Maths teaching

Today and yesterday, I’ve been attending a conference on service teaching, hosted by the maths lecturers of our college. The conference is supported by the National Digital Learning Repository and the Irish Mathematical Society.

Service teaching refers to the teaching of students who are not majoring in mathematics (IT students physicists, engineers etc). It was an interesting conference, with a good few talks from colleagues in other Institutes of Technology. Not many IoTs have degrees in pure maths, so most maths teaching in the sector is service by definition.

Almost all contributors made reference to the problems 3rd level students have with maths. (There are many reasons for this, from the increase in college attendence among the general population, to low entry points, to the dumbing down of society, etc). The conference was mainly concerned with practical strategies to aid students, although Dr George McClelland talked of a large research programme into the teaching of maths and science at the University of Limerick.

A common theme was the introduction of extra support in the form of ‘drop-in’ maths centers – at least three speakers spoke of such centres in their institutions. It seems many students hate to approach lecturers in their office, but find it helpful to have a dedicated help center, with a different lecturer on hand to get them over a particular hump. Once over it, many first-years never look back. Small tutorial groups in a similar setting were found to be similarily beneficial.

This is a very good idea, if a little resource heavy. One speaker, Dr Diarmaid O’ Se of IT Carlow, found that the ‘drop-in’ idea worked better when modified to appointment by email. At the other end of the scale, Prof Tony Croft spoke of a very comprehensive support operation in Loughborough University (UK), with a large drop-in centre manned by permanent staff with very good resources, an initiative that has proved extremely popular with students and spread to several UK universities.

There were good tips concerning teaching methods in maths – Dr Neil Challis of Sheffield Hallam University (UK), had some great ideas on motivation for mathematics through technology. He showed how the simple measurement of physical data ( movement, sound etc) in maths class could help students relate to basic mathematical functions. Another great idea was to get the audience (or students) to participate in the representation of mathematical functions using semaphore !

The function y = -x

My favourite talk was one on the teaching of circuit analysis by Donncha O hEallaithe of Galway-Mayo Institute of Technology. The talk concerned the use of phasors in the analysis of AC circuits, and why students are usually told everything except why! I was one of these students… I could never see the connection between AC current (or voltage) and complex numbers – did this mean AC current wasn’t real?

Donncha explained that students are rarely told that it is simply a matter of representation. Since an ac voltage Vsin (ωt) appears across a circuit element as Vsin (ωt + Ф), the variables are the amplitude V and the phase angle Ф, which we can represent using vectors. However, since vector division is messy, it makes more sense to handle the amplitude and phase angle using the same 2D representation as complex numbers. And then translate back when you’re done. No imaginary current. Tra la!

No-one told me this when I was a student. (I suspect they did – Ed ).