# Don't forget the formula

Michael Brimicombe makes a plea for secondary science teachers to say it with symbols

Only students capable of attaining grades B, A and A* at GCSE can understand symbolic equations. Or so says the Qualifications and Curriculum Authority, which has decreed that only word equations will be examined at grade C and below. Since the majority of students are at grade C and below, what happens when the curriculum is crowded? That's right. Symbolic formulae go on the back burner and words take front stage.

But science at key stages 3 and 4 is full of numbers and patterns of numbers. Take the following:

* burning methane in oxygen. The volume of oxygen consumed is always twice the volume of methane, at the same temperature and pressure; * rolling a ball down a ramp. The distance it moves quadruples as the time doubles, if the speed is small enough; * mating a blue-eyed person with a brown-eyed one whose parents also have brown eyes. On average, one quarter of their offspring will be blue-eyed.

Patterns, patterns everywhere. The world is not magic; it can be predicted. Science teachers use maths to keep numbers under control, and we use symbolic algebra to encapsulate patterns.

Consider a chemical equation: CH4 + 2O2 -

CO2 + 2H2O.

There is a lot of information in the equation. The formula for each molecule, of course, tells you about the quantities and types of atoms it contains. It reminds you that a chemical reaction is a bit like shuffling a deck of cards; you can combine the cards in many different ways, but you can't change the cards themselves.

The equation as a whole tells you the ratio in which the reactants combine. The extra dimension of relative atomic masses allows the exact prediction of the amount of products from a given quantity of reactants.

All that in a simple equation.

Of course, to extract the information from the equation requires training. You need to understand the difference between an atom and a molecule. You need to know that C means carbon, that H means hydrogen and that O means oxygen. You need to know the significance of the numbers, and how full height numbers are different from subscripts.

Even if you don't fully grasp these ideas, at least the equation tells you that the combustion of methane involves two things (phonetically called "see-aitch-four" and "oh-two") reacting to make two other things ("see-oh-two" and "aitch-two-oh").

Now compare the symbolic equation with the word equation for the same reaction.

methane + oxygen -

carbon dioxide + water To my eyes, this says only that one named substance combines with another to create two more named substances. There is no pattern, no logic, no inner meaning. Just words. You might as well replace methane with "see-aitch-four".

A formula may seem forbidding, but it also has precision, economy and mystique. It communicates on several levels.

The use of names, on the contrary, breeds familiarity - and ambiguity. For example, my full title is Dr Michael Brimicombe. My wife usually calls me Micky, reserving Michael for when she is angry. Many overly familiar colleagues at work call me Mike. My students call me Sir or Doc Brim. Their parents invariably call me Dr Brimicombe. The name you use depends on your level of acquaintance. (You can call me Michael.) This is also true of chemistry. Why use two words, when one will do? Many weak students assume that they can safely refer to potassium hydroxide as potassium (or as hydroxide). A dangerous pastime, particularly if they propose diluting it with water. They wouldn't attempt to do it if they only knew and understood the formula KOH (and called it "kay-oh-aitch").

I'm a physics teacher, although I've done my share of teaching chemistry. Physics is famous for its formulae. As Galileo discovered, a ball rolling down a plane obeys the equation: S = 12 at 2.

This mathematical model allows science to do what it does best: make precise predictions which can be tested by experiment. This formula, and others discovered by Newton to describe the motion of objects, have successfully predicted the outcomes of experiments for the past 300 years. They allow modern industry confidently to invest millions of pounds in placing communciations satellites in precise orbits around the Earth.

The minimum number of useful variables in a physics formula is three (think about it). QCA, once again, has implied through GCSE syllabuses that the majority of our students (grade C and below) cannot transpose a formula. That is, they are incapable of converting V = IR into R = VI.

So we don't teach formula manipulation any more. Our maths colleagues gave up long ago, when the national curriculum told them that most of their pupils wouldn't be able to cope with it.

Yet science is nothing without numbers. At key stages 3 and 4, students should be exposed to the full force of formulae, equations and mathematical modelling in science. Mathematics teaching often seems to have its own agenda (maths for its own sake), and science teachers (particularly at A-level) often find that they have to teach the maths they need as well as the science.

Perhaps it's time that the science teaching fraternity faced facts and accepted this. Perhaps we could also be brave and assume that most of our customers can be taught to understand symbolic algebra to a useful level. It's a shame, because we will then have less time to deal with the social, economic and environmental issues surrounding science. Which will leave GCSE science as dry and unpalatable as it ever was.

Michael Brimicombe is head of science at Cedars Upper School, Leighton Buzzard, Bedfordshire, and a principal examiner for GCSE science and physics A-level

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