Thinking Mathematically

For problems arranged by curriculum topics or mathematical habits of mind, visit the NRICH Secondary Curriculum page.

We recommend the following books and articles which address what it means to think mathematically:

Learning and Doing Mathematics by John Mason
Thinking Mathematically by John Mason, Leone Burton and Kaye Stacey
Train Spotters' Paradise by Dave Hewitt
Habits of Mind: an organizing principle for mathematics curriculum by Al Cuoco, E. Paul Goldenberg & June Mark

Age 11 to 16 Challenge Level:

Exploring and Noticing Structure

Problems about exploring and noticing structure for use with Stage 3 and 4 students.

Age 11 to 16 Challenge Level:

Working Systematically

Problems about working systematically for use with Stage 3 and 4 students.

Age 11 to 16

Thinking Strategically

Problems about thinking strategically for use with Stage 3 and 4 students.

Age 11 to 16 Challenge Level:

Posing Questions and Making Conjectures

Problems about posing questions and making conjectures for use with Stage 3 and 4 students.

Age 11 to 16

Visualising

Problems about visualising for use with Stage 3 and 4 students.

Age 11 to 16 Challenge Level:

Mathematical Modelling

Problems about mathematical modelling for use with Stage 3 and 4 students.

Age 11 to 16

Representing

Problems about representing for use with Stage 3 and 4 students.

Age 11 to 16

Reasoning, Justifying, Convincing and Proof

Problems about reasoning, justifying, convincing and proof for use with Stage 3 and 4 students.

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. He describes what it is like to do mathematics, to be creative, to have difficulties, to make mistakes, to persevere, to make progress, to have a dream and love what you are doing so much that you are willing to devote yourself to it for a long time. Of course, each mathematician's experience is different, and most mathematicians do not work alone for such prolonged periods without discussing their work with others, but much of Andrew Wiles' experience is shared amongst mathematicians, and reminds us of the rewards of perseverance in the face of difficulty.

Recommended Books
We have compiled a list of books for young people who are interested in mathematics.