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Thinking Mathematically - 2026 Cambridge Teacher Seminars

 

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From left to right, Viola, Annie, Andrea, Paul, Mickayla and Charlie

 

"I don't expect, and I don't want, all children to find mathematics an engrossing study, or one that they want to devote themselves to either in school or in their lives. Only a few will find mathematics seductive enough to sustain a long term engagement. But I would hope that all children could experience at a few moments in their careers ... the power and excitement of mathematics ... so that at the end of their formal education they at least know what it is like and whether it is an activity that has a place in their future."

David Wheeler

Key ideas that inform the work of NRICH

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Rope with three strands. One strand represents mathematical thinking, one represents curriculum understanding and procedural fluency and one represents mathematical mindsets



Nurturing Successful Mathematicians: the Rope Model
 


Alan Wigley's article on Models for Teaching Mathematics
 


An example of what this might look like in practice:

Tilted Squares and the recording of a lesson
 

 

Our guiding principles

 

Maths is for all
All have a right to shine, and all have a right to struggle
Low Threshold / High Ceiling tasks allow for differentiation

Allow time for exploration and discussion
Start with an engaging problem/context (Wigley article)
Tap into students' curiosity: "What questions are bubbling up for you?" 
"Experience first, formalise later"

Offer students the opportunity to go on mathematical journeys
Exploring, noticing patterns, conjecturing, generalising, justifying, proving
Think-pair-share / Convince yourself, convince a friend, convince others... 

Encourage multiple strategies / representations 
We publish students' solutions

Value a Growth Mindset (Carol Dweck)
It’s ok to make mistakes - learning is a messy business
There’s always help at hand but we still expect students to do the thinking
Celebrate resourcefulness and resilience ("Yet")

To find out more, see What we think and why we think it 
Resources for Professional Development
and Using NRICH Tasks Richly
 

Links to resources to support Secondary teachers:


Links to resources to support Post-16 teachers:

 
Problems we worked on during the week:
Summing consecutive numbers
Unequal Averages
Subtraction surprise
The Number Jumbler
Treasure Hunt
Xavi's T-shirt
Wipeout
Make 37
Take Three from Five
Cyclic Quadrilaterals
What's it Worth?
Fruity Totals
Got It
Crossing the bridge
Charlie's Delightful Machine
Factors and Multiples Game
Square It

In this film (available here if you live outside the UK) the mathematician Andrew Wiles talks about his personal experience of seeking a proof of Fermat's Last Theorem.
Fermat's Last Theorem book
Closing the Gap: The Quest to Understand Prime Numbers by Vicky Neale

Amazing Card Trick
Ace, two, three...
Truth or Lying

Bringing everything together

 

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Further recommendations

Stephanie Prestage and Pat Perks' Adapting and Extending Secondary Mathematics Activities - New Tasks for Old
Peter Liljedahl's Building Thinking Classrooms 
Colin Foster's Mathematical etudes
Productive Math Struggle
Productive Failure - Manu Kapur's 2019 Ted talk and book



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"A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking."

Polya, G. (1945) How to Solve it