Noticing and Wondering

There is a lot of talk in math education circles these days about the power of noticing and wondering. And—pardon the pun—it's no wonder! When we ask math students to notice and wonder, we shift the center of instruction from teachers’ explanations to students’ ideas. Observing (noticing) and questioning (wondering) are simple, powerful habits that enliven and enrich every aspect of math instruction. From the teacher's immediate vantage point, they support formative assessment, lesson and task design, classroom discourse, differentiation, and the potential for greater rigor. For the learner, they develop independence, confidence, curiosity, perseverance, problem-solving, conceptual understanding, reasoning, and creativity.

Does it seem strange that such a simple idea has such profound potential? I invite you to try it. As you and your students spend more and more time observing and questioning, you develop new habits of mind that gradually transform the learning environment, leading to more productive beliefs about what math is and how all of us—students and teachers—learn it. So where to start? A fun and practical approach is to begin with "noticing and wondering prompts." These are just images—sometimes very simple ones—that you show to students in order to elicit their observations and questions. The immediate goal is simple—to get students comfortable expressing their thoughts and realizing that their ideas matter. Ultimately, you would like "noticing and wondering" to extend beyond the prompts and become a natural part of your teaching and your students' thinking. For more about noticing and wondering prompts, please take a look at a post that I wrote on the topic at

Now if, like me, you did not spend much time noticing or wondering in math class when you were young, you may not have many role models for facilitating math discourse or questioning students effectively. And as much as I thought I knew about math going in to teaching, I discovered that I did not have a deep understanding of math concepts that I had considered basic. Fortunately, I discovered noticing and wondering to be part of a "virtuous cycle" that helps me develop these capacities. As I engage in noticing and wondering with students, it creates ideal conditions for supporting my learning as a teacher, which then feeds back into more effective instruction.

On this page, I am assembling examples of prompts that you may try using. Some of them target particular math standards. Others address multiple or more general math concepts. As you become comfortable using the prompts, you may begin to find and create your own. The prompts on this page have one important limitation—they were created by one person. They are limited by my experiences and perspectives. I invite you to share your ideas for prompts. Even better, share some of your students' responses and your classroom experiences. Ideally, my prompts will eventually be only a small fraction of the those available on this page.

In the meantime, to get more information on any prompt below, just click on it. I am still adding comments to quite a few of them, so I ask for your patience with this. However, every prompt does come with a pdf that you can display or print for ease of use—and you don't need my comments to try them out with your students! You and your students will have plenty of ideas of your own. I look forward to hearing from you!


What do you notice? What do you wonder?

What do you notice? What do you wonder?

What do you notice? What do you wonder?