It seems to be okay to say you are useless at maths, and it’s even becoming fashionable. Sure if you’re bad at maths, it may mean you’re creative, the argument goes. Many people feel being literate is extremely important, but that being innumerate or “mathematically illiterate” is not a problem. They feel defeated by maths, hate the subject and pass this hatred in an unreasonable way on to their children and others around them.
The response to this attitude could be: “And were you no good at reading and writing as well?’’ But this is not the way to win friends and influence people.
And yet, recent research makes the striking point that we are not born to read and our brains are hard-wired to speak and to understand mathematical concepts. To read, symbols must be recognised. These symbols are used to create words, and sentences are constructed from the words.
In mathematics, symbols must be recognised; these symbols are used to create mathematical expressions, and these expressions are manipulated to draw conclusions and make other constructions.
A difference between numbers and letters is that we need to be able to read, but the world may not – but should – be bothered that we can’t do mathematics. Politicians don’t mind if we buy their phoney statistics, and banks like it that we can’t understand the different types of mortgage interest payments.
We all have the “maths gene”, and studies have demonstrated how everyone, unless he or she has some physical damage to a certain part of the brain, can understand and do maths to a reasonable level. Maths is not hard, it’s just that we don’t do it enough. If, however, you use the maths part of your brain, it comes to life.
The difference between hating maths and loving it can be a matter of practice. As with many things, success breeds success, whereas failure leads to dislike.
The evidence is clear. It’s not that people can’t think mathematically; it’s that they have enormous trouble doing it in a decontextualised, abstract setting. Arithmetic is important, but mathematics is much more than simple arithmetic, and the exciting parts lie beyond this.
We are not, it seems, pushing people beyond numeracy to the really exciting bits. In languages, people become motivated by exposure to great literature. It is possible to expose people to great mathematics by pointing out where it all leads and why it is so fundamental nowadays.
Google is a fundamental mathematical abstract object consisting of a huge matrix, with certain mathematical properties set up so it can respond in the wonderful way it does. We don’t need to know all the details of how it works, but we should know something about it and how to interpret its results; people working in the area must know the full details.
Google is a big employer in Ireland, as are software and financial companies. All of them need people with fundamental mathematical knowledge and experience.
Down the mathematical rabbit hole
“Then you should say what you mean,” the March Hare went on. “I do,” Alice hastily replied; “at least – at least I mean what I say – that’s the same thing, you know.”
“Not the same thing a bit,” said the Hatter. “You might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see!’ ”
Charles Dodgson (1832-1898), an Oxford mathematics professor, wrote Alice’s Adventures in Wonderland in 1865 under the pen name “Lewis Carroll”. The book is full of such play on the use and misuse of mathematics and its logic.
Charles Babbage (1791-1871), a mathematician who originated the concept of a programmable computer, is quoted as follows: “On two occasions I have been asked [by members of parliament], ‘Pray, Mr Babbage, if you put into the machine wrong figures, will the right answers come out?’ I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.’’
Easy to fool people
If people don’t know a language, then it is easy to fool them in that language. By “language” here we mean the language and logic of mathematics.
Recessions and blips in the markets can be caused by allowing computers to interpret mathematical or statistical results without understanding what they mean. How much oil is gushing into the gulf compared to the gulf itself? What figures are used and how are these devised?
A report claimed “a 300 per cent decrease in profits’’ when profits in an area went from ¤ 100 million to ¤25 million. Going from 25 to 100 does indeed represent an increase of 300 per cent, but going from 100 to 25 is a decrease of 75 per cent.
Another report headlined “42 per cent of those killed in vehicles were not wearing seat belts”, a conclusion reached from the given facts that 16 per cent of drivers killed were not wearing seat belts and that 26 per cent of passengers killed were not wearing them.
These are basic misunderstandings of fractions and percentages, which are prevalent. Innumeracy in society, leading to false misrepresentations and false conclusions, is now common.
The “knowledge-based society” to which we aspire depends fundamentally on mathematical methods and techniques. Lack of lateral thinking and problem-solving abilities in the workforce has made it difficult to establish this knowledge-based society. Yet, in an effort to appease those who don’t “like” maths – and, indeed, to encourage people into areas that actually need maths – quotes such as “This involves problem solving ability but not mathematics’’ are published.
Solving sudoku puzzles is a mathematical recreation that, although not involving arithmetic, involves extensive use of the math gene.
It’s important to change the public perception of mathematics. It is vitally important for the public to understand more about mathematics, where it leads and why it is important.
If our attitudes don’t change, we will find ourselves near the bottom of the league, and, as a consequence, international confidence in our society will wane and our economy and future will suffer. We badly need a National Numeracy Trust.
Ted Hurley is professor (emeritus) of mathematics at National University of Ireland Galway