Busting the “maths brain” myth

Using brain science to foster a growth mindset in maths

Busting the “maths brain” myth 2

Introduction

Where does the “maths brain” idea come from?

“It turns out there is no such thing as a maths brain” - Boaler

The perils of maths memorisation

To group or not to group?

Changing messages in maths class

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Contents Page

Busting the “maths brain” myth 3

IntroductionHow many times have you heard someone say, "Oh I’m not a maths person" or "I don’t have a maths brain." The notion that someone is either logical, creative, sporty, academic, practical (the list goes on) is inextricably linked with how we perceive ourselves and what we believe we can excel in. As adults, we don’t take these personality types too seriously and understand that we exhibit a mixture of these traits. Children are different. As they seek to understand who they are and their place in the world, in school and at home, these labels tend to carry a lot more weight. The impact of labelling children as a type, or even adults for that matter, is that psychologically the message we convey is that we’re good at something and by default not so good at something else. In fact, we can all achieve in a variety of subjects if we put in the effort to learn and challenge ourselves. In this eBook you will learn the brain science behind learning and how new research in this field can positively impact on the way in which maths is taught.

Where does the “maths brain” idea come from?

In education, we accept that history or physics are subjects we must learn, whereas, maths is perceived as a subject that you are either good at or not. The idea of a "maths person" stems from many places but parents’ own belief in themselves about whether they can "do" maths or not influences children significantly. Why do parents believe in the ‘maths person’ idea?

When children are younger they show excitement at learning maths but this changes as they progress onto secondary school. Research by Tom Loveless of the Brookings Institution1, suggests that as children get older their belief in being able to perform well tends to decline. Over the years, maths curricula around the world have favoured a procedural approach to teaching maths over a conceptual approach. This has resulted in a generation of learners becoming fearful of maths because they can’t make sense of it and find it difficult to memorise all of the methods (a fruitless exercise as brain science has revealed, more on this later). Fortunately, maths teaching has changed for the better and includes strategies to help nurture conceptual understanding. Nevertheless, parents’ own negative experience of maths can filter down to the next generation of learners. Jo Boaler is a Stanford Professor and author of the critically acclaimed book, Mathematical Mindsets2. In her book she suggests, ‘Mathematics, more than any other subject, has the power to crush students’ spirits, and many adults do not move on from mathematics experiences in school if they are negative. When students get the idea they cannot do math, they often maintain a negative relationship with mathematics throughout the rest of their lives.’ The maths brain is also a result of parents being exposed to the self-esteem movement of the 80s which advised teachers and parents to praise children for their intelligence.

1 Fennell, (Skip) Francis. http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Skip-Fennell/I-Was-Never-Good-in-Math,-Either/ 2007

2 Boaler, Jo. Mathematical Mindsets, Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. Jossey-Bass, 2016

Busting the “maths brain” myth 4

The outcome of this advice led to a generation of people with fixed mindsets. As these children grew up and became parents themselves, they believed they were no good at maths and you had to have a natural talent for it to succeed. At parents’ evenings across the globe, teachers have heard time and time again "I was never any good at maths either." The message this conveys to children is that it’s okay not to be good at maths, after all my mum/dad wasn’t any good at it and they’re doing alright, aren’t they? This only perpetuates the myth that you are either good or not good at maths and you don’t have to try hard at maths to succeed in life. Unfortunately, this belief feeds into the psychological trap of fixed mindsets. The pattern repeats generation after generation.

Carol Dweck3 explains, ‘When people think that some kids just can’t do math, that success is reserved for only certain kids, thought of as “smart”, or that it’s just too late for kids who haven’t had the right background, then they can easily accept that many students fail math and hate math. In fact, we have found that many teachers console their students by telling them not to worry about doing poorly in math because not everyone can excel in it. These adult enablers – parents and teachers alike – allow kids to give up on math before they’ve barely gotten started. No wonder more than a few students dismiss their own poor performance by declaring: “I’m not a math person.'''

