There is a saying that goes “practice makes perfect”, but I’ve had several people point out to me that a truer statement is “practice makes permanent”. If you do something over and over, it will stick — whether it is the right thing or not.
This principle was brought home to me very clearly by some stories that my instructor told during the First Aid training I had at the beginning of the year (provided by Red Cross).
The first story involved a person who went to the aid of a shopper who had collapsed in a shopping centre. After ascertaining that the person was not breathing, they proceeded to put a plastic bag into the patient’s mouth and then performed CPR. Needless to say, the patient died.
The second story involved a teacher coming to the aid of a student who had gone into anaphylaxis due to an allergic reaction. The teacher fished the life-saving epipen out of the student’s bag and quickly jabbed it into her own leg instead of the student. I never did find out what happened to the student in this situation.
The question is: what on earth possessed these people to do these strange things when clearly it wasn’t going to help their patients?
Answer: that’s how they had practised it during their training.
You see, during our training, we practise CPR on plastic dummies. Part of the mechanism is a plastic bag that goes inside the dummy’s throat and holds the air as we breathe into the dummy’s mouth. In the extreme stress of the moment, the poor first-aider from the first story simply reverted to doing what she had done in her training. The situation is similar for the second story — the teacher had practised putting the dummy epipen into her own leg and so did exactly that with the real-life epipen. (Our instructor had the presence of mind to make sure we used the dummy epipens on each other.)
Of course, these stories came home to me as a teacher because I see the principle in action all the time. I see so many students doing practice exams with all their notes handy, when they are not going to be able to do that in the real exam. I also see students being sloppy with their writing and saying they’ll do it properly for the exam, even though I know full well that they will write sloppily in the exam despite their best intentions.
But the students don’t just inflict this upon themselves — we teachers do it too. We show students a short cut to do something in a particular case, hoping to fix it by showing the “proper way” later, only to find that they keep trying to do the short cut even when it’s not appropriate. And we also find it so hard to avoid doing things for the students — thus forcing the students to practise letting someone else do it for them.
I’m hoping the message of the plastic bag CPR helps me remember to get the students to practise what I want to make permanent, rather than something else!
Category: Reflections
Reflections on learning and teaching and research and life.
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Plastic bag CPR
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Rhapsody’s sunburn
My daughter asked to watch The Fairies (distributed through ABC for Kids) this morning and as we ate our breakfast I watched as Harmony and Rhapsody visited their friend Bubbles the Beach Fairy on Fairy Beach.
Rhapsody was worried that their fairy dresses weren’t appropriate for playing on the beach, but luckily Bubbles did a Special Magic Fairy Spell to bring them Fun and Funky Beach Clothes. However, they did come with a warning: Bubbles implored Rhapsody to be sun-safe and put on her sun hat and sunscreen or she’d get sunburned.
Rhapsody’s response was, “But the sun’s perfectly safe Bubbles.” And she ignored Bubbles and did surfing and dancing and sandcastle-building all day, despite repeated imploring by Bubbles.
When Harmony and Rhapsody got back to Fairyland, Rhapsody discovered her sunburn and learned her lesson about sun safety – even more poignant because, as Harmony says, fairy magic doesn’t work on sunburn.
But why didn’t Rhapsody listen to Bubbles’ good advice? After all, Bubbles lives on fairy beach and Rhapsody should have realised she should therefore be an authority on sun safety.
I have a feeling that Rhapsody just wasn’t ready to listen. Until she felt the consequences of her actions herself, she just wasn’t able to see the danger she was in. The concept of needing to protect herself from the sun just didn’t fit with her concept of the good and beautiful sun.
It put me in mind of our students: every year we moan about them just not getting it, and just not listening to our advice about study. Perhaps they’re like Rhapsody and just aren’t ready to listen yet. They usually learn their lesson later, when they see how their experience matches with our good advice.
Perhaps we need to let our students have some of the responsibility for their own learning. Perhaps they need to get a little sunburn in order to learn sun safety.
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The Bare Drop-In Centre Walls
I took down all the posters in the Maths Drop-In Centre on Friday and the effect is startling.
(The reason I took them down is that the Drop-In Centre is moving to a new location in under two weeks and I needed to feel like I was doing something before the boxes arrive and we can pack properly.)
