Q: Maths often used to be seen as an inaccessible, dreary and boring subject, something to be endured rather than enjoyed. Has its image changed over the decades?
A: I don’t think many of the students or parents at RGS believe this but maths in the wider world is often seen as inaccessible and therefore boring.
“I can’t do maths” are still the first words uttered by the majority of people I meet when they discover I am a mathematics teacher. Believing that mathematical ability is a God-given gift is simply wrong. Mathematics is a long and slow progression and I truly believe, given enough time, anyone can get to any level.
I hope in the not too distant future that phrase becomes as absurd to hear as “I can’t do reading” because sadly, when this attitude is passed down through families, it gives future generations an easy escape route from doing something that scares them a little.
The hard sciences have had somewhat of a renaissance in recent years and are now more popular than ever. The “Brian Cox effect” has certainly helped physics become more ‘cool’ in the eyes of the public, with more interest in the hard sciences than ever.
But mathematics is a little behind the curve in this regard. I would love to see more in the mainstream media about just how ‘cool’ mathematics can actually be.
Q: Do you believe maths can be a creative subject?
A: For me, maths is that great meeting point of precision and creativity that I have only otherwise seen in music.
Drilling algebraic and numerical skills is much like practising scales, making it easier to improvise on unseen problems in the future. No-one would expect to sit at a piano and immediately improvise some top-level music, but people are often under this misapprehension with mathematics.
In maths, the problem-solving itself is also creative, with the same problem being possible to approach in countless ways. The skill is to be able to plan ahead and foresee potential benefits or drawbacks of one approach.
Many students are surprised as they go through their A-level course that they can be as equally successful as their neighbour by employing a completely different approach.
Q: How do you help students enjoy what can often be perceived as a difficult subject?
A: Maths, with all its patterns and symmetries, can be a hugely enjoyable and challenging creative pursuit.
In one of our lessons, for example, we discuss the links between the Fibonacci sequence of numbers - which converges on a special number known as the ‘golden ratio’ - and the natural world.
This golden ratio not only perfectly reflects the visually pleasing spiral patterns and dimensions found in nature, but has been used by man in art and architecture over thousands of years
We usually finish by listening to the song Lateralus by the progressive metal rock band Tool, which has its drum beats and the syllables of its lyrics based around the Fibonacci sequence. Students often enjoy discussing whether this mathematical code could actually hold the key to nature.
I think it also helps a great deal for students to know that success is not achieved overnight but instead earned through a lot of hard work.
Not everyone is going to enjoy all aspects of mathematics (nor life itself) but the more work you put in, the more chance you have of enjoying more of it. That goes for life too.
Just like a language, the more you use it, the better you get. Conversely if you let skills get rusty then it can become tricky again.
Q: What makes a good mathematician?
A: I would stress that even those regarded as ‘good mathematicians’ would likely disagree with that tag. In such a vast subject, there is always more to learn and it is always possible to hit a brick wall in your development, no matter how successful people believe you to be.
I have come to tears multiple times as an adult when tackling something that seemed impossible but tenacity and a good walk in the countryside usually helps you get around all obstacles.
Q: How would you describe what maths is?
A: Mathematics is of course its own language with unique meanings of symbols and letters that allows you to communicate with anyone else in the world. We now follow a standardised format but, of course, this was not always the case.
Maths at its heart is building a set of proven truths that we call axioms, seeing how these interact with each other and building a further set of proven theories.
Large developments tend to occur in finding exceptions to these rules and then exploring them in further detail, making new subject areas to explore and link back to our prior knowledge base. Proof is at the heart of mathematics, irrefutably knowing that something is true.
Science tends to test approximated ideas many times until we are sure to a very high degree of accuracy. Most mathematical disciplines aim to be completely sure of something by building from simple axioms instead.
This is, is in my mind, what makes maths a pure subject in a similar sense to philosophy or logic.
Q: Do students need calculators, or is the joy of maths that you don’t need any tools and it’s all in your head?
A: The use of calculators at a young age is a hotly contested area for discussion in mathematics education. Some argue that allowing pupils to use calculators at an early stage means they can apply skills faster and earlier, allowing them freedom to develop problem-solving skills. Others argue it will shortcut their development in the understanding of number.
I am definitely in the latter camp and believe that using mental arithmetic and written methods, rather than calculators, as a young student can help to develop links and help students spot patterns that strengthen their knowledge of numerical and algebraic topics much further down the line.
In cutting-edge mathematics, computers are becoming ever more essential. Gone are the days when a mathematician can sit and work through ideas simply with a pencil and some determination. Many proofs are now accomplished through exhaustive processes, getting a computer to check every possibility, rather than from first principles. For me, this does take some of the romance out of an area that I do truly love, with less chance of those ‘Eureka!’ moments of the past.
Q: How can students apply the skills they learn in maths in the wider world?
A: We can often get a little caught up with explaining to students where we will use methods in the future. For example, “Don’t worry, trigonometry will be useful when you are a carpenter!”. I feel this short changes my subject a little.
My stock response to students when asked “Where will I use this in real life” is that it allows them to do harder mathematics in the future. In response to the inevitable “Why would I want to do that?”, well it is quite simple: it is fun and challenging and makes you a better person.
Q: What are the greatest benefits we enjoy as a society thanks to developments in maths?
A: Without wishing to sound too arrogant about my own subject, every accomplishment in science, engineering and architecture is standing on the shoulders of mathematics. Maths is used in every single major scientific advancement in history and will continue to do so.
It is worth noting that most accomplishments in mathematics are often centuries ahead of seeing a practical use. Mathematicians tend to ask ‘What if?’ questions to push an abstract topic area forward. Scientists and engineers can then use these ideas and methods at a later date for practical applications.
Pictured: students enjoying Mr White's further maths class at RGS