Happy Pi Day!

March 14th, 2016 Sections: Calendar, Education, Maths-Stats
Happy Pi day

Happy Pi day

I know that I going on about Social Media, but it’s a great thing for someone like me – an expat thousands of miles away from ‘home’ … allowing me to keep in touch with family and friends, to keep in touch and find out what’s happening in their lives.

Sometimes it’s good news – a marriage or birth of a child … but sometimes there bad news as well – like the untimely death of a former pupil.

Some time ago I got a message on Facebook from a former pupil who had tracked me down … “Excuse me, but are you the Ian Claytor who used to teach Maths and Computing at Ashmole School?“.  Fortunately, I recognized the name, (if not the nickname that he was registered under), and was happy to “Yes.

In the subsequent messages he told me that he remembered one particular lesson, (only one?), where I had tried to explain that I had tried to explain an aspect about congruence – that the orientation of a shape does not alter it’s properties.  Apparently, I stood in front of the class and said something like: “a rectangle standing upright has the same area as …“, then lying on the desk, “… one with the same dimensions lying flat“.

I had to admit that I didn’t remember the lesson … but it sounded like the sort of thing I would have done.

I used to like to find graphic ways of getting a point across … it often helped understanding and gave the class an image to help them remember things … it also helped to make things fun!  Maths is a subject that people are often scares people … they see numbers and automatically get ‘turned off’.

I remember, as a student teacher, attending a compulsory art class … it was really designed for those who were going to teach younger children, Primary schools, (where – in Britain –  children are, typically aged between 5 and 11),  When the lecturer discovered that I was studying Theology and Maths, he became quite dismissive … “the two subjects that are the most deficient in using using imagery – as child’s visual abilities”.

He went on to praise Science teachers, (particularly Biology teachers), and Geographers as the most creative users of the visual senses for helping to pass on knowledge, information and understanding.

I wish that I had known then what I know now, because I don’t agree with him and could have had a great time arguing the point with him … but, back then I took what he said to heart and resolved that I would try to ‘break the mold’ and prove him wrong.

I also remember a Psychology lecture where we looked at a survey which looked at how people learn … presenting the same information in three different formats: in pictures, in words and in symbols … and then asked them to rate how helpful or meaningful they found each.

For example, the theory of Pythagoras:

a)      as an image pythagoras-theorem
b)      in words

In any right angled triangle, the square on the
hypotenuse is equal to the sum of the squares
on the other two sides.

c)       as symbols pythagoras-formula-1

The results were interesting and pretty convincing, even though (as I remember it) the sample size was small … probably too small to be considered as significant.  It seems that the visual presentation was preferred by most people, followed by the words … and lastly came the symbolic representation.  More importantly, perhaps, was the breakdown that showed that those who preferred the wordy presentation tended to be those who were good at  linguistics and favoured literature, whilst those whose preference was for the symbols were good at Mathematics and the sciences …

“If you want to get through to the majority”, said the lecturer, “look for visual methods of conveying your message.”

A valuable message that I took away with me.

There were similar studies that pointed to the efficacy of the old Chinese proverb that the Nuffield Mathematics took as its motto:

I hear and I forget.
I see and I remember.
I do and I understand.

Another valuable message that I took away with me, and which inspired my catchphrase when I was Maths Teacher …

Maths is not a spectator sport.

They are lessons that I have brought with me here … and that I try to remember in my dealings with people.

They also come to mind quite regularly these days, as and when I go through the kids homework or review their classwork.  I can’t help much when it comes to Russian or Kyrgyz, History or Geography, because I don’t have the background knowledge and/or the language skills to address the material that they are dealing with … but when it comes to Maths, I am able to understand, check and sometimes help … even if, the techniques used here are slightly different than those I learned and am familiar with.

Sometimes, I am impressed with the topics they cover … which may be a couple of years in advance of their peers in the UK might be learning … but sometimes I am at a loss about the methods employed.  It seems that the answer is all important – and very little is written down to explain how they arrived at the answer.

