What is the Point of Algebra?
As a teacher of the dark art of algebra I am often asked what the point is and I can understand why not everyone sees a purpose to using letters instead of numbers and then creating complicated names like “second order differentials” to completely bamboozle students.
Personally I love algebra (also known as “pure” maths at A-level) and there could be no purpose whatsoever and I would still enjoy it. But the truth is that what transforms maths from the mundane to the answer-to-everything is algebra. With numbers you can calculate how much your shopping will cost and what you owe the taxman but with algebra you can unlock the secrets of the universe.
The power of algebra is that by replacing numbers with letters we are able to generalise to infinite possibilities or to find the single answer that solves a complex problem. It is used by scientists and engineers to understand the world around us and to create new technology.
Maths is very similar to a language, its symbols are shorthand for words; “+” means “add” for example. The shorthand language allows mathematicians to represent problems that would require pages of writing in a concise and efficient way that is understood around the world. When we use algebra we are adding new “words” to that language. Instead of saying “What number would I times by two and add five to get thirteen” I write 2x+5=13. You can read more about the language of algebra and its history at Science4All.
2x+5=13 is an example of an equation with only one answer (x=4) but algebra can also be used to generalise to any number and this type of algebra is used for proof and formulae. The simple proof n+(n+1)=2n+1 shows that when I add any two consecutive numbers n and n+1 I will always get an odd number 2n+1 (because 2n must be even). By replacing “any number” by “n” I open up infinite proofs and solutions.
You can find out more about why x is used for an unknown in this TED talk:
There is a problem with GCSE level algebra though and that is that some of the skills are learnt in isolation of their purpose which is a bit like getting someone to practise their tennis serve over and over again without ever teaching them the rules of the whole game or letting them see a match. So it’s understandable that many students and parents don’t see the point.
Ultimately algebra can be enjoyed as a problem solving activity in its own right – a brain exercise if you like – but it is nevertheless a powerful tool in the hands of a mathematician, engineer or scientist.
