## Sunday, October 25, 2009

### Eleven Plus Barriers

Your eleven plus child is only ten years old. In another ten years he or she could be reading the following passage for pleasure. I came across this piece of informed something or other when I was looking for information about the middle years of the International Baccalaureate. Some of our eleven plus children will be studying the IB when they reach senior school. What I am a lot less certain of is how many children will opt for a study of `free space relativistic electrodynamics'.

1. FREE-SPACE RELATIVISTIC ELECTRODYNAMICS
The sourceless free-space (vacuum) Maxwell’s equations can be written
as [1, 2] ∂r ?E = −μ∂tH, ∂r ΧH = ε∂tE (1) where ε = ε0, μ = μ0 are the free-space (vacuum) parameters and are associated with the speed of light c = (ε0μ0)−1/2, and with the free space impedance for plane waves Z = (μ0/ε0)1/2. Applying the divergence operator ∂r?in (1) and assuming that ∂t∂r ?E = 0, ∂t∂r •H = 0 implies ∂r •E = 0, ∂r •H = 0, the remaining Maxwell equation. In (1) all fields, e.g., E = E(R) are dependent on the
spatiotemporal coordinates grouped as a Minkowski [3, 4, 2] four-space quadruplet in the form R = (r, ict) (2) which so far is only notational, without any further content.

At one level I know what some of the words mean: sourceless, parameters, impedance, divergence - and can guess at what spatiotemporal co-ordinates are, but I am not sure how these words and concepts link up. If any one can give some clue as to what a Minkowski four space quadruplet is, I would be very grateful.

This passage caught my eye because yesterday I worked with a boy who is just 9 years and 4 months old – but he will be sitting his eleven plus next year. We met one of those funny sections in non verbal reasoning where we had to complete the series. To arrive at the answer required many words and plenty of gesticulating and drawing of sketches. We got there in the end.

It would have been easy to give the answer but this boy wanted to `discover’ how to work the relationships himself. I had a sudden picture of him in the actual eleven plus examination becoming intrigued by a demanding eleven plus question – and forgetting the rest of the paper as he tried to solve the problem.

What lies ahead for this boy? He will hopefully go from grammar school to university. He may then want to study mathematics – or even become an engineer or follow some such career. One day he may even want to explain to his children how to apply a divergence operator.

The very quirk of his makeup that could drive him to academic excellence in his twenties and thirties may become little barriers in his eleven plus journey. Yet this is what keeps teachers relatively sane. When we work with a child who is very possible much brighter than we are, and displays a depth of thought that is truly astounding in a little nine year old, we can only feel privileged. What a lucky teacher he must have at school.