be amazing if we could do that!

Elizabeth Johnston says

I like this strategy. I agree that it levels the playing field and creates an access point for all students to engage in some way.

Tom White says

What I love most about activities like this is that they’re “self-Differentiating.” Fluent writers will write fluently, and those who struggle with literacy will write less, but everyone will write something!

Scott Cleary says

I can see how this structure would be valuable in my content area as well. Currently my students are working on the ability to determine central themes in a literary text. For this, they need to move past surface level meaning and interpret what the plot and characters in a story reveal about the author’s opinion on a subject. Having them structure their thinking around noticing and wondering would help scaffold this skill. I could have them notice (a relevant literary element) and wonder (what it reveals about the author’s opinion).

Determining theme is one of the more difficult skills for students to master with sophistication, so I appreciate your insight. I am always looking for strategies to help scaffold and meet diverse learning needs.

Carina Stillman says

Yes, exactly–only more eloquently stated than what I was pondering. Fourth hour students will be “noticing” how Frederick Douglas describes his abuse and “wondering” how those descriptions influenced audience views of slavery–we’ll start with something simple to reinforce the process and then jump in. Thanks for the idea(s)!

Anonymous says

I like this strategy because there isn’t an overt “lesson” here for the kids. Students simply get the sense that their point of views matter and they take charge of their learning when doing so. Such a simple strategy! I’ll have to try it!

Brooke Perry says

Patty, I appreciate how you provided a concrete example of using noticing/wondering in class. I feel like noticing/wondering is all the rage right now, but you clearly showed how students can use those observations in order to help them approach and solve a problem. Noticing and wondering is great… but then what? Thank you for bringing it full circle for me.

Aaron Brecek says

if a student comes up with a wonder different than the rest (for example how much does the box weigh), do you allow them to explore that wondering or do you come to a class consensus that all students explore together?

Patty Reed says

Great question Aaron, I think it depends on how the teacher wants to approach it. In this task about the donuts we used one question that was the consensus of the class. But students who finish early were encouraged to figure out another wonder. Students found out that once they knew how many donuts they could easily figure out box weight or calories in the box.