Let's face it- problem solving is hard! This is the case whether you're an early learner or a research mathematician.

For so many of us:

- it can be tough to work out what a problem's really asking,
- it's often not clear if you're on the right track,
- it's common to get frustrated, and
- it's common to want to give up.

**YET, dealing with uncertainty, coping with challenge, and being persistent are all valuable for independent, motivated and ongoing learning.**

So, what to do?

I want to share two questions that have completely changed my own approach and attitude towards problem solving. These questions, time and time again, help me to untangle messy thoughts in my head and keep track of my ideas (whether big, small or seemingly irrelevant).

And they’re questions that can be used by any learner – no matter their age or the mathematical content they’re tackling.

Here they are-

## Two questions that will change how your students see maths

- What do you notice?
- What do you wonder?

Here's what Amie Albrecht, mathematician and Maths Teacher Circles guest presenter, has to say about these two questions:

“These are powerful prompts to engage students. ‘Notice and Wonder’ helps lower the barrier to entry for all students.

It encourages sense making.

Students are more invested because they are connecting their own thinking to the scenario and are generating questions that they are interested in solving.”– Amie Albrecht, mathematician & MTC guest presenter

## Notice & Wonder: The two questions in action

Let’s look closer at these two questions, using a visual that I recently shared on Facebook and Twitter:

### 1. What do you notice?

This first question helps learners to identify what they know and can see. By responding to it, students often realise that they understand more about a problem or visual than they initially thought.

The ‘Notice' prompt asks for observations alone, not answers or justifications.

This is its power.

**Students can respond, knowing it will be without judgement.**

Looking at the colour tower above, what do you notice about how the colours are arranged? Write a list of what you observe.

### 2. What do you wonder?

This second question opens up a realm of possibility. It helps learners to connect what they have observed with where they might go next.

Importantly, the ‘Wonder' prompt also gets students invested in what they're exploring. It shows them that, in maths class, questions aren’t just asked by the teacher or textbook.

**Mathematical questions can be asked by anyone.**

Going back to the colour tower, what do you wonder? Write down any questions you have.

## Ideas for the classroom

What do you notice?' and ‘What do you wonder?' can be used in a range of classroom contexts, both formally and informally.

Here are some ideas:

- When introducing a new concept, use the questions to gauge students’ current levels of understanding,
- After teaching a skill, present some sample working out and use ‘notice and wonder' as a formative assessment tool,
- When sharing complex information with students, such as a wordy problem, table, graph or some other visual, use the two questions to encourage sense-making,
- When students are solving problems, encourage them to use the questions as a tool for getting unstuck.