garethmetcalfe Education General, Maths discussion

Cultural legacy and achievement in maths

This is an exciting time to be involved in maths education, with positive steps being taken to make the curriculum deeper and more conceptual. There’s also a growing awareness that children need to develop a positive self-concept of themselves  as mathematicians and problem-solvers. Our ambition to replicate the mathematical success of East Asian countries has been the driver behind these changes; without doubt there’s a lot that we can learn (and have learnt) from the teaching and learning of maths in these countries.

However, I believe that we can’t look at the success of these Asian nations in mathematics in isolation, without also considering the powerful influence of cultural norms within these countries. This was highlighted very thoughtfully by Malcolm Gladwell in Outliers, a book which studies the roots of success for individuals or groups of people whose achievements sit beyond normal parameters.

Outliers

Gladwell looked specifically at six nations whose results topped the TIMSS international comparison tests for maths – Singapore, South Korea, China, Taiwan, Hong Kong and Japan. Historically, the culture of these five nations were built, Gladwell described, by the tradition and legacy of wet rice agriculture.

Growing rice required extraordinarily precise management of a paddy: irrigation systems needed to be built; water levels had to be precisely managed; the ground must be perfectly flat; seedlings had to be planted and cultivated with great precision. The variability of a yield could be great, and it would be determined by the management of the rice paddy. Gladwell argued that it was this legacy – a culture rooted in the principle of hard, complex work leading to rich rewards – that has led to the phenomenal subsequent success of these Asian countries in mathematics. But how was Gladwell able to draw these conclusions based on the results from the TIMMS tests?

The TIMMS international comparison tests are long and tiresome, being made up of 120 questions. As part of this analysis, the number of questions completed by participants from each country was also analysed. The results were startling. There was an incredibly strong correlation between the number of questions attempted and mathematical attainment. In fact, the results were almost identical: countries with the most successful mathematicians were those who persevered for the longest when completing the test, and vice versa. The data suggested that the willingness to persevere was an unbelievably powerful predictor of success, specifically in maths.

And which countries’ students persevered for the longest? Those whose tradition and culture were shaped by the lessons of rice cultivation. This attitude is neatly exemplified by the Chinese proverb ‘If a man works hard, the land will not be lazy.’ And how richly this principle applies to success in mathematics.

We clearly have a lot to learn pedagogically from the highest performing nations in maths. Importantly, though, I believe that we must also become increasingly proactive in developing positive attitudes towards maths, even if it’s just within our own small circles. After all, we might not be able to control attitudes towards maths at a macro level – but we do have a powerful influence within our own schools. Ultimately, this is a critical factor in determining the extent of children’s achievement in mathematics.

The blog below shows how we have tried to develop a positive mathematical culture within our own school: https://garethmetcalfe.wordpress.com/2014/08/25/establishing-a-mathematical-culture/

garethmetcalfe Maths discussion

Establishing a Mathematical Culture

How can we learn well in maths? Why do some people find mathematics difficult? What does it mean think and act like a mathematician? These are fundamental questions; the way children answer these questions will to a large extent determine their success as mathematicians. I believe, therefore, that we need to have a stronger dialogue with children about the learning process, specific to maths, that will encourage positive learning dispositions. This is what I call ‘Creating a Mathematical Culture’.

Becoming a successful mathematician is far from being a purely mechanical process. Many people (children and adults) are unable to fulfil their potential specifically because of their inability to deal with their emotional response to the challenge/threat posed by mathematics. The importance of mindset to learning outcomes in maths is supported by neuroscience, the analysis of PISA tests (see below) and, I dare say, the personal experience of many of our teachers.

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In my classroom, I aim to establish the following five principles at the start of the year. These are the tenants that I believe are important to building positive attitudes and habits in maths lessons:

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Firstly, the children must be convinced that by working hard they can develop their mathematical ability. Any notion that mathematical intelligence is genetically determined, or unchangeable, must be addressed.

In my maths training, I go into the detail of how I introduce these five principles to the children: what exactly each statement means, evidence to show the importance of each statement and how they can work in this way in daily maths lessons. These principles will be referred to, exemplified and celebrated constantly throughout the year, and no doubt amended also. They give the children the framework for thinking about the learning process in maths (metacognition), and critically help pupils to embrace challenge and learn from mistakes.

I also see my ‘Mathematical Culture’ as being like a promise that I am making to my class: that I am promising them a rich mathematical diet, set in a climate of support and trust. Not only is it a guide for the children, but it is a vision for me as a teacher: setting out explicitly what I value, and a standard that I will aspire to fulfil.