2 Teaching for mathematical resilience
Developing a ‘growth mindset’ about learning mathematics
Students who have developed ways to work on mathematical problems that allow them to continue, even when they encounter problems, can be said to be mathematically resilient. Such students will have a ‘growth mindset’ (Dweck, 2000), which means that they know that the more they work to overcome challenges and solve problems, the ‘smarter’ they will become. Students with a growth mindset do not accept that they have any ceiling or limit on what they can learn. Hence, they will discuss and question mathematical ideas with anyone who may help them, until they have fully grasped the ideas. Working in this resilient way demands sufficient mathematical vocabulary to explain ideas and to work collaboratively.
Experimenting and questioning are part of being mathematically resilient. Students who are encouraged to ‘play with mathematical ideas’, for example by using ICT tools or manipulatives, develop their resilience because they see that they can explore and start to understand those ideas. Working collaboratively is another important way to develop resilience, as students can receive help from their peers as and when they need it. A resilient student will seek help from a variety of sources: older students, textbooks, the internet, teachers, a clever uncle, etc.
Another important aspect in developing students’ resilience is to enable them to see asking questions as ‘clever’ and to see persistent asking as being ‘even cleverer’. All students have to know that the only one who can take responsibility for their learning is themselves and therefore they have to actively seek understanding. The mathematically resilient student will have a good understanding of their own strengths and will know how to get appropriate help to improve any limitations.
In short, mathematically resilient pupils will assert, in their practice, their right not to be mathematically isolated or feel mathematically stupid; they will resist any expectation that they should passively accept mathematical ideas but they will demand to be allowed to work at understanding them for themselves. They will reclaim their right to progress their own mathematical thinking, using existing knowledge, skills, understanding and strategies, and be confident about their ability to learn new mathematics.
(Lee and Johnston-Wilder, 2013)
Working in ways that develop mathematical resilience
According to Lee and Johnston-Wilder (2013), in order to develop mathematical resilience, students must have the opportunity to do the following:
- Learn sufficient mathematical vocabulary and ways of expression to engage in mathematical conversations, question concepts, work collaboratively, think mathematically and build understanding. This means that pupils have to use mathematical words and ways of expression for themselves, and not only listen to their teachers using the mathematical language.
- Make mistakes and take wrong turns, so that ultimately develop the belief that if they persevere they will be far more likely to succeed.
- Extend their ability to experiment and try out ideas in a mathematical environment and, in our experience, discover that they enjoy it.
- Seek solutions to significant problems. Working on such problems will require pupils to try things out, to make and recognise mistakes for themselves and work for an extended time with other people to produce a well-reasoned solution.
- Acquire a reflective and thoughtful stance towards mathematics. They will know that, if they think hard, talk to others, read about mathematical ideas and reflect on the information gained, they will be able to make headway with seemingly difficult ideas and problems.
The activities in this unit will work on developing these five resilient skills.
1 Resilience and mathematical resilience in learning