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 maths misconceptions 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 articles written by Jo Boaler, Professor of Mathematics Education at Stanford University. She also runs https://www.youcubed.org/, which has a mission – Inspiring Mathematics Success for all Students through Growth Mindsets and Innovative Teaching. Our main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on maths learning into accessible and practical forms.

I have paraphrased it for ease of understanding and added my thoughts and experiences too.

Everyone Can Learn Maths at the Highest 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.  

Scientific research using MRI and CT scanners has established which parts of the brain are active when specific thoughts or processes occur. 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 ‘everyone’ as this is used in the research paper by Jo Boaler. Personally, I think there should be a caveat at this point.

>>>What about children with SEND?<<<<

I think there should be a distinction made 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 moderately to severely impaired by their learning differences.

Realistically, a semi-verbal or non-verbal child with complex needs is unlikely ever 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. 

I am Dyslexic, ADHD and Autistic, and I was undiagnosed and unsupported at school and University. Yet, I gained O Level, A Level Maths and then a degree in Mechanical Engineering, which is basically just really hard applied maths! I also started off with severe Maths Anxiety at Primary school. 

Just because a child initially finds Maths hard in a Primary setting, when it is very fact-based 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. 

The student’s ideas and self-belief about their ability determine their learning pathways and future Maths development

This is probably the most crucial of all of these truths/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 now might be something that they can grasp easily, and they could quite easily do the middle group work. Please don’t make that decision for them by assuming that as they couldn’t do task A, they won’t be able to do task B. 

Please give them a choice. Yes, some will always plump for the easiest option, but I have done experiments on this when I was still in the classroom. I offered 3 or 4 sets of tasks, and only a few children ever opted for the lowest tasks. Over time, the average task level was 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 more than what had been predicted by their previous year’s teacher. This is all an example of encouraging a Growth Mindset in the children. 

Help them believe in themselves and make good choices, and they will aspire to higher attainment.  

Mistakes are Valuable

‘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 correct and not to make mistakes. As previously mentioned, Maths is very fact-based and memory-based at this age. Much emphasis is put on test scores and timed tests of times table recall. This, unfortunately, feeds the myth that any mistakes are bad. 

The target graphic shows the Growth Zone Model. “When pupils are in the Anxiety Zone, healthy learning cannot take place. The aim should instead turn to how to reduce the anxiety as quickly and supportively as possible.” This is all about building resilience in pupils.

Part of the Growth Mindset theory is about the Growth Zone, Comfort Zone and Anxiety Zone. We need to aim to place children in the Growth Zone so learning can occur and not just stay in the safe Comfort Zone. 

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. 

The Comfort Zone is where a learner could be working on familiar activities probably independently, building their self-confidence and providing them with practice opportunities. Children like being in this comforting situation, playing familiar games or activities and feeling happy and secure. This is one of the reasons why in my teaching, we repeat activities until children are completely confident with them. They should feel in their Comfort Zone quite quickly as soon as they understand the task, and then be able to relax and start to enjoy it.

By initially reducing the task’s difficulty to one within the Comfort Zone, their anxiety level will drop. Now that the task is no longer causing them anxiety, they have an excellent chance of understanding the concept and then gaining mastery of it.

If we can keep building on that task, adding more and more concepts, we can move them into the Growth Zone – which is the best zone to be in.

If you have the Growth Mindset and are in the Growth Zone, 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. They personally will only be in their Comfort Zone, and so their brains don’t grow in the same way or same rate. 

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 is something that only sometimes happens in certain schools. I have done long-term supply in a school where all children had to work in pencil. The work in the books had to be 100% correct, and any errors had to be ‘post-it noted’ with the correct answer, and then the child had to rub out their answer and redo it 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!

Those children had no margin to think for themselves or make mistakes. As for them, mistakes required them to miss a break time and redo their work until perfect. So they equated mistakes with punishment and failure. I found the regime at that school unbearable and untenable to my own professional ethics. That school operated from the SLT, fearing 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’ – taking risks and developing resilience to try new things without fear. 

Depth is much more important than speed

‘The children who do their Maths really quickly are the best at Maths….‘

This is again another myth. Maths is not a race. The fastest isn’t always the best. Even though young children are regularly given this message, it isn’t valid long term. Slower and more careful thinking results in higher-level mathematical thinking. 

Children who can whizz through questions easily are just children who need to be sufficiently challenged and be 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 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 to this sort of child many times. 

GCSE and A-Level Maths most certainly isn’t a race, and getting questions fully all the way 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 must be in place. Get these quick recall children having to think and ponder about 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 directly 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! 

Teachers, adults and other children’s messages matter and are hugely powerful

‘You are rubbish at Maths…’ 

This is the sort of throwaway comment that can decimate self-confidence and, consequently, motivation and, therefore, ultimately, attainment. Comments can be made by anyone, but if the child hears it, they will remember it and the powerful negative feelings it starts.

The power of praise and encouragement makes a huge difference in motivation and then in future achievement. 

Children develop ideas about their potential from comments made by their teachers, parents and other adults.  

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 they have put in, and they are likelier to continue to work hard. Bland comments don’t motivate in the same way. 

Always praise what they have done and how hard they have tried. Don’t link achievement to be the most important factor. “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.” 

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If you are interested in finding out more about the Growth Mindset and the Growth Zone or anything else in this blog, do reach out to me at judy@jackpotmaths.com