Fact or Myth?
‘You have to be fast to be good…’ ‘Some people just can’t do Maths, so there’s no point in trying…’
These are just two of the myths around Maths and Maths learning. These myths and others have been debunked in educational research many times over. I have been reading some of this research to keep myself abreast of educational theory.
Most of what I am about to explain comes originally from Jo Boaler, Professor of Mathematics Education at Stanford University. I have paraphrased it for ease of understanding and added my own thoughts too.
All children can achieve at high levels
Sadly it is all too often thought of as ‘Some people just can’t do Maths, so there’s no point in trying… ‘ While in some situations and to some people it will feel true, in fact, it isn’t and is a myth that unfortunately certain circumstances perpetuate.
The scientific research now available using MRI and CT scanners has established which parts of the brain are active when certain thoughts or processes take place. Even after a brain injury, it has been proved that brains are simply amazing and can adapt and grow, given the opportunity and optimum situations.
So, all children can achieve at high levels. Now I have used the word ‘all’ as this is used in the research paper by Jo Boaler. I personally think there should be a caveat at this point. What about children with SEND? I think there should be a division between children who are mainstream educated, but have Non-Neurotypical special educational needs such as Dyslexia, Dyscalculia, ADHD, Dyspraxia and ASD; and those children who are educated in a Special Needs school who are moderate to severely impaired by their disability.
Realistically, a semi-verbal or non-verbal child with complex needs is unlikely ever to be able to reach a level to take and pass Maths GCSE. But, for example, a child with Dyslexia with the right teaching in the right way and at the right pace can grow their brain and go on to pass Maths GCSE with a top grade, take A-Level Maths and even take a Maths related University course. Just because they initially find Maths hard in a Primary setting, when it is very fact and memory-based, doesn’t mean that with the optimum circumstances, they cannot go on to excel.
So please don’t write off a child’s ability at a young age as they may well be able to go on to achieve at a high level.
Students ideas and self-belief about their ability determines their learning pathways and future Maths development
This is probably the most crucial in all of these truth/myths. ‘I can’t do Maths, so there’s no point in trying…’ Again this same statement isn’t true, although it does become a self-fulfilling prophesy – if you think you can’t do it and therefore have no motivation to try you will, in fact, end up not being able to do it.
The concept of Growth and Fixed Mindsets was developed by Carol Dweck 30 years ago. Dweck, C (2017) Mindset – Updated Edition: Changing The Way You think To Fulfil Your Potential If a child can start to have a Growth Mindset rather than a Fixed Mindset and therefore become ‘up for challenges’ and resilient to difficulties, they will achieve much higher.
Don’t limit children’s achievement by giving Fixed Mindset messages by low aspiration groupings or the work set. This is something as a classroom teacher, and now as a full-time tutor, I try hard to overcome. Offer a range of work and allow them to take on the challenge of the more demanding tasks. Giving them low aspirational tasks just because they are usually in the bottom group doesn’t help the situation. The topic you may be doing might be something that they grasp more easily, and they could quite easily do the middle group work.
Please give them a choice. Yes, some will always plump for the easiest option, but I have done experiments on this and offering 3 or 4 sets of tasks, almost no children ever opted for the lowest tasks. Over a period of time, the average task level raised by at least one group. I then added in a 4th level, and many children raised their game again and stretched themselves yet again. Over a term, the overall level of attainment across the class was significantly in excess of what would have been predicted. This is all an example of encouraging a Growth Mindset with the children.
Help them to believe in themselves and make good choices, and they will then aspire to higher attainment.
Making mistakes and having some struggles is extremely important for learning
‘Making mistakes and getting things wrong is bad…’ this is again another myth. Unfortunately, again this is a myth that is grown in Primary aged education situations. Children find themselves desperate to get everything right and not to make mistakes. As previously mentioned at this age, Maths is very fact and memory-based, and a lot of emphases is put on test scores and timed tests of times table recall. This feeds the myth that any mistakes are bad.
