Despite years of research and numerous studies about transferability of skills the teaching and learning of mathematics continues to be a problem. Students are still all too frequently unable to apply their mathematical knowledge and skills outside the confines of the mathematics classroom. Many of them simply do not recognise external situations where a mathematical model would come in handy.
Students (and some non-specialist teachers) often have very fixed preconceptions about what “mathematics” is. In their minds it usually involves a nice sharp, pencil, some squared paper and a long list of calculations to be completed. When I point out that organising events, planning a journey, working out unit costs, etc, are valid mathematical activities the response is often “that’s not ‘proper’ mathematics”.
Outside of education or specific job roles mathematics rarely appears in its pure form. I neither need nor particularly want to calculate the height of a lamppost as I walk down the street or find the angle of elevation of a lighthouse on the rare occasion that I find myself standing on a cliff staring out to sea. However, I do want to know whether I’ll save enough to make it worth driving to the cheap petrol station before I fill my car up at the more expensive one nearby.
So, one way to broaden this mindset and help answer the eternal question of “when will I ever need this” is to set the mathematics within a context. There are two ways of approaching this; we can either mathematise everyday situations or start with the mathematics and apply it to the everyday. However, both of these approaches have pros and cons.
If you start with an everyday situation such as ‘shopping’ and search for the mathematics you can generally find lots of lower level number skills such as arithmetic, percentages and so on. You can easily include ratio and proportion by comparing the cost of your favourite cheese especially as some are sneakily priced per 100g and other per kg. You can take it even further if you start comparing the cost of apples and pears when the apples are costed per kg but the pears are priced individually. The only problem is that I’m not sure that anyone except a mathematics teacher would ever think or even want to do this and I know I’ve certainly got some strange looks in supermarkets while scribbling out my calculations, I certainly can’t see it grabbing the imagination of most 14 year olds!
It’s more difficult to find a realistic context that involves higher-order or some of the more esoteric aspects of mathematics. If I start looking to apply simultaneous equations I might think of comparing energy tariffs or mobile phone contracts, but all my students would simply use comparison websites. In the real world simultaneous equations are used for Radar collision avoidance and missile guided systems but these are probably beyond all but the very brightest of year 10s. Contexts that don’t push at least some of the authentic, useful, relevant, motivating and realistic buttons really aren’t worth using. They’re no better than the lighthouse example I referred to earlier, which was and remains one of my pet hates from my own school days.
Despite what the mirror says, I’m still 21 in my head and always will be…but I’m not a teenager and I can’t think like one. The big problem with using contexts is that what might be an everyday realistic situation for me simply isn’t so for them. The majority of teenagers are preoccupied with clothes, social media, peer culture, relationships, family issues etc not all of which lend themselves easily to a spot of engaging mathematical modelling!
Well chosen contexts can be really helpful but if they’re not related in some way to the experience of the young person then they can simply obfuscate the mathematics yet further. A classic example being a higher-level GCSE question about an electricity bill. Students were given the new and old meter readings and the price per unit in pence and asked to calculate the cost in pounds. The mathematics is quite simple but from the examiner’s report it is clear that a large majority of students simply failed to understand what they were supposed to do with the figures. I doubt that many 16 year olds have ever looked at let alone read an electric meter.
Research from Byron (2009) for the now defunct BECTA showed that 82% of parents felt excluded from their children’s school day. Contexts that parents/carers can relate to coupled with homework activities might help to broaden the students’ experience and help some parents to be more engaged in their learning.
However, not everyone agrees that contexts are always a “good thing” – in 2008 Marcus du Sautoy said that that “an attempt to make the mathematics more “relevant” has ended up just making it boring.”
One alternative to contexts is using rich tasks, but that’s a topic for another day…
Teaching Entry Level Maths
Key Stage 3 Maths for Non-Specialists
Ensuring Challenge in the ‘Top Set’ Maths Classroom
Maths GCSE: High Impact Teaching Ideas
Teaching the New Secondary Curriculum in Maths with Confidence and Creativity
References and useful links
Byron, T (2009) “Oh Nothing Much Report: The value of after School conversation.” BECTA,
du Sautoy, M. (2008) “Without big maths stories our numbers are plummeting”
The Guardian, Tuesday 3 June 2008
National Centre for Excellence in the Teaching of Mathematics (2009)
Parent power to improve pupils’ potential.
Centre for Innovation in Mathematics Teaching
Cre8ate Maths – Mathematical, Motivational & Memorable
Written by Vanessa Bailey
Vanessa is a fully qualified Mathematics teacher and education professional with a broad and varied range of knowledge and expertise with a degree in Mathematics and a Masters in Education Management.
She has been a Head of Mathematics in a secondary school in North-East London and worked in further education and the public and voluntary sectors. She currently teaches part-time in FE and is a freelance course writer, trainer, blogger and general education adviser.
Vanessa is an accredited Professional Development Lead for the National Centre for Excellence in Teaching Mathematics (NCETM) and has designed and delivered a wide range of CPD events, which receive consistently high levels of positive feedback. She has also developed a wide range of teaching materials and resources; including contributions to published mathematics and business resources.