Monthly Archives: March 2015

CPD: How Not To Do It

I’d like to start with a question:

How can we become better teachers?

Some of the answers that have been suggested (not always by teachers) are: performance targets and rewards; teaching from a centrally-designed curriculum; higher qualifications and study; INSET sessions; plain old experience. While all of these have their place, I am interested is something else, and I would like you now to answer a second question – as a way of getting an answer to the first:

How have I become a better teacher up until now?

One thing that I predict features highly on most people’s list is: help from colleagues. So often a chance comment or lament in the staffroom is picked up on by someone else and sparks a helpful conversation, some tips, and some guidance. We then put our friend’s ideas into practice and the next time she sees us, she says ‘How did it go?’. We tell her what went well or badly and she responds again, suggesting further material or an alternative. And what’s more, a year later we in turn will be helping another colleague, passing on that same advice, perhaps with a twist of our own, and perhaps not even remembering where we got the idea in the first place – so much is it embedded in our daily practice.

This informal process goes on in all workplaces, and most of us have gained a lot this way. A culture and network forms around us through which we exchange our ideas. True, there will be some people around you that are bosom buddies while others you learn from simply by determining never to be like them. But the network is vital, and if people are cut off from it – because they have become isolated in their location or alienated from the group, for example – they feel the lack.

When I first got very interested in the idea of professional development, and started to investigate some of the research, I found that the experience I described above is more or less a template for excellence in the transfer of skills.

One piece of research I found, Lieberman and Wood (2002) – link below, explored the connection between teachers’participation in networks and the transfer of practice between the teachers’ learning environment (eg a course they went on) and their classrooms. One of the students in the study gave this description of why they had managed to implement what they had been taught:

“I found that the experience and support passed on by other teachers was much more valuable to me than any workbook [or] step-by-step method that had promised to be the quick fix.”

A problem then arises for someone like me, who is regularly asked to contribute to the CPD of teachers in the form of INSET. Don’t get me wrong: I love doing them, because I like meeting teachers, sharing what I do, planting intellectual seeds, and… well, yes… because I do rather like the sound of my own voice. No, the problem is that I am not sure what good they do for the participants.

I really try to make it relevant, to mix some theory with some anecdotes, to have discussion as well as instruction and I always include a few practical tips that teachers can take into the classroom the next day. I hope this makes me one of the good guys. But where the system falls down is that, however informed or inspired teachers might be when they walk out of the training room, there is no mechanism to continue these ideas into their daily professional lives.

Where INSET does work is to make people familiar with new ideas or get them up to date with statutory rules/best practice. It doesn’t change what you do in the classroom. Or to be fair: it doesn’t change it very much very often.

So does that mean we can all go home – or get back to our lesson prep – 90 minutes earlier on a Tuesday evening and forget about INSET – just leave it all to our wonderful internal network? Unfortunately, one problem with the network is that the ideas that you are exposed to depend on the ones that exist in your own narrow circle of teaching colleagues. And that would leave the direction of your development down to luck.

For this reason, we do need a CPD programme that makes use of external providers and ideas from other schools, industries and traditions. But it needs to mimic our informal network as closely as possible. Here are some of the features that make the informal network effective:

  •  Access – we can find our colleagues quite easily, and find a moment to chat
  • Two-way communication – we are listened to just as much as we listen
  • Time lapse – there are gaps between the stages of our learning, allowing us to process ideas
  • Flexible – your colleague/mentor will respond to your ongoing feedback, constantly altering their advice
  • Open – the goalposts can move as we realise where they should be; let’s see what works!
  • Familiarity – your colleague knows you, your working environment – and often your class!

Here are two ways that we can incorporate these features into a CPD plan:

  1. Send one teacher out for full training in a new approach and then get that person to disseminate the ideas across the school. That doesn’t mean, of course, that you get them to do one INSET for the others and it’s job done. What it means is that after an INSET to introduce the main ideas, the teacher in the know needs to have a series of meetings with interested colleagues. The meetings can be short – 20 mins of PPA time – and irregular but they need to happen. Inevitably a lot of the progress will be made outside of this framework, as the people involved exchange thoughts over coffee and in the corridor, but – and this bit is important – the informal stuff will happen a lot more if there is an official process going on.
  1. Demand that CPD providers abandon the fire-and-forget model of descending on the school for a few hours and then disappearing in a cloud of exhaust; get them to put some thought into continuity. No teacher or training professional worth their salt will claim that parking a group of people in front of a power point and ending with a few questions is a proven way of getting people to learn. We wouldn’t teach our children that way. With online communication so simple now, the least they can offer is a blog or forum for teachers to ask questions once they’ve tried to implement the new ideas. What other lead-in and follow-up can they provide? Can they visit the school again a few weeks later?
  1. Don’t insist that all teachers do all the new stuff. The ‘development’ part of CPD refers to the organic growth process and so we should be considering what is right for each teacher to do next. One teacher might be inspired and invigorated by story-telling or blended learning but those same techniques could end up being the bane of another teacher’s life. That doesn’t mean that those other teachers get left behind; they can’t keep on opting out. They need to find things that they want to explore – and hopefully share.

