Mistakes, Mindsets, METACOGNITION and Mathematics

I’ve started thinking a bit more critically about the wild claims being tossed around about growth mindset because we cannot attribute a learners failure in maths to poor attitude or their own weak will... 

Generic mindset messaging that is all too common, isn’t helpful.  Telling learners  not to worry or give up or that you can’t add fractions yet! – doesn’t do enough to help them add those fractions.

Like everyone else, when I first came across Carol Dweck’s theory of growth mindsets I was pretty psyched. There was something so satisfyingly truthy about the way the labels ‘fixed’ and ‘growth’ mindset could explain why children failed or succeeded at school. I wanted to believe that something as simple as telling children their brains are ‘like a muscle’ could make them cleverer.

 If, for some reason, you’ve been hiding in a cave for the last few years and haven’t heard of Dr Carol Dweck’s Mindset theory, you can read about it here.

A growth mindset is the belief that ability and competence grow with effort. People with ‘growth’ mindsets think, “I need to practise more at maths if I’m going to get good at it”. The really interesting claim, though, is that through the use of relatively minor interventions – things like praising a child for “working hard”, rather than for “being clever” – you can instil a growth mindset. Dweck,  claims that doing so can improve children’s outcomes at school and beyond.

But with growth mindset interventions, the trouble is that despite the enormous effect sizes reported, research fails to replicate this in classrooms.

In the UK, the Education Endowment Foundation’s Changing Mindsets study found that growth mindset interventions resulted in no “statistically significant effect on attainment in either maths or English”. Carol Dweck’s explanation for why attempts to replicate growth mindset interventions don’t seem to work nearly as well as we might expect is down to what she calls the ‘false growth mindset’ and that 'not anyone can do a replication.'

David Didau called her out: “It could be that they’re just doing it wrong and have a ‘false growth mindset’, or it could be that such appealingly simplistic ideas about making profound changes to children’s academic attainment are bollocks?”

If it’s true that replicating the effects of Dweck’s studies cannot be done by amateurs “in a willy-nilly way”, then what chance does your average teacher have? Or a parents or carer?

5 IMPACTFUL Strategies for helping children develop MISTAKES, MINDSETS and METACOGNITION in mathematics...

1. Believe it or not, some people are still of the opinion that learning mathematics is a gift given to some people at birth! Society’s misconception that a person is either born with a mathematical ability or they are not has created a culture where it is socially acceptable for someone to openly proclaim that they are ‘no good’ at mathematics and where a weakness in mathematics is worn as a badge of honour. Unfortunately, these self-proclamations contribute to the development of a MINDSET that becomes fixed and often unwavering. 

DO ENCOURAGE and PROMOTE GROWTH MINDSET and COMBINE with a 'Sense of Purpose'. Recent research suggests combining growth mindset and a 'sense of purpose' intervention may be particularly effective for underachieving students. A sense of purpose is essentially helping people identify what their motivation is and why doing well at this task will help them in the future. Combining growth mindset and a sense of purpose was found to help improve students’ performance in maths.

In a 2015 study, maths-anxious parents who frequently helped their young children with homework saw their children learn significantly less maths by the end of the school year than kids whose parents didn't express an aversion to maths. The kids of maths-averse parents also reported more maths anxiety than kids of parents who were not maths-averse.

Telling our children that their efforts will make no difference and so there is no point in them trying is detrimental.  Indeed, research suggests that the type of comments children aged even as young as 1-3 years old hear from their parents predict their growth or fixed mindset up to 5 years later. 

2. STOP GROUPING AND PEG-HOLING CHILDREN. Intuitively it makes sense to group children as it helps target support and enrich BUT the evidence suggests otherwise. In fact, groupings are an area of education where the practice that happens in schools is far from the research evidence that exists. International research conclude that the most successful countries are those that group by ability the latest and the least. Mixed achievement teaching is associated with higher overall achievement for students of all levels and when schools move from tracking to giving all students high-level math classes, achievement increases significantly.

In her book: Mathematical Mindsets, Jo Boaler details ways to teach mixed achievement groups successfully and describes what happens when we raise expectations! This, in my opinion, is a much more equitable way of teaching. Instead, give children high quality, challenging maths TASKS.  “Students can grasp high-level ideas, but they will not develop the brain connections that allow them to do so if they are given low-level work and negative messages about their own potential.” (Boaler & Foster, 2014) High challenge - Low threshold TASKS are best. These TASKS help learners develop into competent, confident mathematicians. The Low Threshold may mitigate against the development of maths anxiety by making sure that learners do not fail at the first hurdle. The High Ceiling offers everyone the opportunity to develop their resilience.

3. Create a culture that RECOGNISES and VALUES MATHEMATICAL MISTAKES as opportunities to learn. Whilst mathematics can arguable be an experience of the mind and, most importantly, of the heart (Francis Su, 2021) It is still a subject of clear right and wrong answers. A subject of absolutely definitive answer. It is easy to see how getting a question wrong can lead to some learners to believe they have a lack of natural ability. Yet what we need to nurture is mistake making!

Mistakes create learning opportunities. They can give us insight into learners misconceptions and enable them to develop deeper understanding of the mathematics they are learning. Being 'outside' your comfort zone is an extremely important place to be. Encourage learners to lean into their struggle and not be afraid to make mistakes. 

An appreciation of maths mistakes can be desirable and can help learners to  overcome fears of making them, take risks and build resilience. BUT, Not all MISTAKES are created equal. 

• Ask learners to explain their reasoning about whether an answer is correct or incorrect.
• Provide learners with mathematical tasks that focus on strategies, thinking and understanding.

4. METACOGNITION       

This  is one of those terms that gets bandied about in educational circles as if we all know exactly what it is... Errrr.... It's thinking about thinking, isn't it?

Ever since the Education Endowment Foundation cited metacognition and self-regulation as the second highest impact strategy teachers can use in the classroom I've felt I should be a bit clearer about what it actually is.

They describe it as follows:

Meta-cognitive and self-regulation strategies (sometimes known as ‘learning to learn’ strategies) are teaching approaches which make learners think about learning more explicitly. This is usually by teaching pupils specific strategies to set goals, monitor and evaluate their own learning. Self-regulation refers to managing one’s own motivation towards learning as well as the more cognitive aspects of thinking and reasoning. Overall these strategies involve being aware of one’s strengths and weaknesses as a learner, such as by developing self-assessment skills, and being able to set and monitor goals. They also include having a repertoire of strategies to choose from or switch to during learning activities.

 Metacognitive strategies can be divided into three sections. These are: helping learners  plan; monitor; and evaluating their own learning. 

Don’t be put off by the name metacognition. When the science jargon is stripped away, you’re left with developing strategies that help learners become more aware of (thus improving) their thought process. By encouraging learners to use some of the questions below, they will be put on the right track towards improving their metacognitive skills.

The report further states that:

‘Challenge is key to developing self-regulation and metacognition: if learners are not challenged, they will not develop new and useful strategies; nor will they reflect deeply on the content they are engaging with, or on their learning strategies, or stretch their understanding of themselves. Put simply, and somewhat paradoxically, if pupils have to undertake a task that makes them struggle (remember ‘deliberate difficulties’), they are more likely (in the future) to recall information from such tasks from their long-term memory.’

What is an appropriate level of challenge? Looking at John Sweller’s cognitive load theory or Vygotsky’s ‘Zone of proximal development’, we see it is important to make it not too hard, not too easy, but just right (The Goldilocks approach).

If you are interested in MEMORY & EDUCATION check out Jonathan Firth