# Global spin-offs

Teaming up with the maths department could make the world of difference togeography teachers, says David R Wright.

The globe is "chopped up" in the national curriculum, with maths, geography and science all claiming part of it. But pupils need to make sense of the globe as a whole. These ideas may help get discussion going between geographers and mathematicians.

The understanding of the mathematics of our planet starts very well in the reception class. Four-year-olds throw and try to catch a ball: they can discover the shape of our planet. They soon learn that this shape is called a sphere, and discover that it is the same shape from all viewpoints. Later on, when they try to spin a top, they get the idea of an axis. They even think about people not "falling off" the globe in Australia - a start to understanding gravity. All of this is excellent and fully accurate: these are three-dimensional experiences which represent our globe effectively.

But two-dimensional pieces of paper soon take priority over three-dimensional experiences. This creates huge problems - for all of us. Even the curriculum experts make serious mistakes. The world map in the original national curriculum contained an elementary error: it was described as "equal-area" when northern areas were in fact hugely exaggerated in size. The error was never corrected. The second (post-Dearing) national curriculum world map had an even more spectacular error: North is shown in the wrong direction!

With "help" of this sort from the experts, no wonder teachers and pupils misunderstand our planet.

Clearly, we need help from the people who understand the maths of our planet. Specifically, it is the surface area of a sphere that we need to understand.

Simple questions of distance and size need some ideas from maths. In France, pupils know that there are 10,000 kilometres from equator to pole (true within one per cent). (Why do they? See box: Metric system.) They also know that 20,000 kilometres - the "pole-to-pole" distance - is a typical distance for a car to travel in a single year. In the UK, we keep our car-mileage (and our pollution) in a different "pigeon-hole" from our global understanding. Twenty thousand kilometres is 12,500 miles: most cars in the staff car park have "circled the world" several times - and so have millions of other cars on the same small planet. Mathematical hard facts can be more powerful than "eco-doom" messages.

This 10,000 km figure can give us another memorable image: divide by 90 (the number of degrees from equator to pole) and we get 111.111 km - about 70 miles - between each degree of latitude. If there was a straight, flat, north-south motorway, each degree would take an hour by car. Pole to equator is 90 hours of that kind of motorway driving: less than four days by car. It really is a small planet for six billion people. Hard facts and easy calculations make the point.

Still with straight lines - the "great circle" routes are so easy, so important - and so rarely understood. There can hardly be an easier task than stretching a piece of string, on a globe, from A to B. This instantly gives the most direct air route, and a comparison with any other distance from point A. And, because the globe must be all at the same scale, the measurement of distance is quite easy, too. All that is needed is a set of globes for classroom use. Somehow, few geography teachers have ever managed this. Can maths teachers help us? This could lead to a huge increase in global understanding.

Angles on a globe are intriguing. We all know that angles in a triangle add up to 180x. But on a globe, we have three right-angles in a "triangle" (see Fig. 1). Clearly "spherical geometry" has its own rules - but it does go some way to explaining the problems of putting the round world on to a flat map. Peeling an orange is a good way of illustrating the problems - but this "triangle" clarifies the maths very well, even though only one-eighth of the earth's surface appears on this diagram. Suddenly "interrupted" world maps seem to make good sense (Fig. 2).

There are some other mysteries that mathematicians can help us with. How to explain latitude? Imagine a transparent globe and a little man with a protractor at the centre of it (see Fig. 3). He points his arm along an angle from his protractor, say at 30 degrees.Then he holds his fingertip in place as the earth spins and, hey presto! you have the 30 degree parallel of latitude. But the pupils say, "Hey, the earth is hot at its core!" Is there another way of explaining latitude simply? Do we have to bring in the sun and stars and angles of declination, as early sailors did?

The "key diagram" of day and night and the seasons has now become part of the science curriculum. In essence it is a mathematical diagram; its consequences are a core element in geographical understanding. It can confuse, yet the maths is not complex: straight lines (the sun's rays) hit a spinning sphere (the earth), and that sphere rotates round the light-source (the sun). (Fig. 4.) Latitude is far more than merely the means of locating a place. If we know the latitude of a place, we know how much daylight there is, how strong the sun is. Then we can find out how this affects what crops grow. Few things are more important than that.

These kinds of cross-curricular links can also help when we consider the surface area of a sphere. How big are the tropics? In distance, our pole to equator journey is roughly a quarter Arctic; half temperate; quarter Tropical - so simple. But pupils could then assume - wrongly - that the world is only a quarter tropical. We need maths to explain that the surface area of the Tropics (see Definitions, right) is much bigger than the Arctic and Antarctic together.

Our planet needs us all to care for it, and deserves a place in every curriculum. Maths has a key role in this vital task. In an ideal world, maths, science and geography teachers would find the time to talk about how we fit our planet into our curriculum. Meanwhile, we can all contribute to understanding our globe. Isn't it the most important theme for the Millennium?

David Wright is co-author of Philip's Children's Atlas and author of Philip'sWWF Environment Atlas. He was a teacher trainer in Norwich, and is now a school inspector

* DEFINITIONS

Latitude: is measured from the equator (0 degrees) and is numbered to the poles (each 90 degrees). Latitude lines are made by circles that run parallel to the equator and get progressively smaller as they near the poles.

Longitude: is measured from the Prime Meridian (running through Greenwich, England and nominated in 1884), numbered East and West. Longitude lines are made by circles that intersect with both the North and South poles.

Lines of latitude and longitude are used to locate points on the earth's surface.

Tropics: The sun is overhead at the Tropic of Cancer (23 12 degrees North) at noon on June 21; it is overhead at the Tropic of Capricorn (23 12 degrees South) at noon on December 21. The Tropics is everything in between those latitudes.

Arctic and Antarctic: From the Arctic Circle (66 12 degrees North) to the North Pole on December 21 there is no sunlight; from the Antarctic Circle (66 12 degrees South) to the South Pole on June 21 there is no sunlight.

* METRIC SYSTEM

In 1795 the revolutionary Republic of France adopted the recommendations of the Academy of Sciences for new units of length, mass, area, volume and time and instituted its "metrique" system.

A metre, its name derived from the Greek metron, "measure", was decreed equal to one-ten millionth of the length of thearc from the equator to the North Pole, or a quadrant of the earth's meridiancircle.

Although the metric system - also incorporating the kilogram and litre - fell out of favour with the empire of Napoleon, it was reinstated in France in 1840 and has since spread over the world - apart from the United States.

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