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Why we cannot afford to turn our backs on the logic of maths

The number of students registered to take higher level maths in the Leaving Certificate this year is the lowest ever. Figures show just 10,435 candidates had registered to take the exam last Friday, the lowest figure recorded by the State Exams Commission.

It is also expected that the number of candidates who actually sat the higher level paper last Friday could fall below the record low of 2007. One in five students drops down from higher to ordinary level maths on the morning of the exam. In 2007, 10,457 students were registered to sit higher level maths but only 8,388 took the higher level paper on the day.

It has also been widely reported that in the international OECD rankings at the end of last year, the performance of Irish teenagers in maths fell from 16th to 26th place, the second steepest decline among participating countries. Ireland is now ranked as below average in maths.

Both of these pieces of bad news will come as a blow to

one of the key Government stratagems to revive our flagging 'smart economy' -- the rolling out of its Project Maths programme.

This major programme of reform has been under way in all second level schools since September last, building on the experience of 24 schools which began the programme in 2008. Project Maths is designed to encourage better understanding of mathematics, to reinforce its practical relevance to everyday life, and to ensure better curriculum continuity across the system. A key objective is to improve attainment levels and to encourage more students to take the subject at higher level.

Until, at the very least, all higher level students sit the Project Maths-style Paper 2 in June 2012, it is premature to predict whether this initiative with be successful.

As a maths teacher, I am somewhat suspicious of many aspects of Project Maths, particularly the new marking scheme which is highly complex and will allow results to be massaged much more easily than with the present marking scheme. It is this which leads many maths teachers to think that Project Maths will lead to a dumbing down, exactly the opposite of what industry demands.

Also, the new course seems about the same length as the old. This doesn't leave teachers with the extra time needed to emphasise the deeper understanding of the subject which is one of the main objectives of Project Maths.

I am, however, cautiously encouraged by the new-found emphasis on problem solving. The move away from rote-learning is very welcome. Project Maths's focus on thinking rather than regurgitation is at the heart of maths itself.

Maths should be understandable. If it's not logical, it's not maths. Maths should withstand and challenge our critical faculties. All human beings have a capacity for logic, whether we choose to exercise it or not. Logic is how our species made it to the top of the food chain. Turning your back on logic frequently results in disaster.

I believe that maths is beautiful. It is the language by which the universe operates and to know and learn this language is to know and learn beauty. To quote John Keats: "Beauty is truth, truth beauty."

So why do so many people hate maths and live in fear of it? How does it unnerve to the extent that it is shunned, that it makes many feel inadequate or stupid? The day that some decide to stop trying to understand maths is, in a way, the day that people admit that there is a limit to what they are prepared to fathom or discover in their lives. It is as if a steel door comes down from the heavens -- one with 'No Entry' plastered all over it.

Maths is abstract. It exists in a realm outside of us. Its abstraction is part of its enduring beauty and its chilly inaccessibility. One plus one will always equal two even if we humans are not around to do the calculation.

Most people need to see where maths is useful to their lives. Topics such as statistics and probability are more popular with the average student because it is easy to see where they can be applied.

Subjects like arithmetic -- including proportion, percentages, compound interest -- are obviously useful but can be difficult to understand and remember. Proportionality and fractions will always be a challenge to understand. A procedure such as working out the area of a living room, in order to figure out the cost of recarpeting it, has an immediate practical benefit.

For most people, their relationship with maths starts to derail with the letter 'x'. This is where maths takes a swift turn into the truly irrelevant. I mean, if we don't know what we're talking about, then why are we talking about it?

Of course, algebra, trigono-metry and differential calculus are difficult -- it took human-kind thousands of years to develop them. Without algebra and being able to handle unspecified data, every piece of software on the planet would come crashing to a halt.

So how do we halt the slump in our country's relationship with matters numeric, apart from re-engineering our assessment procedures?

Basically we need people who both understand maths and who know how to get it across in the classroom.

There is only one important word in the whole of maths and that is the word "why". "Why" is simultaneously the joy and the challenge of mathematics.

I've come up with the following pattern for my evolved methodology, largely instinctive. When I introduce a topic, I explain how it relates to the world we live in and therefore why we are studying it. I explain every line in a thought progression, problem or proof and why one line follows on from the last. If I decide to skip a line, some student inevitably asks me how I got a particular result and I have to explain why anyway. Lastly, when I get the answer, I explain why it is the right one.

Sunday Independent