Tuesday, April 26, 2011

A Day in the Life Of

In case anyone thinks that teachers don't NEED school holidays...

05h50: wake up. pack marking, school bag, sports bag, lunch.

06h30: leave home

07h05: arrive at school. many staff members already here.

07h10: open classroom windows, switch on computer.

07h15: greet first students who want to come sit in the classroom and chat. listen to long story about friend while checking and responding to the seven emails received since 5pm yesterday

07h30: respond to email from irate parent, cc-ing two senior staff members in case of repercussions

07h45: rush down the corridors to staff meeting. note that its my day for break duty.

07h50: rush back through corridors to take register

07h55: take register. remind class about outstanding reply slips, put two children in detention for failing to pay for photographs, and check on minor uniform defaults. ask the three children absent yesterday if they're feeling better.

08h00: tick off a last late comer. open up teaching slides for the first lessons and check 3 emails that arrived since 07h45

08h05: welcome first class. teach.

08h45: dismiss first class, welcome second class. teach.

09h30: dismiss second class, welcome third class. teach. in a brief gap while they're working put in an announcement for assembly.

10h10: lock classroom and run down the corridor to assembly.

10h40: rush back to classroom to meet two children about missed hockey practice.

10h45: go on break duty. wander around the school sniffing for cigarette smoke.

11h05: back to classroom. two bites of lunch. welcome fourth class. teach.

11h55: free period!! rush out of classroom so another staff member can use it. take marking and lunch. eat in staff workroom in between marking, responding to emails and entering marks. receive a paper to be moderated by tomorrow.

12h45: break. don't leave staffwork room, push on with all the admin. remember to print a worksheet for the next class. manage to finish eating lunch. don't get to moderating the paper.

13h20: rush back to classroom for sixth lesson. welcome class. teach.

14h10: dismiss previous class and welcome new class. teach.

15h00: end of school day. dismiss class. wait for students on classroom cleaning duty while responding to four emails with questions from parents. sms all the parents in the hockey team with a small change in practice times. sms six parents whose children haven't done their homework.

15h05: supervise classroom cleaning

15h15: run to hockey practice. sort out uniform defaults, a fight between two team members and three people who can't attend next practice. sort out the two latecomers.

16h15: back to classroom. respond to emails.

16h45: prepare tomorrow's lessons and print tomorrow's worksheets

17h30: close classroom windows. switch off computer. pack empty lunch box, sports bag, school bag, unfinished marking and unmoderated paper. lock classroom.

17h35: drive out of school grounds

18h15: get home. feed cats

18h20: mark and moderate

19h00: make supper

19h20: eat supper.

20h00: fall asleep exhausted. the rest of the marking can wait

PS I love teaching. No really.

Monday, April 25, 2011

Car Games

Some Variations on "The Number Plate Game"...

The Original: spot all the numbers from 1 to 100 (in order) on car number plates. The digits must be in the correct order and not separated.

Fibonacci: spot all the fibonacci numbers (stop at 144 - otherwise it gets too difficult!). The same rules apply.

Hint - the Fibonacci sequence of numbers works like this. Each term of the sequence is the sum of the previous two terms. It starts 1; 1; 2; 3...

Prime Numbers: spot all the prime numbers between 0 and 100. 

Hint - a prime number is only divisible by one and itself. 1 doesn't count as a prime number.

Powers of Two:
Powers of Three:

The variations are endless. After some experimentation however, I suggest you stop when you get to three digits. Otherwise it takes so long to get the next number in the sequence that everyone loses interest!

Happy long weekend! I wish you a festive lack of traffic.

Sunday, April 10, 2011

Bertie Russell and the Incompleteness Theorem (Part II)

Right, where was I? Bertie has just discovered his crazy uncle and a new fear - of going insane.

Ok, so the next big event in our young hero's life is that his grandmother (finally) hires a Maths tutor for him. Mathematics opened a skylight in Bertie's life. For the first time, Bertie came across the idea of proof. In a world that was full of terrors and things that go bang in the night, he realised that if something is true, you should be able to demonstrate that it is true. And thereafter you need not agonise over it any more - you've shown it to be true. Equally, if something is untrue, you should be able to disprove it and move on.

Of course the other way in which Mathematics changed Bertie's life was that it soon became clear that he was very good at it...and he was only to get better!

At that point we will leave Bertie for a few years. He grew up in more or less the ordinary way, eventually went off to university at Trinity College, Cambridge where he steadily demonstrated himself to be more and more brilliant.

But as Bertie found out more about Mathematics, something began to worry him. Everything was so logical, up to a certain point. Theorems built on theorems. Propositions were proved or disproved. Yet something was still missing. The whole edifice of Mathematics was built on axioms. In one way or another, something foundational had to be assumed.

