Wednesday, April 13, 2011

Tale of Two Teachers (Part II)

In this exhibit, Brian Cambourne relates two very different stories about his own learning. (These can be found in the paper, The Teaching-Learning-Language Connection: How Learning In the Real World and Learning In the Content Areas Are Related.) This is a brain-on exhibit that asks you to identify conditions that support and inhibit learning.

The first story describes how Cambourne learned to iron (see it here).

This story describes Cambourne's attempt to understand a high school topic.
Recently I had cause to call a colleague who teaches Maths Education at the University where I work. I needed some help with the binomial theorem so that I could help with my daughter's homework. Here is a verbatim account of the telephone conversation I had.

B.C. Hello Grahame. I need to help my daughter understand the binomial theorem, (a+b)^2=a^2 +2ab +b^2. I vaguely remember it from my high school days, but I can't remember much about it. Can you explain it in language?

G.W. That's easy. It means: If you want to raise the sum of any two numbers to the power of two then....

B.C. Hang on! You've lost me. What do you mean, 'If I want to'? Do I have a choice. Why any two numbers? What does raise to the power of two mean?

G.W. Uh oh. I'll have to go back a level with you won't I? Try this: If you want to square any two numbers...No wait a minute, That type of 'If' language bugs you doesn't it. Try this: When you want to square the sum of any two numbers then you....(long pause)

B.C. What's wrong?

G.W. I don't like saying it that way. It changes the meaning slightly and will only lead to confusion later.

B.C. What do you mean?

G.W. Well let's say you want to go beyond 'squared' and 'cubed' and you want to raise the sum of any two numbers to the power of 'n' we have no words beyond 'squared' and 'cubed'.

B.C. I'm getting more confused and lost. What do you mean 'When I want to?' When would I want to raise the sum of any two numbers to any power? What's a power? Why the sum of any two numbers? Mightn't I want to do it with any three or four numbers?
Although I'm not sure why or when I'd ever want to do that. And I'm not too sure about 'squared' and 'cubed' or 'n'. And all that conditional language. Why do mathematicians talk like that?

G.W. I'll go back another layer. Let me see: Let's suppose that you needed to add two numbers together and then multiply the result by itself... Uh oh that's even more confusing isn't it? And what's more it doesn't mean what I intended... it's imprecise.. You'll have to call me back later. I need to think about the language I use. I've never reflected like this before.

It is clear in this description that learning was elusive. What made it more difficult for Cambourne to learn the binomial theorem than to iron? Consider current classroom approaches: are they more like mentoring (learning to iron) or the game of telephone (learning the binomial theorem)? Why?

Tuesday, April 12, 2011

Tale of Two Teachers (Part I)

In this exhibit, Brian Cambourne relates two very different stories about his own learning. (These can be found in the paper, The Teaching-Learning-Language Connection: How Learning In the Real World and Learning In the Content Areas Are Related.) This is a brain-on exhibit that asks you to identify conditions that support and inhibit learning.

The first story describes how Cambourne learned to iron.
Firstly there surfaced a need (reason, purpose, motive, desire, intent, commitment) for me to learn how to iron at that particular time in my life. I realised that I had to become a member of the ironers' club.

Secondly when I became conscious of this need I decided to seek help. Usually in situations like this I look for a book or some printed materials that I know will inform me of what I need to know. However this time I found this strategy to be inappropriate. I decided that I needed the opportunity to observe someone who had more expertise than myself. I sought a demonstration. I arranged for a friend to give me a lesson next time she was ironing. We started with a shirt. I stood nearby and observed what she did. She talked as she demonstrated. She explained how she did the sleeves first, then flipped the shirt over, did the front, then flipped it over and did the back, and then the collar. She then told me how she liked to put the area near the shoulder and neck over the rounded end of the ironing board and iron the section where the sleeve joined the the neck and shoulder, She showed me how she did this and flipped it over and did the other sleeve-shoulder area. Then she hung it on a hanger. She explained how to fold shirts in a certain way for travelling purposes. As I reflect on the experience I also realise that she used language in such a way that I could get the general meaning of what she was intending. This meaning was further enhanced by the fact that the demonstrations and the explanations were given simultaneously. She didn't just tell me what to do. She used phrases like, 'I find it easiest to start with the sleeves' and so on. I realise now that we began to share a set of meanings and ways of using words and phrases to represent them. She then demonstrated and explained how to do a pair of slacks. Again I observed, and mentally rehearsed myself doing it.

