Monday, 12 April 2010

Maths is beautiful

A bar somewhere in Scotland at the end of the second sunny day of the year. A group of teachers round the table.

Stephanie pushed the Guardian newspaper across the table. “Have you seen this today?” she asked, excitement in her voice. Dot scanned the article and then sighed.

“The ten greatest mathematicians? There's something wrong with me. I just can't get excited about the achievements of these apparently great minds. Look at this one – guy called Tao gets a prize for finding out that you can find sequences of primes of any length in which every number in the sequence is a fixed distance apart. Um. Good.” It was clear that she was seriously underwhelmed.

“If we forget that maths underpins science, nature and the whole world we live in, we'll be in trouble. It's all exciting!” suggested Stephanie, while Nick spluttered and banged his glass down on the table, almost spilling the contents.

“Are you kidding? Euler and Gauss must be two of the greatest ever minds in history!” he said loudly.

Dot looked incredulous. “So tell me something they found out that will excite me,” she challenged.

Nick picked up the paper, gesticulating wildly as he talked “Gauss gave us the basis for models of how the universe works from the petals on a flower to variations in star cluster to finance. Euler, complex numbers, without which no electronics nor even a.c. power. His maths give you the light you read by. He discovered the square root of negative numbers, Gauss, curved space-time - both new dimensions - literally - of thought.”

He looked around the table. “A fine argument, well made,” said Stephanie with an admiring smile. Robert sitting sleepily in the corner raised his glass in approval.

Dot raised her own glass and one eyebrow “Good with the light thing - that's persuasive. Square root of negative numbers though. Why would that affect me?”

Stephanie nodded “You make a fair point - it's our biggest barrier to teaching and learning sometimes…but Miss, Whyyyyy? Have a look at this video as a start” She scribbled down a web address.

Nick searched for an apt analogy “It's like when your language isn't enough to express an idea, so you resort to painting and music to make your point.”

Robert stirred once more. He swirled his whisky gently round the glass, and spoke with reverence. “It's more than just important. It's… beautiful.”

Dot nodded vigorously “I liked that and I can understand that analogy, Nick. I wish,” she added wistfully, “I wish I could see numbers as beautiful.”

Kenny leaned over from the next table “I'm with Dot on the maths. I once watched a programme though about a guy who could remember pi by visualising it as a landscape…”

Nick looked sympathetic “Dot, you don't need to have all the maths to get it: just listen to people who have the math and the passion like Richard Feynman.”

The musician who’d been playing soothing airs in the corner put down his fiddle and joined them. “JS Bach did,” he said simply.

Dot looked doubtful. “JS Bach created some music that stirs the soul. Numbers themselves don't do that.”

“It's not the numbers, so much.” Nick waved his arms again. “It's the beauty of the universe. When you get it, even the striking of a match is an amazing thing...”

The violin player continued “Bach’s music was maths and maths is music. Literally.”

Dot was not convinced. “Some of it is, Gordon yes. But not the best stuff.”

Gordon pointed to the strings on his violin “Music is sound waves and frequencies. Chords are combinations of these and so on.”

Nick nodded vigorously “The relationships are the textures and the rhythm of the music. The numbers are the score on the page.”

Dot frowned “But I don't need to know that in order to create beautiful sounds, or an emotional response. Maybe maths describes phenomena in a way that appeals to one kind of mind?” she suggested

Nick nodded again “I think it adds depth of understanding. Feynman again, asserting that the scientist can appreciate a flower no less than an artist.

Dot couldn’t help pointing out glumly “The "maths" we do in school isn't like this though.”

Nick grimaced. “It is when I do it,” he asserted. “A suggestion for your kids is to get them solving puzzles: shapes, patterns, connecting ideas, words, sequences. For fun. That’s maths”

Dot smiled. “I understand that maths learning is not linear, so would you say that playing with numbers is as important as playing with language?”

Nick responded, “Both are symbols of something else. Connections and connectedness. That's not just maths, that's knowledge.”

With this profound thought, we leave them and ponder how to reconcile this inspiring and lively concept of maths with the pressures of everyday teaching, and the HMIE requirement for evidence of pace and challenge through test results.

Of course this conversation could not really have taken place in one cosy bar, as Stephanie is in Thurso, Nick is in Edinburgh, Gordon the violin player and Kenny are in Glasgow, Robert (who had his mandolin beside him but was too tired to play it) is in North Berwick and Dot is in the Scottish Borders. North, South, East and West mean nothing to Twitter however, and 140 characters mean everything.

Thanks to @sdisbury (Stephanie), @cullaloe (Nick), @gbrown057 (Gordon), @Kenny73 (Kenny), @jonesieboy (Robert)

Thursday, 15 October 2009

Engaging? Personalised? Relevant?