Dweck goes on to say, 'Where do parents, teachers and students get the idea that math is just for some people? New research shows that this idea is deeply embedded in the field of mathematics. Researchers polled scholars (at American universities) in a range of disciplines. They asked them how much they thought that success in their field depended on fixed, innate ability that cannot be taught, as opposed to hard work, dedication, and learning. Of all the STEM fields (science, technology, engineering and math), math scholars were the most extreme in emphasizing fixed, innate ability (Leslie, Cimpian, Meyer & Freeland, 2015). If this message is passed down from generation to generation, no wonder students are afraid of math. And no wonder they conclude they’re not math people when it doesn’t come easily.’

Schools have recognised that to change children’s fixed mindset about maths, they must also work with parents to help them change their mindsets too. More and more schools are seeing the value in hosting parent maths workshops to help dispel the maths brain myth and build parents’ confidence in maths so they can support their children with their maths learning.

3 Boaler, Jo. Mathematical Mindsets, Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. Foreword by Carol Dweck. Jossey-Bass, 2016

Where does the “maths brain” idea come from?

Busting the “maths brain” myth 5

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Boaler believes passionately that one of the most important ways to dispel the maths brain myth is to teach the science behind how you learn. Technology has been instrumental in unlocking the mystery of how our brains learn. Neuroscientists have only very recently been able to watch brain activity in a way that shows us connections between learning and our emotions. What’s more, research into brain plasticity has astounded the scientific community. It was believed that your capacity to learn was set and once people reached maturity your brain didn’t grow any more. This theory has been disproved and in fact your brain can grow and change in a very short space of time. Research into brain changes amongst London Black Cab drivers (who must go through years of training to learn thousands of routes and roads in London) stunned scientists when at the end of the training period they found that in the taxi drivers' brains the hippocampus had grown significantly (Boaler 2011). The hippocampus is the area of the brain that is primarily associated with memory and spatial navigation.

This shift in our understanding of how the brain changes when we learn had wide-reaching implications. As a result a lot more research into brain plasticity is underway to answer fundamental questions that affect many aspects of society.

‘In a study that I believe to be highly significant for those of us in education, researchers at the National Institute for Mental Health gave people a 10-minute exercise to work on each day for three weeks. The researchers compared the brains of those receiving the training with those who did not. The results showed that the people who worked on an exercise for a few minutes a day experienced structural brain changes. The participants’ brains “rewired” and grew in response to a 10-minute mental task performed daily over 15 week-days. Such results should prompt educators to abandon the traditional fixed ideas of the brain and learning that currently fill schools – ideas that children are smart or dumb, quick or slow. If brains can change in three weeks, imagine what can happen in a year of math class if students are given the right math materials and they receive positive messages about their potential and ability.’ (Boaler 2016)

A study by Jason Moser5 and his colleagues revealed that when your brain makes mistakes it fires synapses which is ‘an electrical signal that moves between the parts of the brain when learning occurs.’6 According to Moser’s study, the brain sparks even when we’re not aware of our mistake. Boaler explains it like this, ‘When teachers ask me how this can be possible, I tell them that the best thinking we have on this now is that the brain sparks and grows when we make a mistake, even if we are not aware of it, because it is a time of struggle; the brain is challenged and the challenge results in growth.’

“It turns out there is no such thing as a maths brain.” - Boaler4

4 Schwartz, Katrina. ‘Not a Math Person’: How to Remove Obstacles to Learning Math, http://ww2.kqed.org/mindshift/2015/11/30/not-a-math-person-how-to-remove-obstacles-to-learning-math/ 2015

5 Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P., & Lee, Y. H. (2011) Mind Your Errors: Evidence for a Neural Mechanism Linking Growth Mind-Set to Adaptive Posterror Adjustments: http://cpl.psy.msu.edu/wp-content/uploads/2011/12/Moser_Schroder_Moran_et-al_Mind-your-errors-2011.pdf . Psychological Science, 0956797611419520.