It’s all gone: the Greek alphabet, the regular and semiregular polyhedra, the characters from the phantom tollbooth, the families of number, the picture of me teaching maths as drawn by my daughter, the “solving maths problems” flowchart, and the aims of the Drop-In Centre – and now the walls look as bare as when I arrived.
I almost cried.
It made me realise what a difference all those posters made to the learning environment of the Drop-In Centre. Without them it’s just like any other classroom that never meant anything to me – a place people occupy rather than live in – a dead place.
Even the students commented on it. When I took down the “solving maths problems” flowchart, one said, “Where will we get our inspiration from now?” and another commented that there won’t be anything to talk about without the interesting posters.
I never knew as surely as now what an effect the environment has on the students. It has helped them to engage with their own learning and to interact with us and each other.
I can’t wait to move so I can put it all back up in the new Drop-In Centre – I want a living classroom again!
This comment was left on the original blog post:
David Roberts 17 Jan 2011:
Ah, those wonderful posters. They certainly helped brighten up our office in the old maths building, when David and I were PhD students. We never quite saw eye to eye about what sort of ‘things’ should have gone in the families of numbers posters. 🙂 But David is right – at some point they stop _being_ numbers. -
Individual Ahas
At the Hmm… Sessions in November, something cool happened when a couple of the students were showing the rest of us the solution to a puzzle.
(For those who don’t know, The Hmm… Sessions are a regular gathering that I run where staff and students solve puzzles together in a group.)
(Update: Later this year, the Hmm Sessions were renamed “One Hundred Factorial” after the first puzzle we ever did.)
The puzzle was this one from the AustMS Gazette November 2010:
Three boxes are on the table. One has red balls, one has blue balls, and one has balls of both colours. Three labels are made for the boxes, but they are misplaced so none of the boxes are labelled correctly. How many balls would you need to retrieve from the boxes in order to determine the correct labelling?
Well, as I said, a couple of the students were showing us their solution to this puzzle at the big whiteboard. As they were doing this, each person watching cried, “Oh! That’s cool!” in turn. Each of us came independently to a sudden realisation of how the solution worked – we had “seen” the solution before it was actually presented.
I think this is very cool because it says to me two things about how mathematicians work:
One: Mathematicians don’t really listen fully to other mathematicians. Our minds are always racing ahead making connections and figuring things out on our own. Perhaps this is because we get the most thrill from seeing things ourselves rather than being told.
Two: Mathematicians come to understanding at their own pace, which may be fast or slow. At the Hmm… sessions, each of us had our Aha momentat a different time.
Apart from these two, the other thing that really impressed me was that none of us looked down on anyone else for taking longer but merely rejoiced when someone did see it. I couldn’t hope for a better atmosphere in the Hmm… Sessions than that!
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Books in the 22nd Century
I’ve just read a book called “Written for Children” by John Rowe Townsend. It was published in 1974 and gives the history of writing for children (in English) up to that time. It was very interesting reading. What I’d like to comment on here is the final chapter, where the author talks about the future of books (p333 onwards):
The question that arises next is whether changes in the book world might be overtaken by technological developments which would make the book itself, or at any rate reading for pleasure, obsolete. … Myself, I have an instinctive faith in the ability of the book to keep going. It is a tough old bird, after all. People thought that the cinema and radio and television would kill it, but they have not done so yet. Perhaps it is not too wildly optimistic to hope that in the twenty-first century, when all the modern miracles and some we have not yet dreamed of have come to pass, a child will still be found here and there, lying face down on the hearthrug or whatever may be then have replaced the hearthrug, light years away from his surroundings, lost in the pages of a book.
It makes me happy to know that Mr Townsend’s vision did in fact come to pass and that children can still be found lost in a book even here in the twenty-first century. And it gives me hope that in the same way that the book was not killed by cinema or radio or television, that it will also survive the internet and the ipad.
And finally it makes me think of a parallel situation in mathematics. I have heard people say that the computer is forever changing the way mathematics is done. This is definitely true, but I don’t believe that the “old ways” will die. I believe that there is a certain joy that comes from doing something yourself, from scratching out a problem yourself on paper, from playing with symbols and pictures, from visualising things in your own mind, from dreaming about new ideas – a joy that is absent when the computer does things for you. So I hope that even in the 22nd century you’ll still see people sitting down with a pencil and paper scribbling as they try joyfully to solve a problem all on their own.
