Mathematics, modelling and application of number

Geoff is Professor of Mathematics Education and convener of the Centre for Research in Mathematics Education. He directs and contributes to a substantial portfolio of research. Before joining in 2011 he worked as Senior Research Fellow/Lecturer/Senior lecturer in Mathematics Education for almost twenty years.

Before this he had been teaching in school and college for eleven years. Geoff's main area of research has involved applications of mathematics and mathematical modelling at all levels. Notably he has worked on substantial research projects that have explored the use of mathematics in workplaces, mathematics in transition from school/college to STEM courses in university and teaching and learning of modelling/problem solving in the secondary school curriculum.

Therefore we were very excited to learn that he had time to talk with the Maths Scholars scheme.

We kicked off by discussing his research. He has been promoting the application of maths in a number of different ways including Assessment and Curriculum development.

Geoff Wake Professor of Mathematics Education University of Nottingham
Geoff Wake Professor of Mathematics Education University of Nottingham

‘I feel that through my writing I’ve come to be labeled as someone who ‘does modelling’. That’s not entirely the case but I feel I have to promote it as it gets much less press and interest than Pure Maths usually does. I felt that no one fights its corner.’

Geoff is obviously passionate about what he does. In fact the Maths scholars scheme follow his Twitter account very closely. There is always much to learn from Geoff’s perspective.

Here are just a few examples of recent tweets:

In maths we continue to have a curriculum focused on content without capturing the essence of what it means to do and apply mathematics

Discussing characteristics of inquiry based maths & science learning this morning Do these apply in your classroom?

What’s your view of the Pisa test results?

Let's not have Grammar Schools at all - forget this nonsense from our unelected PM. Get politics out of education in 2017.

Learn about vectors if you want to be involved in movie special effects like those in the new Jungle Book

How much has the maths curriculum changed since you were at school? Much less than in sciences and other subjects I would suggest.

So you can see it was always going to be a rollercoaster of a ride when you ask Geoff Wake for an interview! He was certainly keen to talk about the knowledge-based curriculum.

“I feel that the emphasis has been on defining content and little about how learners would deal with this. I am labeled as someone who pursues application but really I am interested in people being involved in ‘doing mathematics’. I think the curriculum has gone down the route of atomizing things.’

‘For me kids need to see there is some way that maths leads to something that has utility and purpose.’

I want teachers to say: ‘ hey kids it’s not all abstract.

For example, to be an animator you will have to understand computer interfaces and use vectors all the time. I want them to have seen maths as something different but applicable with in their context. That way of thinking is important. It’s interesting because vectors are the most difficult concepts. Students often find them really difficult. If we can find a way to change the thinking it will help. Maths in context is so valuable’

We asked him what he thought the current challenges might be and the fact Maths has always been a core subject that everyone needs to study.’

Geoff Wake talks to the Maths Scholars scheme  

Geoff Wake talks to the Maths Scholars scheme

‘Other subjects are not compulsory and therefore have to work hard to attract students. Maths is privileged as it’s part of what you have to do. So we need to ask ourselves: if we’d had to attract kids why would they choose to do maths? After all, for some it’s inherently interesting, but not for others.’

Geoff Wake talks to the Maths Scholars scheme

It’s certainly worth considering and there is so much to offer students studying maths today. Mind you it’s not just maths departments in school that need to promote themselves.’

100 lessons available

The University of Nottingham

‘In Nottingham we have been doing some research on design work. But we too are bad at promoting ourselves. That is odd because we do very influential work in the US for example. We are currently involved in a project funded by the Gates Foundation. We have designed 100 lessons. There have been 6 million downloads of those lesson plans that are carefully redesigned and researched. It is an iterative approach to getting things right led by Malcolm Swann. This has been achieved over a substantial period and underpins our desire to have a coherence and connection between lessons and pedagogy. This is controversial I know but many teachers go to publications like the TES and download information. It’s what I call rather pejoratively, I know, as the jumble sale approach because it’s a bit of this and a bit of that. I want to see coherence in the curriculum. That’s what’s missing.’

Avoid the ‘jumble sale’ approach

‘Of course I know why this happens and I have great respect for teachers who have lots to do in short time. They spend more time marking than planning. Having worked with groups of teachers in Japan they using lesson study to research practice in classrooms and they spend hours planning. It’s the same as the Shanghai teachers. It’s a planned program but It’s coherent and not all about curriculum. The Shanghai teachers take standard materials and adapt them slightly but it’s better than going to a jumble sale!

Here you can see why teachers need materials on an ad hoc basis. Priorities are wrong at structural level and they suffer. The Shanghai teachers’ context is very different. Their emphasis is on becoming an expert teacher. Anyone with fewer than 10 years teaching cannot be a Shanghai teacher. There is a respect and value in developing expertise.

Of course context is all. At Nottingham we have worked on two European funded projects that represent very different cultural setting and enquiry means different things. It’s hard therefore to give a definition because it’s different depending where you are.

Students should be questioning, curious and critical

The thing that is important is to develop enquiring minds. It is possible to have a very procedural lesson but with the students being very curious and critical. If the students are very questioning it would change the result. It wouldn’t be an open free for all but a disciplined exploration. Let’s remember, the Japanese are working with us because they want to find out how we develop more independent learners so it’s not all one way.  If we didn’t have creativity in the UK just where would we be going?

Our creativity and independence is attractive

On the one hand Japanese teachers are surprised at the lack of ability in our students but really value our creativity and independence. They do have problem solving lessons in Japan but with a different approach.

They are well designed and working on one problem. In addition they do assess their teachers by observing for development of teaching expertise. They also craft lesson to principles. Therefore they do well in internal and international tests.

The thing is we need iterative change.

A big bang change wont work probably as we have a natural tendency to be conservative. But what I would say is we do need to redesign the curriculum so it’s not divided up into subject areas. We need to ask ourselves: what is it that we need people to be able to do with maths? WE can’t continue with the teaching to a module philosophy where students cram and then forget.

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