Then I tried to apply what I'd been observing. I began with a shirt. I tried to flip it onto the ironing board the way my teacher had. It didn't seem to fall into place the way it did for her. Then I tried to position the sleeve so that I could begin to iron it. When I moved my left hand to flatten out the sleeve and align the seams symmetrically it fell off the ironing board and on to the floor. When this happened my teacher said something like, 'That happens to me sometimes too. Here let me show you again and this time I'll try to explain why I'm doing what I'm doing as I do it, and you ask questions when you don't understand. O.K.?'

My learning from that point was rapid. I had about four more joint sessions like this one. My teacher demonstrated and talked out loud, explaining what needed to be done and why. I found myself attending to and engaging with things I hadn't been aware of before, such as the way one can use the seams in garments to achieve symmetry, or the different functions that the sharp and blunt ends of the iron serve. I asked many questions about why she did what she did. After these initial joint sessions during which I received authentic feedback and praise, I began to practise by myself.

Whilst visiting another friend's house I asked her to show me how she goes about ironing. I found myself observing how she did it and engaged her in a conversation about what she was doing. It was then that I discovered something that I'd never been aware of before, namely that the function of the left hand, the way it held and moved the garment for the iron was absolutely crucial for the whole enterprise. I concluded that the key to effective ironing was the left hand, not the hand which held the iron.

Feeling quite the expert now I decided one morning to impress my daughter. I nonchalantly ironed her school shirt for her. She was obviously impressed. I felt I'd become a member of the ironing club. I was an expert.

Before we go to the second story, make your thinking visible and record what conditions supported Cambourne's efforts to become an expert ironer.

Sunday, April 10, 2011

Theory into Practice - Good Readers

Diane Dahl shares the following exhibit from her blog:
I've wanted to come up with a clever way for students to remember their thinking for reading strategies. A list just seems too boring. One thing I've learned in BrainSMART is to connect information to parts of the body to make it more memorable. So I came up with this Good Reader Boy poster? (The original poster is shown to the right.)

The (updated) poster connects like this:

  • Head: Think. Good readers monitor their own thinking while reading.
  • Eyes: Infer. Good readers look for clues to draw conclusions, make predictions, and more.
  • Nose: Importance. Good readers sniff out important details.
  • Mouth: Questions. Good readers ask questions before, during and after reading.
  • Heart: Visualize. Good readers love to make brain-movies while reading.
  • Stomach: Schema. Good readers are hungry to connect their text to things they already know.
  • Waist: Purpose. Good readers don't waste time ... they choose a purpose for reading and pick the best strategy.
  • Hands: Synthesize. Good readers can 'put it all together' to retell and summarize.
  • Knees: Monitor Comprehension. Good readers know they need to understand text, and know what to do when they don't.
  • Feet: Text Structure. Good readers firmly understand the elements of a story and use it to help them understand.

The Good Readers Poster is available in the "Museum Gift Shop"

When and Where Learning Occurs - New Jersey Preschools

This exhibit is a National Public Radio piece on learning happening at New Jersey preschools in low-income districts.
Young Learners at Play
Unfortunately, some do not recognize that this learning is important:
Sen. Michael Doherty, a Republican from Warren... represents a large swath of suburban New Jersey where resentment toward the extra funding of low-income schools runs deep. He is proposing that the preschools for poor kids be cut to half-day, and the $300,000 saved be spent on K-through-12 education in the suburbs.
Such thinking demonstrates the need for a Learning Museum where people can see why learning for all is so important. 

Comparing/Contrasting Students & Learners, Part I

For those of you familiar with my TEDx Talk, it will come as no surprise that the first exhibit in the Learning Museum involves the following video from the Council on 21st Century Learning (C21L). If we want to know what learning looks like, we need to identify some of its key characteristics. This Venn diagram might help us in identifying these characteristics as we consider what learners do compared to what students do in the video.
Here is the first in a series of three videos available from C21L that attempt to get at the differences between students and learners.

How are students and learners alike and how are they different? Here's some of the characteristic identified by teachers in training:

  • Both students and learners produce products;
  • Students seem extrinsically motivated (e.g. Grades); and
  • Learners seem intrinsically motivated.