tales from the chalk face

Teaching – its like a sharp blow to the back of the head

Thursday breaktime, the day before February half term, six tough teaching weeks in the cold, dark winter months are coming to a close as I stand in the staff room, enjoying a coffee and chatting to a colleague …

Thwack!

I feel a sharp, heavy blow to the back of my head. Shock, surprise and pain wash over me in equal measure as I drop to one knee to try and take stock of what has just happened. My wits return and I realise that the colleague apologising profusely had accidently knocked over a speaker, which had swung down like a pendulum, striking me a blow on the back of the head. “Was I alright?” everyone was asking me, and I was asking myself the same question. The back of my head hurt, but was there anything else to worry about? I wasn’t too sure – I’ve seen a few nasty head injuries in my time (mainly on the sports pitch) to know you need to be very careful and cautious with any blow to the head.

I did think that if I was compos mentis enough to worry about being concussed, I probably wasn’t, but I couldn’t shake that nagging doubt, so 30 mins after the incident I self-referred myself to the school nurse who checked me out, said I was probably OK, but gave me a head injury advice sheet, which included a list of symptoms to watch out for, and to take further medical advice if any of them manifested themselves.

And this was where my problems really began!

How could I differentiate these from just being a teacher 6 weeks in from the last break?

• Feeling tired, no energy
• Irritable
• Bothered by light or noise
• Difficulty concentrating
• Headache

I would say I was exhibiting all those symptoms, but I probably had them all before my accident.

It turns out I wasn’t concussed, and as soon as half-term arrived the next day all those symptoms rapidly dissipated with a bit of rest.

But it did make me realise a half-term of teaching is like a blow to the back of the head, it just takes a little longer for the effects to materialise.

Stay safe (and, unlike this blog post, always treat any head injury with respect and caution – it could be serious.)

Mea culpa.

In my time, I may have made a few things up. I’ve “created” a new meaning for the verb: “to pythagorize”, and I regularly tell my students of the “Forgotten Formula”

(The first: to pythagorize means to “to philosophize in the manner of the Pythagoreans”. In my classroom it means to use or apply Pythagoras’ theorem. For example, to find the magnitude of a vector I may tell my students to “pythagorize the i and j (and k if working in three dimensions) components.” I think it may be stretch to suggest we are philosophizing in the manner of the Pythagoreans when doing this.

The second is a bit of cod psychology. The most useful item not included on the A level formula sheet is, imho, the identity:

sec²x = tan²x + 1

yet my experience has taught me that students often grind to a halt in a question when remembering this identity would unlock the problem for them. Hence I have christened it “The Forgotten Formula”, have it labelled as such on my wall, and refer to it by this name. On more than one occasion, I have had to explain to my students that this is one of my little (many?) quirks and if they start talking of “the forgotten formula” with other teachers and mathematicians they will, at best, look back at them blankly. But if it helps my students remember, than I’m happy)

So it should have come as no surprise to me when introducing my students to “well behaved functions” they thought it was more of my make-believe (although they loved the concept, and I may have embellished my teacher talk with tales of mis-behaving functions having to spend Thursday lunchtime in detention.) So I had to convince them it was “a thing” and that we describe a function as well behaved if it is continuous and all of its derivatives are defined and continuous. For our purposes, in A level maths, we were exploring the sign change method to find a root between a pair of values, and discussing when this method may not work (if the function is not well-behaved!)

I’ve taught this class for two years, I hope I’ve managed to teach them something. I suspect that, in ten years time, they may not remember much maths, but probably will remember when we talked of well behaved functions!