I remember teaching Statistics to one student, back in the UK – a very good student.  His answers, however, often were not quite right … but as he never showed any working, I had to resort to putting a red ‘X’ by them, writing in the correct answer … and witholding the points from his final mark.  Then, one day, I asked him … “Why don’t you ever show your working, so that we can find the mistake and correct it?  Your answer is so close, but it won’t get you any marks in the exam.”  He told me that the question said “Estimate …” and that’s what he had done.

The ‘penny dropped’ … I sighed, smiled and tried to explain … “In Statistics, ‘estimate’ means calculate … not ‘guess’ – not even ‘make an informed guess’  … He nodded, said, “OK” and from then on started showing his working out … getting the correct answer  … and full marks – I said: he was a Good Student!

I suppose that there is no problem, of course, if they get the answer correct, but when it’s wrong, it can difficult (if not impossible) to find their mistake and correct it.  If I ask, “how did you get that?“, often they cannot explain … leaving me to conclude that they don’t really understand what they have done.

If I try explaining, then they ‘return the compliment’ and ask, “how did you get that?”, so they do want to understand …

To make matters worse, however, when I do try to explain and write things down, step by step, (showing my ‘working,’), there’s no problem until we get to the end … when copy it out … but missing out steps … to fit a template of a specimen answer’ worked out in class.

It’s as if they have ‘learned by rote’ a technique which needs to be followed exactly ‘to the letter’ in order to gain points … divorced from reality … rather than an approach which can taken and applied in different circumstances to solve problems of a similar type in the real world – even if the precise setting is an unfamiliar one.

  It helps to make the subject, and the lessons, memorable … relevant … fun …

I am not sure, however, that I would have gone to the extent that some Maths teachers go.  Here, for example is a Rap about Pi … just one of several that you can find on youtube or the other sites where users can post video:

To be honest, I am not a poet and I am not that fond of Rap … also , on top of that, many of the raps I have come across seem to be artificial and contrived, so I question how successful it would be as a teaching aid.

On the other hand, (maybe because I like Don McClean’s American Pie), I prefer this version by Ken Kerrier and Antoni Chan – sorry there’s no video, (the link on Chan’s wepage seems to be dead), but if you want to sing along … here are the words:

3.141592653589793238462643383279502884197169399375105820974944592307816
(or Mathematical Pi to the tune of ‘American Pie’)

by
Ken Ferrier and Antoni Chan

INTRO:

A long, long time ago
Long before the Super Bowl and things like lemonade
The Hellenic Republic was full of smarts
And a question resting on the Grecian hearts
Was “What is the circumference of a circle?”
But they were set on rational numbers
And it ranks among their biggest blunders
They worked on it for years
And confirmed one of their biggest fears
I can’t be certain if they cried when irrationality was realized
But something deep within them died
the day they discovered pi.
They were thinking

CHORUS:

Pi, pi, mathematical pi
3 point 14 15 92
65 35 89 7
932384 62
6433832 7 (not rounded)

VERSE:

Well this kind of pie is different than most
It hasn’t got berries, ain’t spread on toast
And that’s how it’s always been
We keep extending its decimal places
Pushing our computers through their paces
But we’ll never reach the end
So why the fascination with
A number whose end is just a myth
Whence the adulation
For mental masturbation
It might have something to do with the stars
To calculate distances from afar
But that’s just a guess ’bout the way things are
Regarding the precision of pi
I am pondering

CHORUS:

VERSE:

Now I feel that I should mention
Pi is applicable in any dimension
At least as far as I know
If there were no Pi we’d be missing things
Like marbles and mugs and balls of string
And sports such as soccer and curling
The orbs in their celestial paths
Navigate along elliptical graphs
Ellipses have pi in them too
Just one side of them has grew
You can see pi in most everything
It’s in Cornell’s Electron Storage Ring
And also in slinkies and other springs
And that’s why it’s important to know pi
You should memorize

CHORUS:

OUTRO:

Once one night I had a dream
That pi was gone and I had to scream
Cause all pi things had disappeared (pause)
Can you imagine a world like that
Circles aren’t round and spheres are flat
It’s the culmination of everything we’ve feared
‘Twas a nightmare of epic proportions
One that gave me brain contortions
Oh wait! I mean contusions
They put me in some institutions
But then I escaped and now I’m free
To sing of the virtue of pi

CHORUS:

 

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