What Do Mathematicians Notice?

Ever since hearing Annie Fetter talk about Notice and Wonder at the Atlantic City NCTM Regional Conference, I have been obsessed with the strategy. What I immediately noticed (no pun intended) was that my students didn’t notice much. Because I believe so strongly in the power of the strategy, I kept asking them to notice and it didn’t take long before they started noticing more. But…their noticings were really just scratching the mathematical surface. They were saying things like I notice numbers or I notice shapes. I wanted to stimulate deeper mathematical conversations, so I came up with an anchor chart suggesting different ways in which mathematicians notice. My list included:

  • details
  • vocabulary
  • connections
  • relationships
  • patterns

Now, I encourage my students to refer to the chart and try to notice a little more deeply. For example, if a student says she notices numbers, I ask her to give us details. Are the numbers whole numbers, decimals, fractions? It’s been a big help, and it’s definitely helped increase their use of academic vocabulary. I finally turned my hand-written anchor chart into a digital version with examples of each.

Mathematicians Notice

Grab a free version by clicking here.

So, how do you help your students notice deeply as a mathematician and develop academic vocabulary? Please share in the comments!

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      1. Sorry for the problems, Cindy. Were you able to download it? Did you get some kind of error message?

  1. Donna, thanks for the post! I really enjoy following your blog. I was wondering what your thoughts were on the vocabulary example in your poster? I’ve been encouraging staff not to each “key words” in story problems to students as that takes away from the content of the actual problem, and it also sometimes confuses students when it doesn’t always work. I’m just curious what you think about it! Thanks for all you do!

    1. Thanks for your comment, Yvonne. I completely agree that we can’t teach key words. Difference is, however, a word associated with subtraction, just like sum is associated with addition. I’m very careful with my wording so as not to say that difference always means subtraction, which is what we used to do with key words. I have found that students are often not familiar with the operational words (sum, difference, product, and quotient), so we have high error rates on questions like, “What is the product of 2 and 3?”

      1. Thanks Donna. You’re right I totally agree that many students lack the vocabulary to support their understanding of what a problem is asking for. And I see what you mean about that being a vocab word vs. a “key word”.

  2. I love this idea, but can we get one where we can fill in the blanks to customize for content we are teaching at the time?

  3. I love this idea. I have my students make “Graph and Data Observations,” where they notice the title, type of graph, categories, and data. Then we practice making inferences that are supported by the data. I love the way you have more general categories that would apply to all areas of mathematics. May I have permission to present your idea and anchor chart to my staff? I would of course give you credit! Thank you, Rachel.

    1. Yes, Rachel, so often kiddos just overlook all the labels on graphs and diagrams. I have seen huge growth using this approach, and the students really enjoy it. Of course you may share!

    1. With the younger kiddos, it’s mostly verbal, rather than referring to the poster. Other than that, the language is very much the same. Just examples on their level.

  4. Do you have a checklist for student data? I could make one, but just wondered. Thanks so much. Love your books.

    1. What type of checklist are you looking for? Like one tied to the TEKS? If that’s what you’re looking for, I have a set in my store.

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