Teacher's dream makes calculus cool

Math teacher Philip Lloyd with a model of a phantom graph showing the real position of imaginary solutions. Photo / Brett Phibbs.

Very few people wake excitedly every Sunday at 3am thinking about calculus.

But that is what happened to Epsom Girls Grammar teacher Philip Lloyd, who has come up with a new way of teaching complex numbers to Year 13 students.

The teacher of 43 years is now receiving international praise for his concept.

"It came to me at 3am on a Sunday morning," Mr Lloyd said.

"In simple terms the solutions of an equation are where its graph crosses the x axis. Some graphs do not cross the x axis but we still say they have solutions which people call imaginary."

It was this "imaginary" concept which many students struggle to understand - because they can't see it, many tended to find it difficult to believe.

"I found that graphs have extra bits on them which I call phantom graphs and these actually do cross the x axis. In fact, I found that the imaginary solutions are at real places."

Mr Lloyd said this came to him one bit at a time over several weeks, but always on a Sunday and at 3am.

"I'd think of one thing at a time and the next week something else would pop up. It was so exciting.

"I would get up in the morning and I'd start making these models."

After spending most of his school holidays on the perspex models, Mr Lloyd demonstrated the complicated concept to his students.

Suddenly they could see what he was talking about and they "absolutely loved it".

Mr Lloyd has been using his models for three years now with great success.

"No teacher has ever thought of it before. It makes me feel so cool."

Not only do the students love it, but his concept is gaining momentum in mathematical circles, so much so he has been invited to share his idea at an international mathematics conference in South Africa next year.

A letter from the head of the conference says Mr Lloyd's paper on the concept is "quite exceptional and exciting, it is a rare thing to see such a new idea in maths education".

"That's just about the highlight of my career," Mr Lloyd said of the praise.

Students have told the Herald it's admirable that their teacher has developed something new.

"It's the subject of complex numbers and these numbers are actually imaginary so it's really hard to visualise where they are. With his graphs you can visualise where they are," said Year 13 student Rochelle Fernandes.

The result has made that part of maths exams a breeze.

Another student, Angela Sargent, said Mr Lloyd's teaching style is the highlight of the day.

She said students now fly through that part of the exam thanks to being able to visualise Mr Lloyd's concept in their mind.

Dilworth School's head of maths, Philip Glass, who has attended a presentation on Mr Lloyd's phantom graphs, said he'd produced "a clever methodology for applying the logic of graphs to an abstract calculus mathematical concept".

Mr Lloyd had showed a real enthusiasm and generosity in sharing his concept so other schools could benefit from it.