If you are the sort of person who makes these decisions for the school, you may be getting a nasty feeling that some of these projects might cost more. They will. But you may be comparing them to the cost of things that don’t work. Perhaps consider having fewer initiatives and CPD objectives than you have now but for the same budget that you have now.

If you are reading this as a teacher, you may not be the main decision-maker on some of these issues, but remember that headteachers need people like you, reading articles like this, and telling them which CPD providers you want next term. After all, they have to get their ideas from someone too.

Originally published by The Teacher Development Trust. Thanks to Alistair Jeffrey for this:

For further research on what makes effective CPD for teachers, see the paper from the AQA Centre for Education Research and Policy here https://cerp.aqa.org.uk/research-library/effective-continuing-professional-development-teachers

 

Lieberman & Wood 2002 – http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCIQFjAA&url=http%3A%2F%2Feducationalleader.com%2Fsubtopicintro%2Fread%2FASCD%2FASCD_413_2.pdf&ei=VZoSVe3tMob3UsmSg8AC&usg=AFQjCNFiml2ZJ8apf2F7PElDo0i2RT6FEA&sig2=srLXP3dUedDn6R415hT6uw&bvm=bv.89184060,d.d24

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The Talking Skull – thinking about making claims

From Peter Worley’s new book due out in September 2015, given here as part of Keystone Workshop held on March 25th in St Albans.

Equipment needed and preparation:

  • (Optional) something to stand in for the skull and Enitan’s head, such as two balls (in addition to the talk-ball).
  • (Optional) have the Thoughting ‘Talking is like…’ ready to project or handout.

Starting age: 9 years

Key concepts / vocabulary: knowledge, belief, reasons, miracles, magic, talk, communication, communicate

Subject links: RE, Science, Literacy, PSHE

Key controversies: Should we believe people’s accounts of miraculous events? Is talking a good thing?

Quote: ‘There are only three possibilities. Either your sister [Lucy] is telling lies, or she is mad, or she telling the truth. You know she doesn’t tell lies and it is obvious that she is not mad… we must assume that she is telling the truth.’ – The Professor in C.S. Lewis’s The Lion, The Witch and The Wardrobe

No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavours to establish.’ – David Hume ‘Of Miracles’

Key facilitation tool: Quotes. Discuss. – In the extension activities section, this session suggests the use of a quote (from C.S. Lewis’s The Lion, The Witch and The Wardrobe) as a stimulus. Statements can be very effective catalysts to thought, sometimes more effective than a question, as they can provoke a visceral response. Compare these two ways of putting an issue to someone: a) ‘Are girls or boys better at writing?’ b) ‘Girls are better than boys at writing.’

Session Plan:

Do: read or tell the following story. It is only a little more than a synopsis, so feel free to embellish the story in your retelling, if you choose to tell it. (See Once Upon an If: ‘Sheherazad’s Handbook’ pp. 20-55.)

Say: A long time ago, somewhere in Africa, there was once an honest, sensible man, called Enitan. One day, while walking through the jungle by himself, he found a human skull lying on the ground. He wondered how the skull had come to be there so he said, out loud to the skull, ‘How did you get here?’ not expecting an answer.

         ‘Talking brought me here,’ said the skull. Amazed and terrified at what he had just witnessed, Enitan ran all the rest of the way home.

He went to see the village chief and told him about the talking skull he’d found in the jungle, thinking that this would make him famous in the village.

Start Question: Should the village chief believe Enitan?

Possible Further Questions (you do not need to go through all of these):

  • The man’s story is extraordinary, so should the chief believe him?
  • If the story is true, then should the chief believe him?
  • Should Enitan believe himself?
  • Is it a miracle?
  • What is a miracle?
  • Could there be any other explanations for the skull talking?
  • If someone tells you something unbelievable should you believe him or her?
  • If so, under what circumstances should you believe an unbelievable account?
  • Try using the Professor’s test from The Lion, The Witch and The Wardrobe with Enitan’s claim (see quote above). Is the Professor’s test a good way of testing people’s claims?

