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Published 2024
Exploring and Noticing is part of our Developing Mathematical Thinking Primary and Secondary collections.
This page for teachers accompanies the Primary and Secondary Exploring and Noticing resources.
You may wish to watch the recording of the webinars, which draw on the resources below to discuss how teachers can offer students opportunities to explore and build on their discoveries.
During this webinar, we had a go at the following tasks:
The Number Jumbler
Add to 200
Cyclic Quadrilaterals
Tilted Squares
Mathematicians take great pleasure in being challenged by a problem they don't immediately know how to solve, and are excited by exploring a mathematical idea or question for the first time. They will often play with ideas, try some examples and test different approaches. Along the way, they look out for patterns and structure that might move their thinking forwards, and try to
make connections with what they already know.
If students are to work as mathematicians, willing to be 'playful' while being uncertain about how to proceed, then we may need to think about the following:
Values and ethos
Structural considerations
Facilitating
"What have you tried so far?"
"What do you notice?"
"Is this linked to...?"
"What's the same and what's different?"
"What could you do next?"
"Can you find other examples?"
"Will this always work?"
"What might a mathematician ask next?"
As a result, students learn to believe in their own mathematical powers ("Can I have a bit more time to think about this?").
"Ooh that's interesting!"
"That's surprising!"
"I think this might be linked to..."
"Ooh I wonder whether that always works."
You may be interested in this collection of follow-up resources:
Peter Liljedahl's book, Building Thinking Classrooms, in particular Practice 3 (Where students work in a thinking classroom), Practice 4 (How we arrange the furniture in a thinking classroom), Practice 5 (How we answer questions in a thinking classroom) and Practice 6 (When, where, and how tasks are given in the thinking classroom)
Mitch Resnick includes Play as one of his 'Four Ps of Creative Learning', and talks about all four in this recording of his Richard Noss lecture 'Sowing the seeds for a more creative society'
In their book Adapting and Extending Secondary Mathematics Activities, Stephanie Prestage and Pat Perks offer ways to create alternative versions of tasks, which will offer students a richer mathematical experience