Given that in some ways Bertie's happiness and sanity depended on the certainties of Mathematics, he did not take kindly to this, and quickly set about trying to remedy this foundational problem in the field. Between a marriage (begun and ended), several affairs and multiple academic papers; conferences and international unrest; Bertie attacked the problem with vigour. Together with his great friend Arthur Whitehead he wrote a massive tome on the fundamental principles of Mathematics. He became extremely famous. But he still couldn't settle the foundations of Mathematics to his own satisfaction.

And then something really remarkable happened. A young Mathematician called Kurt Gödel proved what became known as the Incompleteness Theorems. One (and only one) of the shattering implications of these theorems is this: there will always exist some things that are true, but not provable. And there will always exist some things that are untrue, but not disprovable. Another way of saying this is that is impossible to have an entirely internally consistent set of axioms for Mathematics.

Wait...just think about that for a second...

Can you imagine how devastating this must have been? Bertie's life goal was crushed in one (or two) little theorems...

We will leave Bertie at this point. As a brief postscript, I am happy to report that Bertie survived this setback and went on to make many more contributions to Mathematics, Philosophy and even politics (particularly as a pacifist during both World Wars).

I leave you with the thought of the Incompleteness Theorems.

May they keep you awake at night.

They truly are remarkable.

As was Bertrand Russell.

Saturday, April 9, 2011

Inaugural EOTSDS: Bertie Russell and the Incompleteness Theorem (Part I)

I have inducted a new tradition...the last-day-of-term shaggy dog story (otherwise known as the EOTSDS)! After all, no-one wants to be at school, but we all have to sit in class and try to be reasonably productive. So I've decided that the thing to do is tell a very long, moderately entertaining and somewhat educational shaggy dog story.

This is the first EOTSDS of 2011. I took it (loosely) from a remarkable book called Logicomix http://www.logicomix.com/en/, which you should all go out and beg, borrow, steal or even (gasp) buy immediately. You'll have to forgive inaccuracies in my version and kindly take into consideration the conditions underwhich this story was first told. You'll also have to fill in a lot of shaggy dog details which just don't work in text...

Are you all sitting comfortably?

Once upon a time, a very long time ago, there lived a small boy called Bertrand Russell, but everyone called him Bertie.

Now Bertie got off to a very unfortunate start in life, due to both his parents dying. So he had to go live with his grandparents, who were very important people who lived in a stately home. Think gloomy, old, important, and really not very nice to live in, especially as a very small boy.

Poor Bertie was given a large, dark drafty bedroom all on his own in this ominous dwelling, and on his first night he heard this terrible groaning noise from somewhere in the attics. Being very young, and since the night was very dark and there was no one to call, he lay in bed and trembled with terror. Was it a ghost? Was it a demon?

This nightly groaning continued to terrify Bertie for many years. All in all Bertie was growing into a very frightened little chap. His grandmother's approach to child-rearing didn't help. She was extrememly strict and extremely religious. She didn't believe that children should ask questions, and she told Bertie lots of stories about the awful things (such as burning in hell) that would happen to him if he was naughty. So of course Bertie was convinced that the groaning was a devil sent to punish him for his misdeeds...

Well, the years went by, as they do; and Bertie grew up, as one does. And soon enough, his grandmother started to hire a series of tutors for him (in those days the children of the very rich didn't go to school, they had private tutors). He fell in love with his beautiful German teacher of course, but much more important was the science teacher. He didn't exactly learn brilliant scientific method, but even the simple observations that they made together began to make Bertie think. And one of the first things he thought was about ghosts and devils. In fact not to put too fine a point on it, Bertie began to have serious doubts about the "ghost/devil theory" of the nightly groaning.

So, one night Bertie snuck off and followed the sound of groaning. He made a momentous discovery, which was to cure his fear of ghosts forever. However that fear was replaced with a far more serious one... What he discovered that the groaning came from a mad uncle whom his grandmother had been keeping hidden in the attics. True story. In grandmother's defence, attitudes to madness or mental illness in those days were such that hiding a crazy relation may have seemed like a very good idea. Mental illness was seen as hereditary, and no-one would want to marry into a family in which there was a known "madman". And the official mental asylums were so horrible that you would not want to send any family member to one of them, no matter how serious his condition (see the opening scene of the movie Amadeus...)

So Bertie's fear of ghosts was replaced by the very real fear of going crazy; a fear that would stay with him throughout his life. But at first it wasn't just a vague fear. It crippled him.

Do not fear, good readers. All is not lost. Stay tuned for the next exciting episode (my fingers are getting tired of all this typing).