Developing Mathematical Habits of Mind

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

In What we think and why we think it, we argue that students learn better when they are curious, thoughtful, determined and collaborative.

In this film 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.

Here are some collections of mathematical activities designed to give Stage 3 and 4 students opportunities to develop these desirable characteristics.
Stage: 3 and 4

Being Curious

These problems will exploit students' natural curiosity and provoke them to ask good mathematical questions.

Stage: 3

Being Determined

These problems require determination. Encourage your students to persevere - there's often a great sense of achievement when we've had to struggle.

Stage: 3 and 4

Being Thoughtful

These problems require careful consideration. Allow your students time to become absorbed in them.

Stage: 3

Being Collaborative

These problems are ideal to work on with others. Encourage your students to share ideas, and recognise that two heads can be better than one.