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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Thinking Mathematically - Secondary Teachers

### Exploring and Noticing Structure

### Working Systematically

### Thinking Strategically

### Posing Questions and Making Conjectures

### Mathematical Modelling

### Reasoning, Justifying, Convincing and Proof

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*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

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

Age 11 to 16

Challenge Level

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

Age 11 to 16

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

Age 11 to 16

Challenge Level

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

Age 11 to 16

Challenge Level

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

Age 11 to 16

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.