         The chief did not believe him. ‘But I DID see a talking skull! I did! I DID!’ Enitan protested.

         ‘Okay,’ said the chief, ‘I, and two of my guards, will go with you; if the skull speaks I will reward you with treasures and fame, but if it does not… then I shall reward you with death.’

The chief, his guards and Enitan returned to the place where he had found the skull. Enitan bent down and said to the skull, ‘How did you get here?’ The skull said… nothing.

         ‘HOW DID YOU GET HERE?’ said Enitan again, louder this time. Still the skull remained silent. The king turned to his guards and said, ‘This man has also wasted my time! Kill him!’ So they chopped off his head which fell to the ground next to the skull with a thud. The king and his guards returned to their village. Once they had departed, the skull opened it’s grinning mouth and said to Enitan’s head, ‘How did you get here?’ and Enitan’s head replied, ‘Talking brought me here.’

Comprehension Question: Why did Enitan’s head reply, ‘Talking brought me here,’?

Start Question: Is talking a good thing?

Possible Further Questions:

  • What is talking?
  • What does talking help us achieve?
  • What would we loose if we lost the ability to talk?
  • What would the world be like without talking?
  • When and how might talking be bad?

Say: No one noticed: not Enitan, the chief or his guards, but lying in or on the ground, littered all over the place, were many more human skulls!

Comprehension Question: Why are there lots of skulls?

Extension activities:

Task: Communicate something without talking

  • Have someone leave the room.
  • Identify an item in the room to another child.
  • Set the second child the task of communicating something – anything – about the item but without talking or using words in any way.

Questions:

  • Can they do it?
  • How easy is it?
  • What methods did they use?

‘Talking is like…’: a simile exercise

Do:

  • Go round the circle and say ‘Talking is like…’ to each child.
  • Give them 3 seconds to say a word without repeating another child’s suggestion (employing ‘the different answer rule’).
  • Gather the words on the board as you go around.
  • Once everyone has had a go, ask all the children to challenge the words: for example, ‘I don’t understand how talking can be like X…’
  • Ask the class, as a whole, to respond and attempt to explain why talking is like X.
  • Here is a Thoughting based on the exercise that could be used in a similar way: ask the children to challenge the words in the Thoughting and have the class respond in its defence. If the children struggle to grasp the simile/metaphor essence of the task you could read the Thoughting first, in order to give them a flavour of the task, and then run the activity, stipulating that they should not repeat anything from the poem.

Talking is like…

A tool,

An instrument,

A cloak,

A weapon,

A map,

A metal detector,

Medicine,

Poison.

A virus,

A wireless

Kind of

Connection.

A finger

That Points

To the farthest

Location.

With talk

I walk

But do not

Move.

With talk

My thought-

Hawk flies

To you.

Thoth and Thamus: for-and-against

In The Philosophy Shop (page 256) Claire Field retold an Egyptian myth told by Plato called ‘Thoth and Thamus’. In it, Thoth (the ancient Egyptian god of intelligence) is a god who invents new things and Thamus is a king who has to agree to Thoth’s new inventions before they will be given to the people. Thoth invents writing and the two argue about the merits and demerits of giving writing to the people. Claire has the class argue, with each other and on behalf of Thoth and Thamus, the ‘pros and cons’ of writing. When the myth is used in this way, its general application can easily be seen. A part from the ‘for-and-against’ dialogue opportunities Thoth and Thamus affords, it also has potential for the children’s written work. Have the children write their own dialogue with the two characters Thoth and Thamus arguing over the merits (Thoth) and demerits (Thamus) of X. ‘X’ could be ‘writing’ or ‘talking’, but it could also be ‘cars’, ‘plastic’, ‘green energy’, ‘democracy’ and so on. (See ‘The Cat That Barked’ in Once Upon an If, page 112, for more on dialogues and dialogue writing.)

Talk Ball

Play the BBC Radio 4 game Just a Minute! (Here called ‘Talk Ball’ because a minute is too long). This is when a player has to speak on a subject, while holding the talk-ball, for a set time period without hesitation, repetition or deviation. I begin with a 10 second time period, then, when someone succeeds, extend the time to 15 seconds, then 20 seconds etc. (See also Robert Fisher’s Games For Thinking.) The class choose up to eight topics, but which of the topics each speaker has to speak about, is chosen randomly.

Related Resources:

Ted Hughes’s poem The Thought Fox

The Philosophy Shop: The Txt Book, Thoth and Thamus in The Philosophy Shop and conduct the same discussion around talking instead of writing. Task Question: If you were Thamus would you allow Thoth to introduce talking to the people?

