Developing students' resilience
This page for teachers accompanies the Being Resilient Primary and Secondary resources, and the content formed the basis of the webinar that focused on developing students' resilience
If we are going to offer students opportunities of working and thinking like mathematicians, we will need to require them to do more than just copy and imitate what the teacher demonstrates. In Alan Wigley's article, his 'Challenging Model' offers a useful framework for structuring lessons. NRICH resources are developed with this framework in mind and require students to be curious, resourceful, resilient and collaborative. You may wish to read the article before going on.
“In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work - brains and talent are just the starting point." (Dweck, 2015)
Carol Dweck has provided evidence that students with a growth mindset are much more likely to succeed. How can we promote a growth mindset in our classrooms? How can we encourage students to keep going and work hard when faced with challenges?
A growth mindset classroom provides an environment in which:
- Students feel safe to make mistakes
- Students and teachers replace "I can't do this" by "I can't do this yet"
- Students are offered opportunities to work collaboratively in a supportive environment
- Students are praised for their efforts, and willingness to share partially formed ideas
- It is recognised that being stuck is a springboard to learning
- It is accepted that learning maths can be difficult and making mistakes is inevitable
- Students are given opportunities to play around with ideas without the pressure of having to be right at the first attempt
- Students are encouraged to appreciate the value of 'messy' work
- All students feel valued and are regularly given feedback that convinces them that their teacher believes they can make progress.
Four NRICH ways of scaffolding tasks to bring them within reach of students, without doing all the work for them:
Showing a potential map or route through the problem
5 by 5 Mathdokus (age 7-16)
Product Sudoku with possible route (age 11-16)
Latin Numbers (age 14-16)
Showing some possible methods and encouraging students to build on them
Different Deductions (age 7-11)
Three Neighbours (age 7-14)
Odds, Evens and More Evens (age 11-14)
What Numbers Can We Make? (age 11-14)
Quadratic Patterns (age 11-14)
Marbles in a Box (age 11-16)
Offering proof sorting activities
Strike It Out (age 5-11)
Diagonally Square (age 7-11)
Kite in a Square (age 14-18)
Pythagoras Proofs (age 11-16)
Pythagoras Perimeters (age 14-16)
Using 'hide and reveal'
We often choose to hide the scaffolding under a "Click to reveal..." button, so that students can choose when they want to access it. In the classroom, we imagine teachers might provide the scaffolding in an envelope that students can choose when to open.
You can find many more activities in the Being Resilient Primary and Secondary resources
Questions to consider with your colleagues:
Where might your students get stuck?
What is the thinking that you will expect students to do for themselves?
What's non-negotiable?
Are we offering too much (or too little) scaffolding?
Does working in this way give students the sense of achievement we want them to feel?
Are students likely to "hang on in there" for longer than they otherwise would?
How can we nurture this habit of mind whenever students are confronted by new problems?
You may be interested in this collection of follow-up resources:
Models for Teaching Mathematics - article by Alan Wigley
What might a lesson look like, in which students work collaboratively, sharing insights and discoveries in a safe environment? Here is one possible example.
Peter Liljedahl's 14 Practices for Building Thinking Classrooms, in particular Practice 5 (How we answer questions in a thinking classroom) and Practice 8 (How we foster student autonomy in a thinking classroom)
Resilient mathematicians recognise that we all fail sometimes, and when this happens, they bounce back and try alternative approaches. In the film What Does it Feel Like to Do Maths, Andrew Wiles talks about his personal experience of seeking a proof of Fermat's Last Theorem.
Matthew Syed's Bounce: The Myth of Talent and the Power of Practice
In Mindset Carol Dweck analyses how a growth mindset can boost achievement - here is a link to her TED talk
An interview with Dylan Wiliam, focusing on effective questioning in the classroom
In Getting into and staying in the Growth Zone Clare Lee and Sue Johnston-Wilder explain how the Growth Zone model can help develop resilience in learners of mathematics.
Anxiety and Recall - The Mathematical Association's Autumn 2017 edition of Equals
If you'd like to know more about the beliefs that inform the work of NRICH, take a look at What We Think and Why We Think It
“I remember the day not long ago when Ruth opened my eyes. We had been doing math, and I was pleased with myself because, instead of telling her answers and showing her how to do problems, I was "making her think" by asking her questions. It was slow work. Question after question met only silence. She said nothing, did nothing, just sat and looked at me through those glasses, and waited. Each time, I had to think of a question easier and more pointed than the last, until I finally found one so easy that she would feel safe in answering it. So we inched our way along until suddenly, looking at her as I waited for an answer to a question, I saw with a start that she was not at all puzzled by what I had asked her. In fact, she was not even thinking about it. She was coolly appraising me, weighing my patience, waiting for that next, sure-to-be-easier question. I thought, "I've been had!" The girl had learned how to make me do her work for her, just as she had learned to make all her previous teachers do the same thing. If I wouldn't tell her the answers, very well, she would just let me question her right up to them.”