• Alex Box

Notice & Wonder - 3 key uses in Maths

Updated: Jun 5


Recently, I've discovered the power of the Notice & Wonder (N & W) routine for engaging and connecting whole maths learning communities. Notice & Wonder helps create positive and inclusive maths learning cultures where all contributions are valued equally and as part of the collaborative learning process.

I love how the N & W routine replicates various aspects of a mathematician's work: observation, questioning, sense-making, communicating (to name a few).


By slowing down and taking time to observe (notice) and ask questions (wonder) in this way, the group practise listening to and valuing each other's ideas. It's fun and it creates a space for us to be curious; curious about what we will see and discover, curious about what others mean when they describe what they see, and curious as to what more there is to ponder.


With a carefully chosen prompt, N & W is a conversational space where mathematical and other ideas naturally emerge. It can be used as a 5-minute, stand-alone opener; or as a way to tune into a longer lesson. I've found it's a nice and productive way to settle a group after recess or lunch. Read on for a typical N & W format and 3 strategic uses in Maths.


A Typical Format

1. Invite students to notice and wonder. This is dedicated quiet time to look, notice and wonder individually. It might be about 30 seconds or whatever feels right for the group.


2. Invite students to share their thinking. Students volunteer their ideas. The teacher asks clarifying questions to encourage precise explanations.

For example, if a student noticed 20 of something, the teacher could ask "How exactly did you see 20?". Or if the observation was "I see symmetry", the teacher could ask "What do you mean by symmetry?" Once this was explained, the teacher could then go back and ask "Okay, so where exactly did you see the symmetry?"


One thing I think is important, is that students decide whether and when to respond to clarifying questions, and whether they want input from peers who think they can help.



I see this as something that needs to be explained and accepted as a norm.


Here's a Tweet I once saw that highlights these kinds of considerations ->




Three Strategic Uses

Notice & Wonder is very versatile. Once students are familiar and confident with the routine, the choice of prompt starts to become a bit more dependent on my hidden, maths teaching agenda (shhhh!). Here are three strategic ways I like to use it in maths.


1. Introducing or revisiting a mathematical tool

My hidden agenda might be to help students become familiar with five frames as a tool to support counting and number facts.


Chances are, someone in the group will notice something about the five frames. When that happens, I can ask some clarifying and probing questions until we get to the point of describing the tool accurately (a row of five boxes or squares), naming it as a five frame and understanding its use as a mathematical tool.



2. Introducing or revisiting a mathematical idea

If I'm wanting to help students investigate and use the properties of odd and even numbers (VCMNA151), I'll plan ahead of time to run some Notice & Wonder conversations with inclusive visuals that touch on this topic. Running the routine with a whole class almost guarantees someone will bring up the ideas you're nudging towards. I have to remember to keep my poker face though to maintain a culture where all ideas are valued equally. I don't want it to seem as thought there is, despite the openness of the questions, any kind of 'right' answer.

With this visual, I'm pretty sure that someone will notice the odd sock! Or an odd number of socks. So then I can ask a couple of clarifying and probing questions about that. I may decide to invite one or two other students to paraphrase in their own words what they mean to really highlight that point. Then move on.



3. Launching an investigation


Free play investigations

Before launching any structured investigations (i.e. using any kind of lesson plan), I've found it really valuable to give time to freely explore materials. At the start of the year it's a nice way for students to become familiar with key manipulatives. It's also a powerful way for me to get to know them as learners and mathematicians. So where does a Notice & Wonder come in here? If I were launching a play-based investigation using pattern blocks, I might tune in with one of these Notice & Wonder visuals.

Photo sources: 1st photo, 2nd photo, 3rd photo.

Students will notice aspects of number, geometry as well as relational attributes of the pattern blocks which will support future lessons and investigations using them. The very first hands on investigation using the manipulatives then, is to explore the possibilities. The big question here is - What's possible with pattern blocks?


This is a beautiful opportunity to model curiosity about what students discover, and to ask them what they notice and wonder about their own, and each others', creations. Many personalised investigations are happening. I can have casual conversations that provide rich information about student personalities, working styles and mathematical knowledge.


I really like Dan Finkel's four go-to questions for helping nudge play towards mathematical ideas when exploring materials early in a new school year.


Or at any time really!




Focussed investigations Once students have explored the materials, and I've got a sense of what kind of task would create a nice balance of success and challenge for all students, I'll look to run a focussed rich investigation like Hopeful Hexagons.

Having explored this task myself, I know it is a beauty that goes off in lots of fascinating directions. Potentially accessible to all year levels, I'd recommend it more for Year 3 onwards (adults loved it!). As you'll see in the lesson plan, we start with a Notice & Wonder before posing the investigation questions:

  • Are hexagons with more than 6 pieces possible?

  • Is it possible to make hexagons with any number of pieces?


Extra things I'm thinking about:

  • Where possible, I try to include a few (but not too many) extra things to notice and wonder about - like colours. The more there is to notice, the more success all individuals will have.

  • I think it's important to regularly run a Notice & Wonder without any hidden agenda. It's a nice reminder and opportunity to be genuinely curious and explore joyfully together.

  • I sometimes wonder whether it would be better to separate the Notice & Wonder as sequential steps. I don't want it to become too rigid nor harder to participate in. I'd love to hear what others have found, especially for really young children.

  • The best ways and places to source Notice & Wonder prompts. I like making my own. I also like taking snaps of student creations that have mathematical ideas in them to use later on. Look at the richness of this design! -->


Your thoughts and experiences:

I'll be learning to teach maths forever and am grateful for the online community in supporting my development as a learner and educator. I'd love to know:

  • What are your experiences of, and motivations for, using Notice & Wonder?

  • Do you have tips, tricks or variations on Notice & Wonder you've found to work?

  • How do you use N & W with really young leaners?

  • What is your favourite place or way for choosing Notice & Wonder visuals?

Wishing you a great start to 2021!


If you’re looking for more ways to engaging all students in maths,

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