Mine Do It Already: Nought To Reasoning In 60 Seconds

Are your children reasoning in the lesson? Not sure? Or maybe you want to prove that they are?

Here is a simple activity that is fun for the children and shows you – or anyone else – how they are reasoning. Before I go on to explain it, it may be useful to give a definition of reasoning that we can use here – just so we know what we are talking about.

Reasoning is described this way by ACARA, the Australian curriculum authority:
‘Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false and when they compare and contrast related ideas and explain their choices.’

A simpler, neater, definition is that when we reason, we use information that we already have to prove information that we don’t have. So, for example, we use DNA evidence to reason that someone must be guilty. We use the lengths of a polygon’s sides to calculate its area.

It also helps to define something negatively – in this case, to say what is NOT reasoning. And here are some examples:

Guessing
Copying
Remembering

Not that those things are bad in themselves. Sometimes we have to guess to get started. Sometime the best thing to do in a given situation is just copy someone who seems to know what to do. And sometimes it is great to realise that you know the answer because you remember it from before. That’s all fine. It is just that where we rely on these strategies we are not, at that point, reasoning.

Here is the activity…

The simplest way to explain is to say that it’s 20 Questions, but with numbers. So 20 Questions goes like this:
• One individual thinks of a type of object at random – such as ‘chair’.
• The rest of the group can ask him/her questions. The individual will only answer Yes or No.
• If the group can guess the word in 20 questions or less they defeat the individual.

For maths, the individual thinks of a number instead of an object. Usually I say it has to be between 0 and 100. With Year 2 or lower, you might want to set it at 1-20. Also, instead of a limit to the number of questions, our goal is to get the answer in the lowest number of questions, improving our score with practice.

If you play this game you will be able to see the reasoning of your class and the people in it. At primary level, the person who finally guesses the answer often wants to claim maximum credit from the others even though he or she may have contributed very little to the hunt. That is a sign that reasoning – using reasons to move from one question to the next – is not taking place, at least with that person.

Between each game, I ask the children to say which questions were good and why (so it’s a good idea to write the questions, or short forms of them, on the board as you go). At the beginning, some may say that ‘Is it 17?’ was the best question because the answer was 17. But gradually the children will start to spot that the final shot was the easy one as all the other numbers had been eliminated. And if not enough numbers have been eliminated then glory-seeking stabs in the dark like ‘Is it 17?’ are a waste of a question (unless the questioner happens to get lucky). The class often takes a while to articulate the idea that a good question ‘narrows it down’. In other words, it reduces the possibilities to a narrower range.

Children also fail to realise, to begin with, that a ‘No’ answer is not worse than a ‘Yes’ answer, necessarily. If you ask ‘Is it an odd number?’, then either a Yes or No answer gives you exactly the same amount of help. And there are some Yes answers that tell you very little. For example, if you ask ‘Is it a two-digit number?’ the answer will probably be ‘Yes’ but it doesn’t get you far because you still have so many possibilities left. Now, you may still feel that ‘Is it a two-digit number?’ is a pleasing answer for you the teacher, because it shows the children recruiting prior knowledge to apply to the task (i.e. they’ve been learning about one/two/three-digit numbers, have remembered it, and are trying to apply that knowledge here). I couldn’t agree more, so you may want to praise some questions while preparing to nudge the questioner towards a more effective strategy.

After a few runs through, I ask the children if they can come up with a strategy that will always get them the answer in a set number of questions – so, can they guarantee to get the answer in 10 questions, or 5? Children then explain their strategies and we try them out. This is crucial because they are now thinking about their reasoning.

Most classes latch onto 0-50 as the first question before long. Either that or ‘Is it even/odd?’. However, it can go in two ways from there. Usually, you have two different strategies being used within the class. For example, after ‘Is it between 1 and 50?’ with the answer No, we might get:

Is it odd? Yes
Is it between 50 and 75? Yes
Is it in the 3-times table? No

Now it is quite hard from here to work out which numbers that leaves. Try it yourself! It’s better to stick to one strategy. So:

‘Is it between 0-50?’ halves the possibilities should be followed by a question that halves what’s left in a predictable, memorable, way. So if the answer was No, then the next question should be either 50-75 or 75-100, and so on, halving each time. For example:

0-50? No
50-75? Yes
50-62? Yes
50-56? No
56-59? Yes
56-57? No
58? No
The only remaining number is 59.

Using the ‘halving’ method outlined above, the class should be able to guarantee to find any number within 7 or 8 questions. You may able to refine this further. I’ve only had a couple of classes who got that far (I generally teach primary).

When I’m playing the game, though, I’m content for the children to circle gradually closer to a strategy like this, and don’t worry if they never quite nail it. What I’m interested in is them looking at a task and saying to themselves: ‘How do I make this simple? How do I work steadily towards the answer?’.

One side issue that comes up here is a problem with the edge of the range. For example: is 50 itself between 0 and 50? You might be sure that it is. But imagine if you have a group of children sitting in a row in this order:

Floriana, Luke, Chester, Adibola, Polly.