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Pushing your own “Dawn Treader”
I went to see the new movie version of The Voyage of the Dawn Treader on my birthday and I was sorely disappointed. I liked The Lion the Witch and the Wardrobe and I was a little disappointed with Prince Caspian – if the pattern continues I wonder what depths of disappointment I might sink to if they ever make The Silver Chair.
But my disappointment itself is quite another matter – the point of this post is why I’m disappointed: I’m disappointed because they removed most of the wonder and innocence of the book. They decided their version would be more exciting or interesting or mysterious, but in the end they just made it less than it was before. Many of the scenes of the book with the most meaning and feeling for me were cheapened by the film-maker’s agenda. And as to some of my well-loved characters – like the Dufflepuds – the film-makers thought that merely including them somewhere was the important thing, but I think it would have been better not to include them at all rather than the half-hearted cameo they got.
*sigh*
But what has this rant got to do with Maths or Learning or living in the Maths Learning Centre? Well here’s my thought – how often do we, with our students, do the same thing to the subjects we teach?
In order to serve some agenda – say the usefulness of a particular bit of maths to some obscure application – we remove the wonder and innocence of our subject. The joy of discovery and learning, and the meaninfulness that comes from an encounter with something rich and wonderful are lost in the agenda we must keep.
And we keep some things in our courses in order to appease the people who say it must be there, but it would be better to leave it out entirely than leave behind the shameful passing wave they have – like “informal induction” in the current South Australian year 12 maths curriculum.
But what are we to do?
If we have the choice to change our curriculum we are like the writers of the film – we have a responsibility to capture the wonder of the original and not push our own agenda.
If we must teach the curriculum we have, then we are like the actors in the film who have to do the best we can with the script they’re given, even if it is only a hollow copy of the original story. We can put as much emotion and feeling as we can into our delivery.
And if we are neither and like me aren’t directly involved in the curriculum at all, what then? Well the film did remind me of the book, and made me think of all those things I did love about it (even if they weren’t in the film), and it will probably inspire many who have never read the book to read it now. In the same way, maybe I can work with those students who are involved. I can tell them about the story I remember that is similar but so much better than the version they have seen; I can encourage students to have their own moments of wonder; and I can encourage them to investigate the half-hearted cameos further and gain a true love for the characters they missed out on the first time.
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Wisdom from the Dodecahedron
The Dodecahedron is a character from the book The Phantom Tollbooth by Norton Juster. He lives in the city of Digitopolis at the base of the Mountains of Ignorance. Here is his description from the book (page 145)
He was constructed (for that’s really the only way to describe him) of a large assortment of lines and angles connected togehter into one solid many-sided shape – somewhat like a cube that’s had all its corners cut off and then had all its corners cut off again. Each of the edges was neatly labelled with a small letter, and each of the angles with a large one. He wore a handsome beret on top, and peering intently from one of his several surfaces was a very serious face. Perhaps if you look at the picture you’ll know what I mean.
Now we can learn a lot from what the Dodecahedron says. Look at this exchange (page 148):
“I’m not very good at problems,” admitted Milo.
“What a shame,” sighed the Dodecahedron. “They’re so very useful. Why, did you know that if a beaver two feet long with a tail a foot and a half long can build a dam twelve feet high and six feet wide in two days, all you would need to build the Kariba Dam is a beaher sixty-eight feet long with a fifty-one foot tail?”
“Where would you find a beaver as big as that?” grumbled the Humbug as his pencil point snapped.”I’m sure I don’t know,” he replied, “but if you did, you’d certainly know what to do with him.”
“That’s absurd,” objected Milo, whose head was spinning from all the numbers and questions.
“That may be true,” he acknoledged, “but it’s completely accurate, and as long as the answer is right, who cares if the question is wrong? If you want sense, you’ll have to make it yourself.”To me, this encapsulates a lot about how mathematicians think: to a mathematician, it’s the problem that’s the interesting thing, not the usefulness. In fact, we even define usefulness differently – note how the Dodecahedron uses his beaver example to show the usefulness of problems. Clearly this is not the same as the Humbug’s definition of usefulness. I rather suspect that to the Dodecahedron, it’s useful because it highlights how maths can solve problems – whether the answer is realistic or useful is a side issue.
Still, Milo clearly doesn’t get it, but I’m not sure it’s the maths itself that’s the problem – it’s the mathematician: Milo and the Dodecahedron think differently about what is useful. Maybe as teachers, we should help the students understand mathematicians a little more, as opposed to just understanding mathematics.