And back to the real world.

This sort of sheet is what my Head Teacher wants me to provide for "spelling homework" in P3 on a weekly basis next term. She is responding to what she perceives to be parental demand.

I am calling it homechores.

I should say that below is the sort of online spelling activity task they could have done last term (and actually still can since I've set it up with all the patterns we'll be learning up till December.)

or this:


I spent 2 hours (of my holiday) yesterday joining a Flashmeeting, supplemented by tweets from those in the meeting room itself, linked to a presentation at LTS by Greg Whitby.

Although my webcam normally works perfectly well, on this occasion, presumably in honour of Greg’s origins, it chose to transmit my picture upside down. And perhaps this was appropriate in more than that respect, for Greg is someone who would like to turn much of our thinking about school, and learning and teaching on its head.

His website tells me that: “Greg Whitby is the Executive Director of Schools and leads a system of approximately 80 Catholic schools serving the Catholic community of greater Western Sydney. He has 30 years combined experience in K-12 schooling and senior system leadership.

In recognising the critical link between good teaching practice and student learning outcomes, Greg is working to build the capacity of school leaders and teachers through a whole-of-system approach to professional learning.

As a regular speaker at national and international conferences, Greg talks about the key areas underpinning a new model of schooling for today’s world: de-privatising teacher practice, personalising student learning and ICTs as enablers to facilitate deep learning.

In 2007, he was named the most innovative educator in Australia by the Bulletin Magazine in its annual SMART 100 awards. Greg has also been awarded an ACEL Presidential Citation for his contribution to Australian education."

An impressive CV, and he is also an inspiring and stimulating speaker of sufficient stature to have his feet firmly on the ground, whilst describing his elevated view of the road ahead. Already I’ve read some excellent blogposts about the talk, (eg Neil's, Ollie's) and look forward to reading more. I can’t summarise the whole talk, so here are just some of the ideas Greg described that struck me most powerfully.

First would have to be his definition of personalisation of learning. Personalisation, he said, does not mean individual learning programmes for each child. Instead it means having “a deep understanding of both depth and breadth, creating continuous rich learning opportunities that are real and of their world not apart from their world.” Hurrah! I wishhe’d come and speak to some of the parents in my school though.

He talked also about his strategy of having one hundred 5-year olds in one room, alarming parents, but finding favour with the teachers who tried it. The atmosphere in the room is purposeful and the children are engaged appropriately. In the teacher prep area they have a 100-square and anyone who has contact with a child writes a note on a post-it and puts it on the board on the child’s square. Teachers can then see patterns and plan. Simple but effective.

I liked his idea of developing a “learning story” for an individual child in the class. A nice way to talk about progression and one I think I will work on with the children in my class next week. At the moment they have “achievement books” they brought with them from their previous class, which they like. But the learning story idea would give more emphasis to the continuous, developing nature of what they are doing every day. How to make this relevant for all of them, and not a writing exercise? What about a diary room a la big brother? How can I set this up? Would I need video? Could they use the little TTS microphone? or Voicethread maybe?

It reassures me that, even after all these years, I still feel excitement when I hear a speaker whose words immediately point me to ways to make my teaching, and more importantly the children’s learning more effective. That’s what the best CPD does, doesn’t it?

You can watch the whole presentation on the Flashmeeting replay here.

Sunday, 2 August 2009

Pentatonic playfulness

Thanks to Nick Hood aka Cullaloe for the link to this fascinating audience participation clip.

The audience has no difficulty in knowing exactly which note to sing, even when he extends the range below and above what he has sung to them, and adds his own harmonic patterns. Amazing!

Friday, 31 July 2009

The glistening trail of snail mail

What a lovely surprise!

It was our 30th wedding anniversary and our 4 children collaborated to give us a card signed by all of them!

After a week of concentrated focus here and having used digital technology extensively to collaborate, it's a timely reminder of how satisfying it is to receive a personal communication which took a lot more effort to make.

The stamps on the envelope trace its journey from New Zealand, to Iceland, to Edinburgh and finally to Peebles.

And tomorrow they have arranged for us to go to Stobo Castle for a relaxing afternoon, including a massage. Bliss! and just what we both need...

They are a lovely lot.

Wednesday, 22 July 2009

Meme power

Jenny, the daughter in iceland, sent me the link to this video which is very relaxing as well as totally amazing.
What's also amazing is how the viewing stats rocket from 7K to 74K in 6 days!

Monday, 20 July 2009

I know it has to happen, but it would be at the very time I wanted Glow to be available!