Part of the Growth Mindset theory is about the Growth Zone, Comfort Zone and Anxiety Zone. We need to aim to have learning take place in the Growth Zone and not just stay in the safe Comfort Zone.
If you have the Growth Mindset, the act of making and learning from errors results in significant brain growth. Making some mistakes is, therefore, a good thing not a bad thing.
When children make mistakes in Maths, extra brain activity happens that does not happen when students just safely get all their work correct.
Children shouldn’t just be given work that they can instantly do and succeed without any challenges as this doesn’t place them in the Growth Zone, and their brains don’t grow in the same way.
The Growth Zone is where new learning happens – so here, it should be safe to make mistakes, get stuck, require support, and find activities challenging and tiring.
Open-ended tasks that allow children to explore and find several solutions really help the brain develop. Stepping away from recall tasks and into problem-solving and exploration tasks is the way forward for children to develop their Maths ability.
But, this isn’t something that always happens in certain schools. I have done supply in a school where all children had to work in pencil, and the work in the books had to be 100% correct, and any errors had to be ‘post-it noted’ with the corect answer, and then the child had to rub out their answer and redo until it was correct. Every single book looked identical, and like model answers, which is what they were! This was in a school repeatedly ranked Outstanding by OFSTED!
There was no margin for those children to think for themselves or ever to make mistakes. As, for them, mistakes required them to miss a breaktime and redo their work until perfect. So they equated mistakes with punishment and failure. I found the regime at that school unbearable and untenable with my own professional ethics. That school operated from the SLT a fear of any mistakes being recorded for OFSTED to see. This is obviously an extreme case, and I hope to God that there aren’t many other schools out there operating the same system.
Reward children and encourage them to be comfortable and OK with not getting everything ‘correct’ and taking risks and developing resilience to try new things without fear.
Don’t always think of a link between Maths and speed
‘The children who do their Maths really quickly are the best at Maths… ‘
Fastest isn’t always best. Even though young children are regularly given this message, it isn’t true long term. Slower and more careful thinking results in higher-level mathematical thinking.
Children who can whizz through questions easily are just children who aren’t being sufficiently challenged and aren’t in their own Growth Zone. Give them a more suitable challenge, and they will also slow right down as they are required to think more deeply.
I have taught many children who seem to equate Maths with being in a race. It isn’t, and shouldn’t be a race. Trying to explain that as they go further up the educational system, the ONLY thing that matters is getting it right is something that I regularly have to emphasise many times over to this sort of child. GCSE and A-Level Maths most certainly isn’t a race, and getting questions fully out and with clear working is all that matters.
Regrettably, this race scenario is encouraged in many schools at a Primary age. This is where a choice and more challenging and open-ended tasks need to be in place. Get these quick recall children having to think and ponder on the route through a problem.
The second point regarding speed is the pernicious concept of timed tests. I could write forever about how dangerous the timed element of testing is. It makes all the wrong things happen and causes Maths anxiety and reduces achievement. It is harder to access your working memory when in timed situations. Please take out the timed element wherever possible.
Teacher and adults messages matter and are hugely powerful.
‘You are rubbish at Maths…’ This is the sort of throwaway comment that can decimate self-confidence and therefore motivation and therefore ultimately attainment.
The power of praise and encouragement makes a huge difference in motivation and then in future achievement.
Children develop ideas about their own potential from comments from their teachers, parents and other adults in their lives.
When given bonafide praise and encouragement, children are far more likely to make good positive choices, and they will then aspire to higher attainment. Scattergunning overly positive comments doesn’t work long term as children are very good at sussing out if someone is just being nice and making platitudes or if they really mean it. Make genuine comments to a child about the level of effort that they have put in, and they are more likely to continue to work hard. Bland comments don’t motivate in the same way.
Always praise what they have done, not just them. “It is wonderful that you have learned how to add numbers together”, “I really like your thinking about that” not “wow, you can add numbers, you are so smart.”
If you are interested in finding out more about the Growth Mindset and the Growth Zone please look at my other blog posts where this topic is discussed further.