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Thinking Mathematically - 2025 Cambridge Teacher Seminars

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Standing, from left to right: Karen, Lisa, Stuart, Emma, Chris, Dana, Chad, Kim, Gohar, Gene, Sara, Ingrid, and Charlie, not standing

"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

Nurturing Successful Mathematicians: the Rope Model

The Iceberg 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
 

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Enriquecer \la enseñanza \de \las Mátematicas

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?" 

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 
and Resources and Professional development
 

Links to resources to support Primary teachers:

Links to resources to support Secondary teachers:

Links to resources to support Post-16 teachers:

Problems we worked on during the week:

The Number Jumbler
Summing consecutive numbers
Unequal Averages
Wipeout
Xavi's T-shirt
Cyclic Quadrilaterals

Generating triples
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.

Amazing Card Trick
Truth or Lie
Ace, two, three...
Matt Parker's favourite card trick

Some interactivities on the Secondary mapping document, and on the Secondary interactive resources page:

More less is more
Dozens
Square it
Fruity totals

Bringing everything together

Poster 1
Poster 2
Poster 3
Poster 4
Poster 5


Further recommendations

Peter Liljedahl's Building Thinking Classrooms 
Colin Foster's Mathematical etudes
Productive Math Struggle
Productive Failure - Manu Kapur's 2019 Ted talk and book
NCTM's 5 Practices for Orchestrating Productive Mathematics Discussions
Henri Picciotto and Robin Pemantle's There is no one way to teach Math
Mathematica: A Secret World of Intuition and Curiosity by David Bessis, and a discussion about the book.
Mihaly Csikszentmihalyi's Flow
Yōko Ogawa's The Housekeeper and the Professor
Steven Strogatz's Infinite Powers: How Calculus Reveals the Secrets of the Universe
Matt Parker's Humble Pi
Arthur Benjamin and Michael Shermer's Secrets of Mental Math
Math Circles - connecting mathematicians of all ages


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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