6 Boaler, Jo. Mistakes grow your brain. https://www.youcubed.org/think-it-up/mistakes-grow-brain/ 2016

FACTMYTH

Busting the “maths brain” myth 6

Getting recent neurological research into schools and informing teachers about its significance can be powerful in halting, or even preventing, the next generation of people with fixed mindsets. Teaching children that mistakes are good as it grows your brain takes the fear factor out of attempting a challenging task and shows children that mistakes are part of everyone’s learning.

By explaining the results from brain science to students, as well as discussing mistakes and praising effort over results, teachers can help nurture growth mindsets in their classrooms.

Education authorities across the globe rely on timed tests to measure performance in maths. From the academic year of 2018/2019, all year 6 children (ages 10 – 11) in the UK will be tested on their times tables up to 12 x 12.7 Knowing number facts, such as your times tables is not the issue here, rather the conditions in which students are expected to "perform." The underlying message that timed tests convey is one that feeds directly into the psychology of a fixed mindset. To work something out slowly is failure and to avoid failure, children place a higher value on getting the answer right rather than focusing on the learning journey itself.

Speaking in the TES in 20158, Boaler said that in an ideal worldshe would ban times tables tests. 'It’s not that times tablesaren’t worth learning, but the greater goal of maths educationis more important,' she argues. 'Therefore, perhaps we shouldseriously think about whether it is worth risking some childrenbeing turned off the subject, aged 8, for the sake of ensuringthey can answer 7 x 6 under pressure, without hesitation.'

Of course, there are some children that will be fine under timed conditions but for those that aren’t, the temptation to memorise facts, to get the answers right, is overwhelming. ‘Mathematics is a conceptual domain. It is not, as many people think, a list of facts and methods to be remembered.’ (Boaler 2016)

“It turns out there is no such thing as a maths brain.” - Boaler4

The perils of maths memorisation

7 http://www.bbc.co.uk/news/education-39053483, 20178 Espinoza, Javier http://www.telegraph.co.uk/education/educationnews/12033514/Ban-times-table-tests-in-

schools-says-academic.html 2015

Busting the “maths brain” myth 7

To help create Mathematical Mindsets it is important to recognise the need to work flexibly and conceptually with numbers. Research into students with varying levels of ability has revealed that children engage in maths in diverse ways. Students aged between 7 and 13 were studied by Eddie Gray and David Tall, and ranged between low, middle or high-achieving. Each group were given number problems. The researchers found that the low achievers stuck to recall and using a standard method even when it was problematic to do so. Whereas the high achievers took a different approach. The strategies they employed allowed them to work flexibly and conceptually with numbers. ‘After extensive study of the different strategies that the students used, the researchers concluded that the difference between the high- and low-achieving students was not that the low-achieving students knew less mathematics, but that they were interacting with the mathematics differently. Instead of approaching numbers with flexibility and number sense, they seemed to cling to formal procedures they had learnt. The low-achievers did not know less, they just did not use flexibly – probably because they had been set on the wrong pathway, from an early age, of trying to memorize methods and number facts.' 9 (Boaler 2015)

Unfortunately, students that are deemed as underperforming are given more practice to consolidate their learning. It’s this misdiagnosis and incorrect guidance on how to tackle the “problem” that further cements children’s ‘belief that math success means memorizing methods, not understanding and making sense of situations.’ (Boaler 2016)

Another aspect of brain science that is not fully appreciated or understood in education is that of brain compression. ‘When we learn a new area of mathematics that you know nothing about, it takes up a large space in your brain, as you need to think hard about how it works and how the ideas relate to other ideas. But the mathematics you learned before and know well, such as addition, takes up a small, compact space in your brain. You can use it easily without thinking about it. The process of compression happens because the brain is a highly complex organ with many things to control, and it can focus on only a few uncompressed ideas at any one time. Ideas that are well known are compressed and filed away. Many students do not describe mathematics as a “real joy” – in part because they are not engaging in compression. Notably, the brain can only compress concepts; it cannot compress rules and methods. Therefore, students who do not engage in conceptual thinking and instead approach mathematics as a list of rules to remember are not engaging in the critical process of compression, so their brain is unable to organize and file away ideas; instead, it struggles to hold onto long lists of methods and rules.’ (Boaler, 2016)

