Noticing and Wondering: Empowerment in Learning

June 2021

What are you noticing and wondering today? What have you seen or heard that brings to mind noticing and wondering about mathematics around you? When we share a picture, a numberless problem situation, a graph, or even a pair of equations or number sentences and then ask students what they notice and what they wonder, we engage them as active thinkers and doers of mathematics. We position them as authorities in the classroom, valuing their voice and ideas.

Several years ago, I met a middle school mathematics teacher from Colorado who encouraged her students to use mathematics as a lens to see their world, that is, she wanted them to have a math encounter as she termed it. It was empowering for her students, and they began to see the world around them through mathematical eyes. That is what noticing and wondering does. When students approach what they encounter with a notice and wondering lens, they have opportunities to broaden their understanding of what mathematics is through understanding and critiquing their world and engaging in the wonder, joy, and beauty of mathematics. Sound familiar? Yes! It is the first recommendation from the Catalyzing Change series!

This month NCTM has been leading us in exploring notice and wonder through a series of professional learning webinars. Annie Fetter kicked it off with a session on how a notice and wonder instructional routine provides the opportunity for all students to engage in problem solving, supporting students in generating ideas and making connections among mathematical concepts. Then Graham Fletcher built on this with a focus on mathematical modeling with Three-Act Tasks. Aaron Rumack continued the next week by reminding us of the power of notice and wonder as a way to create a structure for engaging teachers and students in reasoning and sense making in planning for equity. The four-part series closed with a final session led by Naomi Jessup on using notice and wonder as a tool for critical reflections and engagement. Together these sessions helped us unpack the possibilities in supporting students in developing this approach to noticing and wondering in mathematics. NCTM members can revisit all of them on the NCTM website.

But notice and wonder are not just for our students! We as mathematics teachers can use this lens when we are examining and reflecting on our own practice. In the February 2021 issue of Mathematics Teacher: Learning and Teaching PK–12 (MTLT), Tracy Dobie and Eleanor Anderson note, “These questions can also be useful for teachers looking to deepen their discussion with colleagues” (p. 94). They go on to share that this approach can help us in learning from one another, pushing our thinking, providing a safe and inviting professional learning environment, and strengthening our collaborative learning community. Noticing and wondering is a powerful learning tool for all mathematics educators and students.

Recently I was engaged with teachers in professional development, and we explored the noticing and wondering routine on the first day, beginning with only a picture that I provided from the MTLT Problems to Ponder department. The teachers shared what they noticed about the picture (without the problem stated) and then what they wondered and what they thought their students might notice and wonder. Their responses spanned from nonmathematical to mathematical ideas. This led to observations from them about how this instructional routine provided a space for all students to enter the conversations as an equitable teaching practice, sparked creativity and curiosity, empowered students, fostered positive mathematical identity, shifted to students as the authority in the classroom by giving them voice, and promoted more discussions and questioning among peers rather than only student-to-teacher interactions. What was interesting is how the teachers continued to use notice and wonder throughout the remaining days of the sessions and the connections they made to questioning strategies, equitable teaching practices, classroom discourse, and their own mathematical learning. Many identified it as part of their action plan for thinking about beginning the next school year.

So, have you met our two mathematics-loving characters Notice, the snail, and Wonder, the owl? If not, I invite you to check them out and all the great Notice and Wonderinstructional resources. While you are exploring these, consider binge watching the four-part Notice and Wonder webinar series with Annie, Graham, Aaron, and Naomi. Be ready to notice and wonder! As you continue your teaching journey, you may find that you will see the world through a notice and wonder lens every day, and that is a good thing!

Trena Wilkerson
NCTM President
@TrenaWilkerson