Tidbits from the High School VP: Notice and Wonder – A High School Tale

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Notice/Wonder is often associated with elementary classrooms. I feel lucky to have learned about it as a high school routine from Sara Van Der Werf a few years ago. If you are unfamiliar with Sara’s Stand and Talks, you can learn more here. 

When I started using Notice/Wonder in my classroom, I stressed out about having them planned for each lesson. Where was I going to find something? Now, I find that they often happen spontaneously, although I still have plenty planned within my lessons. 

One of my favorite lessons is for my Trigonometry class. I use it to introduce the graphs of sine and cosine. Before the lesson, I give the students pre-marked graph paper (see below) and have them graph using the unit circle (they already know how to use the unit circle to find sine and cosine of the common angles). 

They come to class with the graphs finished like the ones below. Some have drawn in the curves, others wait for me to give them permission to draw in the curves. We spend a minute discussing how they know there will be points between the graphed points to justify drawing in the rest of the graph.

Now for the fun part. In Thinking Classroom style (although this works well in groups at desks), I randomly group them and send them to the boards with their graphs in hand. I have them place two titles at the top of their boards: 1) Notice and 2) Wonder. I give them 10 to 15 minutes (or more if they are still discussing) to find ten things they notice and five things they wonder. I have them write their noticings and wonderings down for later reference. Then I listen to their discussions. This isn’t the time to interact with groups, they need the time to notice for themselves and discuss what they notice and wonder with each other. Their conversations are insightful and delightful!

When time is up or their conversations quiet down we start the next phase: sharing with the class. I like to go around the room having each group share one thing they notice until they have all been shared. They also mark them off as they share them or someone else shares the same thing they have written. During this time I annotate on a graph projected on the board and I interject with vocabulary or clarifying comments, but not too much because I don’t want to take anything away from their wonderings.

Sharing the wonderings tends to be pretty short because many of their questions get answered during the notice sharing. But we still have a few that we look at. Most of the time, the class can figure out the answer themselves or I can guide them to the answer. Rarely do I have to outright answer the question myself.

I have done this lesson for several years and the same thing happens every time. By the time we are done sharing, the entire lesson has been taught. My goal for the lesson is that they learn:

    • Sine and Cosine are cyclical
    • The period for sine and cosine is 2π
    • The range is -1≤y≤1
    • The domain is all reals
    • The graph is continuous
    • Sine is odd
    • Cosine is even
    • There are 5 critical points in a cycle: Maximums, minimums, and x-intercepts
    • The critical points break the cycle into 4 equal-sized pieces
    • The amplitude is 1

Not only do the students know these things by the end of the hour, they know WHY and HOW. Although this lesson takes a bit longer than the lecture I used to do, I do not have to repeat myself 578 times the rest of the unit. They are way more invested in the information and own the knowledge.

Note to self: I really should do this structure of lesson when I am introducing the graphs of quadratics and exponentials to my younger classes.

The MCTM Spring Conference is coming up. If you haven’t registered, please consider doing so soon. You can register at: https://www.mctm.org/event-4541070

I will be presenting two sessions about the Thinking Classroom:

Thinking Classroom: Student Engagement, Discourse, and Thinking

    • This will be an introductory session for those who are new to the Thinking Classroom

Building Thinking Classroom: Tasks and Tips

    • This will explore how to create your own tasks and thin-slicing tasks

Jessica Strom
Win-E-Mac School
High School Vice-President