Maths - Imagine all the people

22nd February 2013 at 00:00
Population growth provides interesting models for study

As a fresh-faced young guitarist, I once helped to stage an original student musical, innocently called Grass. Drugs played no part in it; the story revolved around a country whose main energy source was, well, grass. The writers were boldly aiming to create a parable on the topic of ecology and at the time my friends were baffled that I should be taking an interest in green politics. "It's a fringe movement that will peter out," they said. This was back in 1979. I can now glumly say: "We told you so."

Green issues are everywhere. We have our first Green Party MP; in fact, we have a "green" version of almost everything. We might ask: is there such a thing as "green mathematics"? The internet tells us that such a phenomenon is indeed emerging.

We are told that economics prior to the current century sometimes made implicit assumptions that are now seen as unjustified - for example, that the earth's resources are virtually limitless, and that the effects of climate change are negligible. Economics needs a rewrite. Maths is "purer": Pythagoras' theorem is a universal truth regardless of how profligate humankind is. But take A-level mathematical modelling, for example - we make assumptions here, too. We also choose the questions we pick to study, and we could focus on greener, more urgent topics.

One such area is population growth. The United Nations has three projections for the world population in 2100: high, at 14 billion; medium, at 9.1 billion; and low, at 5.5 billion (see page 27 at bit.lydnegG2). The eventual outcome will be the sum of myriad human choices, and the consequences are critical.

At A level, differential equations are part of the Core 4 syllabus for Mathematics in Education and Industry (MEI), including the exponential growth and decay of populations. To refine these models, progress to the logistic equation - a subtler way to simulate population growth. This makes an excellent introduction to the maths of chaos and the butterfly effect. For helpful resources, accessible to top Year 11s, try the Chaotic Population activity on the Nuffield Foundation website. A spreadsheet does the tricky calculations for you (bit.lyVbb2Rr).

The MEI further maths syllabus includes a differential equations module, where population growth within predator-prey systems is considered. The Nrich site also has wonderful population growth resources, which start modestly before becoming something to stretch the very brightest (nrich.maths.org7827).

Population is an emotive issue. China's one-child policy, for example, can be defended or attacked with great vigour. A recent book on the ideal number of children in a Western family was called Maybe One. Parents of large families resent being told to think this way. We need to ensure that the maths we construct about the situation is as truthful as possible.

Jonny Griffiths teaches maths at a sixth-form college in Norfolk

What else?

Carry out a green classroom audit with this activity from California Academy of Sciences. Help pupils to work together to establish new environmentally friendly practices.


How much do social and economic policies affect the environment? Encourage group discussion and consider the economics behind issues of sustainability with pladley's Venn diagram.


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