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Complexity matters: the importance of collaboration

Serious number wizards, those for whom advanced calculations are their sole focus, have a fascinating system in which a mathematician can earn the kudos of an ‘Erdős number’. Although it is common to think of academics and researchers as isolated individuals who think, research and write alone, the truth is more complex…

Paul Erdős (pronounced Erdosh) was a prolific and inspirational Jewish-Hungarian maths genius who wandered the globe throughouerdost his academic life searching for mathematical challenges and, according to one commentator, ‘managed to think about more problems than any other mathematician in history’. By the time he died aged eighty-three, Erdős had written nearly 1,500 mathematical academic papers, many of which were co-authored with 511 other mathematicians he directly collaborated with over four continents. This is where Erdős numbers come into play. An Erdős number denotes a link across time and around the world, through academic partnership, back to Paul Erdős*.

The Erdős number system is an acknowledgement of the power of collaboration, and not just to maths-magicians: Erdős numbers are interdisciplinary. Physicists and economists also have Erdos numbers, along with those who study biology, chemistry and medicine. They are a testament to the importance mathematicians and others place on thinking and learning with each other, as opposed to writing and working alone.

a sunday on la grande jatteThis Wednesday at Alma Primary we held a Culture and Creativity Day. Children across the school learnt about the picture ‘A Sunday on La Grande Jatte’, by Georges Seurat. As well as creating their own individual paintings, using a pointillism technique, children in Years 1 and 2 worked together to create dramatic recreations of the image, while children in Year 3 worked with artist Miki Shaw to create a collaborative modern interpretation Seurat’s work. The children told us they found it ‘difficult’ because not everyone agreed, but that they enjoyed sharing ideas, helping each other, collaborating and creating something together.

Our children are growing up in complex societies and communities, but there is a worrying tendency to reduce complex, multi-dimensional issues to simplistic, mono-dimensional questions and binary solutions, which don’t help us, our children or the communities we are part of. Good teachers know that asking simplistic, binary questions produce simplistic and binary answers, which don’t enable children to develop deeper understanding. To develop children’s thinking we need to expose them to complexity and allow them to struggle with problems and difficulties.

Teaching children to appreciate complexity and to collaborate, to seek consensus when part of a group, to find ways to get along with those around them is one of the ways we can support children to thrive in the future. This will enable them to build a better world, a world of consensus rather than conflict and isolation.

It is because collaboration is so important that teachers at Alma Primary seek ways to enable children to work together, to learn from each other and to solve problems in teams or groups. As Erdős numbers highlight, we often achieve our best by working together, rather than through division and isolation.

*To ‘earn’ an Erdős number, someone must co-author a research paper with another person who already has an Erdős number. Paul Erdős himself has an Erdős number of 0 and during his lifetime he directly collaborated with 511 other mathematicians, each of whom have an Erdős number of 1. Those who collaborated with those collaborators have a 2, while those who collaborated with the people who collaborated with Erdos's collaborators have a 3. Anybody else's Erdős number is x + 1 where x is the lowest Erdős number of any co-author. So if Jane collaborated with Freddy who has an Erdős number of 5, then Jane has an Erdős number of 6; if Tony collaborates with Jane (but no-one who has a lower Erdős number) then Tony gets an Erdős number of 7; and if Sammy then co-authors a paper with Tony (but not with Jane or anyone with a lower Erdős number) then she gets an Erdős number of 8.

Thanks to Micha Ben-Gad for introducing and explaining Erdos numbers to me!

This is the first in a series of blogs about 21st century learning curriculum, an approach used at Alma which seeks to provide children with skills and dispositions that go beyond the core curriculum in order to help them make the most of opportunities both in and out of school.

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