And there’s no end of voyaging when once the voice is heard

This post’s title is a line from Gerald Gould’s poem: Wander-thirst.

I have just spent a couple of days ‘doing the exhibitions’ of Melbourne’s National Gallery of Victoria and the Australian Centre for the Moving Image. I went to see the Howard Arkley exhibition at the Ian Potter Centre, Eyes, Lies and Illusions at ACMI, Juan Davila, Tezuka: the Marvel of Manga, Picture to Print: Reproductive Prints, Sneakers: Classics to Customs and After Image: Social Documentary Photography in the 20th Century at NGV International.

The Eyes, Lies and Illusions exhibition ‘explores the art and science of visual perception from the Renaissance to the present day’. One section of the exhibition concerns Tricks of the Light. Of particular interest to a mathematics educator were the anamorphoses. (Phillip Kent’s website on these is intriguing) An anamorphosis is a deformed image that appears in its true shape when viewed in some ‘unconventional’ way. There are two common forms:

(1) Oblique: the image must be viewed from an extreme angle. See below for one of Holbein’s paintings that has the picture of a skull on the floor (if viewed from the extreme right of the painting)

 The Ambassadors, by Holbein

(2) Catoptric: the image can be seen when reflected in a distorting reflecting surface (usually in the shape of a cone or cylinder). See below the picture of an umbrella that can only be viewed when you look down at the apex of the reflecting cone in the centre.

 Gallery

Mathematics is used to construct the perspective required in order to view the image without distortion. On Kent’s website he notes that we are used to ‘seeing’ as being a direct perception of reality and that our brains are constantly interpreting and giving structure to visual input. Comments have been made to me over the course of the last few months that school mathematics is somewhat akin to magic and relies more on illusion than intuition…. that students give up trying to make sense of what they are being taught in classrooms and resort to elaborate memorisation techniques rather than thinking things through.

The other exhibition that moved me sufficiently to make this post was After Image, a series of about 30 photographs acting as a ‘social documentary’. A quote from Susan Sontag – ‘In these last decades, ‘concerned’ photography has done at least as much to deaden conscience as to arouse it’ – got me thinking about parallels to maths education. Does the way we teach the subject do as much to deaden our students’ conscious understanding as to arouse it? With one of the photos presented was a quote from Walker Evans (1903-1975): “Stare. It is the way to educate your eye, and more. Stare, pry, listen, eavesdrop. Die knowing something. You are not here long.” Sometimes in education we don’t give sufficient time to ‘stare’ at something or someone.

And what of this quote from Bill Brandt (1904-83)? (He’s referring to a photographer but I think I could make the case for an educator as well) “…[he] must have and keep in him something of the receptiveness of a child who looks at the world for the first time or of the traveller who enters a strange country”. Does the way we teach mathematics prevent students retaining this enthusiasm for the new and unexplored? Do we smother something within them?

Once one starts to ask these questions and begins the journey down these paths of thought, one cannot help but look at what one does with a reflectively critical eye.

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About Linda

I have been involved in secondary mathematics education in Victoria, Australia for over 25 years.
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