We wouldn’t say that Floriana is sitting ‘between’ Floriana and Polly (we’d say that Luke, Chester and Steven were). So the word ‘between’ can be applied differently. You can introduce the word ‘inclusive’ here to help the children, (‘Is it between 0 and 50 inclusive?’) and they will have learned a valuable lesson about the definition of a range. In a similar way, by the way, the question ‘Is it below 50?’ doesn’t make it clear (for some children) whether 50 itself should be judged above or below! You could argue that ‘below’ is not ambiguous at all – 49 is below 50; 50 isn’t – and that’s exactly the kind of precision in the use of terms that we want the children to learn.

If, instead of the ‘halving’ method, children try to extend the ‘Is it odd?’ question into a strategy, another set of problems is thrown up. Because to extend that strategy means using times tables:

• Is it odd?
• Is it in the 3xTable?
• Is it in the 4xTable?
Etc.

This is much harder to operate, and soon challenges the reasoning of the child. For example, if the answer to ‘Is it odd?’ was Yes, then there is no point in then asking if the number is in the 4xTable (or the 6, 8, or 10xTable, come to that) as odd numbers won’t feature in any of those times tables.

Another issue is that it is very hard to know what numbers are left if you eliminate them through timestables. You could do it with a number line or square, crossing out the eliminated numbers, but few of us could do it in our heads.

And finally, and most fascinating, is that if the person choosing has chosen a prime number, then it is not in any times tables – except of course its own. So you’d have to wait until you got to ‘Is it in the 97xTable?’ to eliminate 97.

All of these knotty problems are rich pickings for reasoning. Lead the children again and again back to a discussion of their strategies. Do that by asking ‘What did the answer to that question tell you?’ to develop the children’s logical thinking. Try not to jump in and tell them – stick to questions. If you feel they’re falling short of what you’d hope, just keep encouraging them – that’s more valuable than getting them to the best strategy fast. After all, it’s only a game – not a SAT.

Trust me, you can spend a whole hour on trying to crack this. Alternatively, you can use it to warm up/down at the beginnings or endings of lessons or weeks. Just remember that its main value as a teaching tool – rather than a mere time-filler – is in developing awareness of reasons, and how a chain of reasoning can solve a problem.

Once they have exhausted the possibilities of this game, you could try some of the games on the NRICH website. I particularly like Strike It Out

http://nrich.maths.org/6589

…and Got It – where the whole class can play against the computer

http://nrich.maths.org/1272

I am indebted to Peter Worley at The Philosophy Foundation for showing me this game, and Andy West (also TPF) who reminded me of its value.

For more on how to introduce Enquiry into your set of teaching skills, try my book The Numberverse: How Numbers Are Bursting Out Of Everything And Just Want To Have Fun.

http://www.amazon.co.uk/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=numberverse

You can also buy it here:
http://www.philosophy-foundation.org/resources/philosophy-foundation-publications/the-numberverse

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Reasoning & Problem-solving – The New Black? The New Brain Gym? Or Just The New Curriculum?

Reasoning and Problem Solving

When the new Australian curriculum goes live in 2015, teachers across the country are being asked to – among other things – get students thinking mathematically. Two of the four proficiency strands are Problem Solving and Reasoning, (the others being Understanding and Fluency).

There is a great deal of overlap between Problem Solving and Reasoning. After all, it would be hard to solve problems without reasoning about them and it would be hard to demonstrate reasoning ability without some sort of problem to get our teeth into.

At the foot of this post is a link to the helpful ACARA curriculum website and I have also pasted in the clear definitions they give there.

In England the new KS3 curriculum says students should:
• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions

To help any teachers trying to incorporate these aims into their practice, here are some thoughts about Problem Solving and Reasoning, their difference and similarities, and what to do…

We can begin with problem-solving. People use certain skills, or develop certain habits, to solve problems. Take a jigsaw puzzle, for example. There are certain things that a skilled puzzler might do, such as: search for corners and edges, group pieces of the same colour, stand the box lid up to compare its picture to the one being formed, use both piece-shape and picture detail to match pieces, and so on.

However, it is possible to use some of these skills without reasoning all that much. So someone may ‘do the edges first’ because that’s the way they were taught to do it, but they would be unable to explain why it is better to start with the edges. So when pupils do exam questions, they may be solving problems quite effectively because they have encountered problems of that type before (like the puzzler who’s done lots of jigsaws) and ‘know the rules’.

Problem-solving skills are very important. An electrician uses them to identify a fault, logically testing until the cause of a problem emerges. A doctor uses them to diagnose a single condition from a set of symptoms and test results. And although I have given a very narrow picture of problem-solving above, with someone knowing the rules and being familiar with the problem, it is fair to say that really good problem-solvers attack unfamiliar problems effectively too. According to ACARA ‘Students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations’.