The If Odyssey: ‘Nobody’s Home (The Cyclops)’ especially the online supplement on the companion website ‘Through a Philosopher’s eye: Cyclops’. In some versions of the Greek myth of the Trojan war, the character of Palamedes meets an ironic, tragic end when, he – the so called inventor or writing – is undone by a written letter. In revenge for Palamedes’s uncovering of Odysseus’s attempt to escape being sent to Troy, Odysseus fakes a letter from Palamedes to Priam. Palamedes is stoned to death by Odysseus.

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From the Chalkface

by Steve Hoggins

I had a breakthrough with one of my pupils this week, all initiated by a great learning support mentor who has also helped with our Young Philosophers group (a termly meet up of children from across Lewisham who are good at philosophy, and who don’t normally get these opportunities. The aim of the group is to inspire children, raise attainment, and also for us to keep in contact with children who would benefit from extra support).

Our class had a new arrival last term, an extremely quiet pupil who wasn’t making friends and refused to speak in philosophy. The quiet pupil was assigned a learning mentor after the first few weeks and a couple of weeks after the learning mentor approached me to say that this pupil had been talking about philosophy in their one-to-one lessons.

At the learning mentor’s suggestion the pupil would come to the class a little earlier and we’d have a chat. It transpired that she had ideas but couldn’t get them out straight and was a little intimidated by the rest of the class. We made a deal that every Talk Time (moments in the session when the children talk with each other about the question under consideration) I would listen to her idea one-to-one, and then share it with the class. At first I would share it anonymously and later we agreed that I could say it was her idea.

This week the class were discussing friendship and some argued that, ‘you can be friends with something as long as you like it; you can be friends with a teddy bear’. My shy pupil told me in Talk Time, “That’s not right, I like food but I eat food and you don’t eat your friends”. So, per our agreement, I shared this with the class. There was some healthy disagreement but some had clearly just missed the point. All of a sudden, after one particular misapprehension of the shy pupil’s idea, that same shy pupil raised a hand and with a bit of a stumble clearly re-stated her argument, speaking in front of the class for the first time since joining – whoop!

I think there are 4 things of note here:

  • This quiet pupil was actually engaging in philosophy, despite not speaking.
  • The other people around the pupil can bring valuable insight.
  • The child was drawn out from a desire clarify her idea rather than being asked/persuaded (intrinsic motivation, rather than extrinsic)
  • Some days are just brilliant.

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Maths In Singapore: Why You Don’t ALWAYS Want To Start With A Concrete Example

Question: How do you introduce new concepts in Maths?
One Answer: You demonstrate and explore them in a concrete way, then get students to represent the concept pictorially, then record it numerically – from the concrete to the abstract, in other words. So if you were introducing fractions, you’d get students to cut up a cake, then draw or arrange pictures of cakes cut up, then use digits to record the process.
That all makes sense to me, and apparently it’s the main principle behind Singapore Maths, the curriculum and methods that started in Singapore and have been followed by schools around the world attracted by the country’s performance in Maths teaching.

However, I spent last week at the impressive UWCSEA international school in Singapore. They don’t use ‘Singapore’ Maths, though, because they are an international school and so outside the Singapore system. I was there to work with the teachers on Enquiry Maths, an approach I came to through doing philosophy in schools.

The central insight of my book The Numberverse – the thunderbolt that hit me when I first got into this area – is that children will explore numbers in the abstract. So yes, they are helped enormously if they can proceed from concrete to abstract, and see how concepts are applied first. But they also, at times, can make strides by pursuing their own curiosity about numbers in the abstract. I’d like to give an example of how.

One of the many challenges the teachers at UWCSEA set me was how to use enquiry to introduce the multiplication of fractions by whole numbers, e.g. 3/4 x 7. When I learned this topic, in about 1980, it certainly wasn’t by enquiry. I had a good teacher that year but she was the sort that just showed you how to do stuff: I was told to multiply the top number (numerator) by the whole number, e.g 3 x 7 and keep the bottom number (denominator) the same, e.g. 21/4. Bingo. This gives you a correct answer, though you may need to simplify the fraction, e.g. 5 and 1/4.

I learned to do this mechanically, and as the arithmetic involved is pretty simple even for someone like me, successfully. It was some time – perhaps years – later that I twigged that 3/4 multiplied by 7 is exactly the same as three-quarters OF 7.  My confidence with the procedure wasn’t matched by a confidence with the concept, the problem lying in wait being that when I needed to apply the knowledge (whether in practical situations or abstract ones, like algebra) I was hesitant.

