Everyone can do maths – the research proves it

BY DR J LIEBENBERG
Neuroplasticity is the ability of the brain to grow new neural pathways.

It happens when we are exposed to new knowledge, have new experiences and master new skills. As these new neural pathways form, we are increasingly able to complete tasks (like mathematics problems) which we were unable to master before. As Jo Boaler1 puts it, this means that students’ brains “can adapt and grow in response to any learning opportunity, and ideas that some students are not capable of learning high-level content should be rejected”. This is a very strong claim and it means that any student is capable of mastering school mathematics. But why is this so different from our real life and real classroom experiences, and how can we change that?

Belief about ability determines success, irrespective of ability

The work of Carol Dweck2 on mindset is well-known. Significantly, her research has shown that our success is more a result of our mindset and effort than of our genes. Simply put, if students believe they have a limited, fixed capability for mathematics they will perform accordingly. However, the
opposite happens if they have a growth mindset, believing through practice and effort they are able to overcome obstacles. The research on this is sound, but the problem is that if parents and teachers do not know this they will use test results to judge students’ capabilities, ultimately leading to practices like sidelining students from mathematics to mathematical literacy.

Mistakes and struggles lead to success and
do not indicate a lack of capability

This point is based on research4 that shows that students with a growth mindset react differently to mistakes than those with a fixed mindset. Students, especially those with a growth mindset, learn and master content as they make mistakes and struggle. The authors remark: “We have therefore shown that growth-minded individuals are characterised by superior functionality of a very basic self-monitoring and control system”. This article shows clearly that a growth mindset is not simply a touchy-feely concept, but that it has an actual impact on brain activity. In order to get students to grow their capabilities, we need to provide them with open-ended problems where they do not mainly get it correct. It ties in closely with what Bjork (1994) calls desirable difficulties,5 and the fact that students seem to learn better and understand more deeply if they are presented with work that provides significant challenges. The challenge for mathematics teachers and parents, is to not get fooled into believing that students who only get their “maths right” after multiple attempts, are not quite as capable as those who get it right the first time. It is likely that it will turn out later that the ‘slower’ learners actually grasped their mathematics at a deeper level than their counterparts.

Speedy completion of mathematics problems
does not imply superior capability

The prevailing view among parents and teachers alike is that “quick = clever” and “slow = not so clever”. This view is held about most subjects, but especially so for mathematics, with many tests or quizzes designed to force students to provide their answers as quickly as possible. However, this is a completely mistaken view of reality, and perhaps one of the most well-known examples to the contrary is the 1950 Fields medal winner for Mathematics, Laurent Schwartz, who famously remarked in his autobiography:
I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully. Towards the end of the eleventh Grade, I secretly thought of myself as stupid. I worried about this fora long time. I’m still just as slow. At the end of the eleventh Grade, I took the measure of the situation and came to the conclusion that rapidity doesn’t have a precise relation to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant.

Parental and classroom language can make or break students

The focus here is on well-intentioned language that is nevertheless harmful because it conveys and perpetuates a mistaken view of intelligence – again mostly tied to fixed mindsets. For example, Dweck and colleagues (1998)7 have shown that praising students for being smart rather than for working hard has the exact opposite effect of what one might expect. When the students she studied had the opportunity to choose between a difficult or easy task, after the smart or hard work comments, more than 90% of the smart-labelled group chose the easy task, while the majority of the hard- work labelled group chose the difficult task.
In a 2012 study by David Scott Yeager,8 he and his colleagues divided high school students into two groups with both groups receiving critical feedback after a test, but the feedback from one group (without the teachers knowing the identity of the students) included the sentence: “I am giving you this feedback because I believe in you”. A year later, those students performed better in tests than those who did not have this sentence added to their feedback. Language matters, and this is just as true for mathematics as for any other subject. The point is, are we willing to accept the research and start acting accordingly?

But what about common sense?

For most of us, the idea that everyone can master mathematics goes completely against our common sense understanding and experience of the world. It just does not seem to tie in with what we “know” from experience to be true. However, if we are unwilling to accept the research, it simply shows our own difficulty in changing deeply ingrained beliefs.

Dr J (Lieb) Liebenberg is the CEO of ITSI.

References:
1. See: https://ed.stanford.edu/faculty/joboaler
2. See: https://fs.blog/2015/03/carol-dweck-mindset/
3. Everyone may not want to do mathematics. I am not advocating we should
force everyone to do mathematics – just that we should not allow misconceptions to determine how we think and act about students and mathematics.
4. See: https://journals.sagepub.com/doi/10.1177/0956797611419520
5. See: https://bjorklab.psych.ucla.edu/wp-ontent/uploads/sites/13/2016/04/
EBjork_RBjork_2011.pdf
6. Schwartz, L. (2001) A Mathematician Grappling with His Century. Basel: Birkhäuser.
7. See: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.583.9142& rep=rep1&type=pdf and http://mereworth.kent.sch.uk/wp- content/uploads/2015/04/growth_mindsets_dweck-praise-effort.pdf
8. See: https://www.apa.org/pubs/journals/releases/xge-a0033906.pdf

Category: Winter 2019

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