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I am a first-year Pre-Calculus teacher at a public high school in the United States. The curriculum I am using often contains "Notice and Wonder" activities whenever a new concept is about to be introduced. The purpose of this type of activity, at least from my perspective, is to get the students to make sense of something that is unfamiliar to them. Students also get to hear their classmates' ideas on how to make sense of what is presented, which encourages a classroom environment where finding multiple ways to approach a problem is valued and appreciated.

I have tried to implement a few Notice and Wonder activities but I do not think I carried them out successfully. What I usually do is give students about 1 minute to observe the task and then I ask for volunteers to share what they noticed and wondered. For whatever reason, this is when I get a lot of blank stares; not many students have been willing to share what they noticed. I tell my students that there is no wrong answer when it comes to sharing what they noticed, but this has had little effect. Since I teach older students (11th and 12th graders), perhaps they are less enamored with the idea of Notice and Wonder.

My questions are:

  1. Is my understanding of the purpose of a Notice and Wonder activity valid?
  2. What is the best way to implement a Notice and Wonder activity?

Some ideas:

  • Do a Think-Pair-Share so that more students are confident enough to volunteer.
  • Call on students regardless of whether or not they raise their hand (i.e. use a lottery system for randomness).
  • Continue to maintain a classroom environment where the product (i.e. correct answer) is far less important than the process.
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    $\begingroup$ Do you feel like the activities from the curriculum are authentic? If so, perhaps model for them what you notice and wonder. (I do that a lot, even though I don't have anything labeled as 'notice and wonder'.) $\endgroup$
    – Sue VanHattum ♦
    Nov 10, 2021 at 2:46
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    $\begingroup$ I think @Sue has hit the nail on the head: authenticity. Observations and (inter- and intra-) connections should continually be made throughout the curriculum, and as the concepts recur. Wonderments, whether interwoven or as prefaces or epilogues, are better hooks when organically motivated. $\endgroup$
    – ryang
    Nov 10, 2021 at 5:28
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    $\begingroup$ First thing would be to realise that edu-consultans create "activities" (I cannot write this word without quotation marks, so much I hate it) and names for them for a living. Second thing would be to drop the infantile name. Third would be to continue teaching as usual, slowing down where additional explanation is needed, asking the students relevant questions, here would be your implicit Shock and Awe... I mean, Notice and Wonder moment. $\endgroup$
    – Rusty Core
    Nov 10, 2021 at 16:19
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    $\begingroup$ I agree that "edu-consultants" often add things of little value. However, I believe that this particular idea came from math bloggers, who for years read and responded to each others' blogs (often through google reader, now gone), and developed some great teaching strategies through that conversation. $\endgroup$
    – Sue VanHattum ♦
    Nov 10, 2021 at 19:55
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    $\begingroup$ Many high school curriculum "Notice and wonders" are really "guess what the teacher is thinking" that rewards students with tutors, extracurricular training, or elder siblings. Most of the "N&Ws" provide far far too few cues as to what it is you want them to N&W, and so rewards students who already know the math to the detriment of students who don't already have a good idea what they are about to learn. N&W can make perfectly capable students feel stupid because they couldn't guess what you were thinking. As said be authentic. Also, lead generously. Very generously. $\endgroup$
    – Michael G
    Nov 11, 2021 at 23:35

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  1. Yes, I think your general understanding of the purpose is correct.

In my view, it has four goals. For the weaker student, it gives them a chance to find the footing to start asking questions. For the average student, it gives them a chance to start making connections to prior knowledge. For the gifted student, it gives them a chance to hypothesize and see if their intuition is valid. For you, it allows you to gauge where students are in this continuum on this topic.

  1. There is no best answer to this question; it will depend on you and your students.

Do your best to understand why your particular students may not be engaging -- if you have a good rapport with them, you can even try asking one or two apart from the crowd. If the problem is authenticity (as was mentioned in the comments), try creating your own similar activities to increase relevance. If the problem is anxiety at being wrong, given them low risk activities that are harder to opt out of, like Vote With Your Feet/Valley of Values until they start feeling comfortable with sharing. If the problem is not understanding the expectations, modeling a question or two for them will help quite a bit. Sometimes, though, especially as a new teacher, it's that we simply aren't waiting long enough for a response. As an AP Calculus teacher, my students are very mathematically inclined, and yet sometimes I still get the blank stares when I ask certain questions. As long as you've created a classroom environment where it's safe to be "wrong", there's no harm in letting those quiet moments stretch out while you're waiting for an answer to be offered

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