Teachers can ensure compression happens by helping their students to approach mathematics conceptually and encouraging children to be flexible when making sense of numbers. As Boaler explains, ‘Research has shown definitively the importance of a growth mindset - the belief that intelligence grows the more you learn, the smarter you get. But to erase math failure we need students to have growth beliefs about themselves and accompany them with growth beliefs about the nature of mathematics and their relation to it. Children need to see math as a conceptual, growth subject that they should think about and make sense of. When students see math as a broad landscape of unexplored puzzles in which they can wander around, asking questions and thinking about relationships and their role as one of thinking about ideas, and making sense of them, they have mathematical mindset.’ (Boaler 2016)

The perils of maths memorisation

9 Boaler, J. What’s math got to do with it? How teachers and parents can transform mathematics learning and inspire success. New York: Penguin. (2015a)

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The majority of schools in the UK rely on ability grouping to help teachers focus and adjust the pace of instruction to suit the needs of students with similar abilities. Grouping allows teachers to provide more positive re-enforcement to children who are struggling, whereas, middle to higher achievers may get more opportunities to explore the theory and apply their skills freely. Supporters of ability grouping believe that it not only helps teachers deliver the best teaching for their students but that it does not compromise students’ ability to achieve.

But is ability grouping fair? One of the main concerns about ability grouping is that teachers take on an idea about the type of learner within those groups, which creates different expectations of children’s learning potential. This can lead to students not being given the chance to use numbers flexibly, relying more on procedural maths learning and practice, rather than providing an environment where they learn conceptually and make mistakes freely, helping to grow their brains. Boaler suggests, ‘The most productive classrooms are those in which students work on complex problems, are encouraged to take risks, and can struggle and fail and still feel good about working on hard problems.’ (2016)

Whilst a lot is done within schools to keep grouping anonymous from students, such as naming groups colours, rather than lower, middle and upper, eventually children realise they are different to others within their class and as they get older they accept they are given different work to do, which can become a self-fulfilling prophecy. Research by Dixon in 2002 suggests that in England 88% of students placed in ability groups (or sets) at the age of 4 remained in the same sets for the rest of their school lives. (Boaler 2016)

A 2004 study by William and Bartholomew analysed data from the General Certificate of Secondary Education and Key Stage 3 tests. ‘The data analysis provided the basis for measuring achievement which is independent of the individual's ability. William and Bartholomew noted that grouping by ability level had little impact on overall Mathematics achievement. Moreover, the group placement produced increments in academic achievement for high-achieving students at the loss of these gains among the low-ability students. Also noted is that performance in mathematics did not vary across school type and ability group placement.’ 10

However, there are also studies that contradict William and Bartholomew’s research that ability grouping does not lead to greater levels of achievement. In fact, ability grouping is one of the most researched topics in education, which suggests how dividing a subject it is within the education community.

To group or not to group?

10 https://www.ukessays.com/essays/education/advantages-and-disadvantages-of-ability-grouping-education-essay.php 2015

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Boaler strongly believes that the key to creating mathematical mindsets is to change the messages in our classrooms.11 She suggests that it’s difficult to create a growth mindset in maths when children are given short, closed, right or wrong questions which play into the notion that maths is a fixed, procedural subject that lacks creativity. Perhaps giving children questions that have space to learn and explore maths conceptually is a better way forward. Combining this with positive, inspirational messages that encourage self-belief and teaching the science behind learning can help nurture growth mindsets in maths.

Changing messages in maths classes

Mistakes are valuable

Maths is about creativity and making sense

Maths class is about learning, not performing

Everyone can learn maths to the

highest level

11 Boaler, Jo. How you can be good at math, and other surprising facts about learning. TEDxStanford. https://www.youtube.com/watch?v=3icoSeGqQtY 2015

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