So I wanted the group I worked with last week to ground the new concept in the knowledge they already had. I followed the principle of starting with the known as the gateway to the unknown. I wrote this on the board:

6 x 6 = 36

6 x 5 = 30

Without saying anything about what I was doing, I asked if anyone could continue it. They wrote the 6x table backwards down to 6 x 1 = 6. I asked if we had finished. Someone added 6 x 0 = 0. Have we finished now, I asked. After discussion in pairs the children said that you could continue by ‘doing minus numbers’. I agreed that you could. Then I asked:

‘Does anything go in between these?’ and pointed to two lines in the list. The room buzzed with activity, and after a few minutes each pair had suggested another entry to the list, where 6 was multiplied by a fraction or mixed number. They wrote their ideas in the gaps between the lines. Although they used the word ‘fraction’ when they discussed it out loud, they mostly switched to decimals when writing. The children attempted:

6 x 1.5
6 x 1.75

… and so on. Some of their calculations weren’t correct, but two of the children thought through how to test the calculations practically: by imagining six people all with one and a half cakes each, for example, and counting how many cakes there are in total.

What these two children were doing was working the opposite way to the concrete-to-abstract method I mentioned at the beginning. I’d got them to think about it purely as a matter of logic: i.e. there must be something in between 6 x 0 and 6 x 1, so what could it be? Now they were testing that abstract reasoning by applying it to a concrete scenario. Some felt more inclined to do that testing than others, and that’s fine.

So my point is that you can start at either end – concrete or abstract. Different topics, different students, different teachers and resources – all of these may influence a teacher’s decision about which angle to come from.

Where this comes into its own is if you extend this from multiplication to division of fractions. So now you might write:

6 divided by 3 = 2

6 divided by 2 = 3

6 divided by 1 = 6

Now if you just stop a moment you might spot something new this time. Whereas last time moving on to 6 x 0 was quite straightforward, 6 divided by 0 is far from that. In fact I once set this to a class as a starter and asked them to figure it out, having stumbled across the problem myself and got very confused. I initially thought the answer must be 6 or 1. But neither makes sense: 6 by 1 is 6 and 6 by 6 is 1, so neither of those can have the same answer as 6 by 0… surely?

If you try the concrete approach of physically trying to share 6 oranges, say, between zero people you find that you are in fact left with 6 oranges as you have no-one to share them with. But then the whole point of sharing is that I should share out all that I’ve got till I have nothing – not have everything still left.

Working at an abstract level was something I found more helpful on this occasion. It took me a while to figure this, but I remember one boy who came up with it within about 10 seconds of being presented with the problem:

‘You can’t do it. Because you can’t do it backwards. If 6 divided by zero had an answer, that would mean something multiplied by 0 equalled 6, but it can’t.’

This is a perfect reductio ad absurdum argument. It shows that if we allow that 6 divided by 0 is possible then we have to allow also that something multiplied by 0 equals 6, which is absurd. This boy was thought not to be very academic, by the way, but OK because he was good at sport. I’ve got a feeling he’ll do just fine in life.

If you’re interested, you can see Matt Parker prove it more mathematically and entertainingly here <a href=”https://www.youtube.com/watch?v=BRRolKTlF6Q”>

But that’s all a digression! The point is that by running the same enquiry for dividing by fractions as you did for multiplying them you might get the children filling in values like this:

6 divided by 3 = 2

6 divided by 2 = 3

6 divided by 1 = 6

6 divided by 1/2 = ???

If children can spot a pattern in what comes above they can make a conjecture about what comes next. For example, they might say that the answer must be higher than 6.  Good start.  How much higher…?  Tricky to say.  Or they could see that the inverse operation works in each line, so they ask themselves: ‘what do you multiply by a half to get six?’, or ‘how many halves make six?’. Then the answer is quite straightforward: 12.

Were you, on the other hand, to try and start from a concrete scenario, then what? You imagine yourself giving six oranges to half a person?! I would be genuinely interested to hear from anyone who has managed this, as I’d like to be able to come at it both ways. Until I hear different, though, I’ll go on believing that sometimes the concrete-to-abstract is perfect, but that the purely abstract sometimes blows it away.

[Since posting this I’ve seen an excellent round up on the x & ÷ fractions issue: http://www.resourceaholic.com/2014/08/fractions.html ]

If you’d like to take a peek at The Numberverse, try:
http://www.amazon.co.uk/The-Philosophy-Foundation-Numberverse-everything/dp/1845908899
<a href=”
http://www.philosophy-foundation.org/resources/philosophy-foundation-publications/the-numberverse&#8221; target=”_blank”>http://www.philosophy-foundation.org/resources/philosophy-foundation-publications/the-numberverse

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