Classroom Resources

Becoming curious as a Problem Poser

Although we want to give students opportunities to share their thinking and be curious about the world, not everyone is ready for that yet. The ‘What do you notice? What do you wonder?’ prompt provides a structure for discussion and sharing with a built-in differentiation continuum. As we ask students to think deeply about their own observations and ponderings, we are also exploring the concept that we might all see things differently and that it’s exciting seeing things from another’s perspective.

The How?

Looking at a photo, ask the class:

• What do you notice?
• What do you wonder?

“What do they notice?”: This question is asking students to simply look at the image. These responses are typically more straightforward observations and might start simpler before becoming more intricate.

“What do you wonder?” This question asks students to think deeper still about the photo. What are they curious about? What are they interested to know more about? If they could speak to the photographer, what would they ask them? Once again, these ‘wonders’ can become deeper and deeper, sometimes taking on an unexpected line of inquiry or thinking. This prompt can act as a precursor to asking more complete questions.

What do you notice?

I notice that every pencil has a marker of the same colour. 
I notice they are all evenly spaced.
I notice the up-down patterns of the pens and pencils.
I notice, in each pair of pencils, one has the label and the other doesn’t.
I notice the lids of the pens are going back and forward.
I notice only one marker where you can see the brand.
I notice some of the pencils are sharp and some are blunt.

What do you wonder?

I wonder if someone made this from their pencil case.
I wonder if the table underneath is real wood.
I wonder if this could be a repeating pattern if it continued long enough.
I wonder about the quality of the pencils (because I’m thinking of my own pencils.)
I wonder if I can make my own pattern.
I wonder why only one pen has the brand showing.
I wonder if you could make another pattern using the same pencils and pens.

Being a Problem Poser: 

So often the discussion stops at problem-solving. But looking at Bloom’s Taxonomy, there are many more exciting stages beyond application. We ideally want students to move beyond the maths given to them and be their own mathematicians. After all, this is often the requirement for beyond a standard C grade or different objectives within senior mathematics subjects.

The How?

After putting an image up, have students consider ‘What questions could we write or ask using this photo as a reference?’

Problems posed could involve all different types of maths. Sometimes the initial problems posed could be more ‘classic maths’ and simpler. However, with facilitation and appropriately given time, the problems posers will become more creative and reflect deeper thinking. This is an excellent opportunity to facilitate the conversation to grow and flourish.

Depending on your class, you may like to differentiate (enabling or extending) with the different questioning words (who, what, where, when, why, which, how, how often, if etc).

If you’d like to take this further, the class or students might like to pick a particular question/s to go investigate and solve, including different ways of answering the problems posed.

What mathematical problems could we pose from this picture?

What shapes combine to make these stairs? 
What would the net look like?
Are there any angles that aren’t right angles? Why/Why not?
Why are there different stair designs?
What happens when the steps are not the same height?
How much space would it take to make a safe ramp for the same flight of stairs?
What angle or incline of the ramp makes it unsafe?
What is the total volume inside the stairs?
What is the surface area of the stairs?
If concrete cost $6.50 per cm3, then how much would it cost to build these stairs? How much would the railings cost too?
Does it matter if there is an odd or even amount of steps?

Be your own Problem Finders:

What better opportunity to demonstrate to students that maths IS everywhere than by asking students to find their own photos in the world to pose problems from.

If technology allows, students could go discover and take their own photos to pose problems with. Alternatively, students could explore and then draw a representation of the image to pose problems. These photos could then be used as references to pose problems, as students work individually, in groups or as a whole class. This could also be a great learning-from-home or remote learning activity.

Don’t forget to share! If students do take their own photos while exploring, please share and contribute as the resource continues to grow. All images will be credited when shared with the wider community! Click here to find out more. 

Great new school year activity: 

Beginning maths class away from the textbook is an easy way to break misconceptions around mathematics and its limited applications. This resource offers the opportunity for students to feel heard, actively engaged and interact with both you and their class peers. Plus, these discussions and interactions could give some valuable anecdotal information – social-emotional, subject-specific, personalities, level of interest or engagement or simply a jumping-off point of reference to reflect back on throughout the school year. Students can safely participate while switching back on after an extended break by being low-risk.