Mathematical Sociology... Maths is not just for geeks!

As a mathematician I am often met with the comment:

"I never used maths in my life.  Useless subject!"  

Word of advice:  Not only is that one of the most irritating comments that will drive every maths geek in the world to prove you wrong by citing multiple examples of applied mathematics, but it is so far from true that it's alarming.  It's not just about algebra, trigonometry or calculus.  Its about logical thinking and having the ability to model situations in order to aid our understanding of a complex situation.

Recently I have been reading an amazing maths book which has really deepened my understanding of networked learning - yeah, maths and education #interdisciplinartity.  I hope that this short blog post will  help to illustrate my point.  

("Social network diagram - spokes" by IN 30 MINUTES Guides is licensed under CC BY 2.0)

Imagine two people, Bobby and Billie, represented by two blue dots.  They become good friends, so we join them together with a line to represent the fact thatvthey have a strong bond/relationship.  Bobbie and Billie socialise a lot and develop a group of friends, so more people join the group (the red dots) and start talking.  Individuals in this group might not talk to everyone, but instead might become close friends with one or two other individuals, and that's ok.  But, importantly, the number of connections increases and with each person that joins the group the potential for information exchange and learning  increases.  

This simple mathematical model is called a graph - not in the sense of a bar graph or pie chart, but in the sense of representing the relationships between different points in a network.  In terms of learning theory, what I'm describing is called the Network Effect (Ferguson and Sharples, 2014) which implies that the value of the network increases as more people join because the potential for information exchange increases.   Another closely related theory of learning is Connectivism (which I've written about in previous blog posts).  

There are a number of things for educators to consider there.  

Congestion - the sheer volume of information transferred across the network can be overwhelming.  (Sound familiar?  Anyone one else think their email inbox has never been quite so full).

And...

Closure.  Now this one I really want you to think about!  What happens when no new people are allowed to join the network?  The same information gets cycled round and round within the same network of friends and eventually that information becomes redundant.  Everyone knows everything about everybody else.  Now, think about your professional development!  Have you been stuck in a rut? Looking for new ideas, but wondering wondering what needs to change?  Wondering what you need to do differently?

Here's an interesting story.

Mark Granovetter (1973, as cited by Bonacich and Lu, 2012) was a sociologist and he was working on his PhD in which he wanted to investigate how people got jobs.  Where did the information come from  the lead that would get people a job? He looked at the relationships between the people and his theory was that the information that would lead to people getting a job would come from close friends, family, those strong ties within a person's social network.

When you think about it that would make complete sense - the people who love you the most and the people who you are closest to are most likely to have your best interests at heart.  So they look out for job opportunities for you.  Plausible right?  Wrong!

What do you think he found?  

That's right - because of closure, the same information would cycle round between the same circle of friends, so is it any wonder that they couldn't help each other find new job opportunities.  Much though thats what you might have expected,  that's not where the job opportunities would come from.  The job opportunities came from looking beyond their usual social circle by making new connections.  It wasn't the strong ties in the network that mattered - it was the weak ties, because that's how new information got into the network.  

("Hand-shake" by nicolasnova is licensed under CC BY-NC 2.0)

Remember Bobbie and Billie (the blue dots)?  Well Bobbie was looking for a new job - she was a car mechanic to trade.  She asked around all her friends and there were no opportunities going.  One day Bobbie bumped into an old friend from school, Charlie.  They chatted for a while and Bobbie discovered Charlie's dad owned a garage and was looking to hire mechanic.  It wasn't long before Bobbie landed that new job with Charlie's dad.  

I've recently started a new module in my studies with the Open University #H818 and it's called The Networked Practitioner.  Reading about the work of Mark Granovetter has really made me realise the importance of openness and networking both on a professional and personal level.  But I also wanted to share this because I think its something that perhaps we need to highlight to our students - the importance of networking, both physical and online, and the need to nurture both the strong and the weak ties in our personal learning or social networks.

Think about all those students who join your class and who might have a very close circle of friends.  A clique perhaps?  Is that not closure by definition?  Think about those students who might come in to class and just sit quietly, not speaking, doing their work, getting good grades.  What's the rest of the class missing out on by not getting to know that student?  What's that student missing out on by not talking to the others in the class?  What can we as educators do better to facilitate that peer to peer connection?

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@McintoshMclean.

References

Bonacich, P. And Lu, P. (2012) Introduction to Mathematical Sociology.  Oxfordshire, Princeton University Press.  

Ferguson, R. And Sharples, M. (2014)  Innovative Pedagogy at Massive Scale:  Teaching and Learning in MOOCs [Online].  Available at:  https://www.researchgate.net/publication/300360641_Innovative_Pedagogy_at_Massive_Scale_Teaching_and_Learning_in_MOOCs (Accessed 8th November 2020).