So how does reasoning differ? Basically, it is more abstract. Whereas we can judge problem-solving according to outcome, to a large extent, (so electricians or doctors who fix things – or have good ways of fixing things – are good problem-solvers), someone could possibly demonstrate good reasoning without managing to find a solution. A scientist might observe a phenomenon and show that it needs explaining, but have no answer. He/she may observe ‘Sunrises look different to sunsets: sunsets have a warmer, redder light and are more likely to cast spectacular colours across the sky. This must be because of a difference in the air the light is passing through or a difference in the objects it strikes, as the sun’s rays themselves would not be affected by the movement of the Earth.’ There is no problem to solve here, as such. And the scientist may be wrong about the reasons too, or even the observation itself, but he or she is reasoning: noticing, asking why, and attempting to work out where explanations might be found. Think of that great reasoner Isaac Newton: when he saw the apple fall out of the tree and wondered why, it wasn’t because gravity was a problem!

In my opinion, though, there is no need to ponder at length over the difference between problem-solving and reasoning, as so much of it is the same – especially in practice. The one useful distinction for me is that reasoning ability is a far more open thing, and problem-solving might not be enough. Reasoning leans more towards independence and creativity.

Can teachers teach these kind of skills? Those that say No have a point when they say that a lesson on ‘problem-solving’ is unlikely to be effective. I agree with that, but you could say the same about things like discipline, imagination, initiative and conscience. None of these things are taught as topics in themselves but… and here is the key thing… children learn them from adults or peers and they learn them (if indeed they do!) the whole time. The adult can teach by being a role model or by guiding children through experiences in such a way that these skills, or virtues, are acquired almost imperceptibly.

And so I believe that I have, on occasion, taught both problem-solving and reasoning through enquiry. An enquiry is an attempt by a group of learners to explore a topic. The exact question or problem to be explored is not automatically provided by the teacher. The teacher is more likely to present a stimulus that is rich in possibility and controversy. The question the pupils will be trying to answer will emerge from their own reactions and reflections.

Here are three possible stimuli, or starting points, for enquiries:
1. The children make a number line on the floor with each number on a separate piece of paper. Questions that might arise are:
Where will the line stop? How do we know?
Is there anything before zero? How do we know?
Is there anything in between the numbers? What?
2. Give the children a 10×10 number square. Challenge the children to find patterns in it. The class vote for which patterns they find most interesting. Questions or observations arising from the class or teacher might be:
If you draw a straight line through any group of numbers can you always say what the pattern is? (e.g. if you draw a vertical line, you always add 10 to get the number on the next line; if you draw a horizontal line, you add 1 – a diagonal line… then what?)
3. Show the children a set of different shaped drinking glasses. See what emerges. If nothing, then prompt them by asking which glass is ‘the biggest’. Then ask if the biggest one will take the most water, and how we can find out.
The process of facilitating an enquiry mainly involves reducing the length and frequency of teacher interventions to the minimum, and – more importantly – withholding judgment of the content of the children’s discussion.

Teaching Maths – or anything else – through enquiry gives a teacher a chance to nurture reasoning in the children. It treats mathematics as a field of discovery – as it once was for earlier mathematicians in history and still is for those high-fliers at the cutting edge of maths today. It allows students to pursue their own thoughts rather than rely on the teacher always to present them with a problem, still less a ready-made solution.

This is not to say that they wander aimlessly; the mere fact that children have freedom would not guarantee useful learning. Nor is it to say that teaching styles that are not enquiry-driven are ineffective or wrong. It is more that if children never have freedom to follow their own curiosity, then learning – if it is taking place – is more limited in scope, and less likely to allow young minds to fully flourish.

For more on how to introduce Enquiry into your set of teaching skills, try my book The Numberverse: How Numbers Are Bursting Out Of Everything And Just Want To Have Fun.

The ACARA definitions:
Problem Solving
Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.
Reasoning
Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false and when they compare and contrast related ideas and explain their choices.

The above are excerpts from:

http://www.australiancurriculum.edu.au/mathematics/content-structure

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What’s Philosophy Got To Do With It? Or… We’re Mates With Maths

When I told people that my work with philosophy for children had moved me into mathematics for children, and how we teach it, a lot of them were surprised. They are still surprised when I insist that philosophy and maths are closely related. For many, those two subjects would seem opposite ends of the spectrum: at one end is cold hard mathematics with its truths set in stone, and the other is philosophy, as vague and elusive as a puff of smoke. But this is to misunderstand them both.

Historically, mathematics and philosophy went hand-in-hand for centuries. The mathematician whose name is probably known to the most people, Pythagoras, was a Greek philosopher. And one of the most famous of all philosophers, Descartes, was also a mathematician.

These days, both disciplines have come so far that it would be asking a lot for even a genius to master both. So there probably won’t be another Descartes or Pythagoras, with a foot in both camps. But the two subjects are still linked. One reason why is that they both combine the mental abilities of logic and imagination.

As most of us know from school, we need logic to solve the mathematical problems we are set. When we say to ourselves, ‘The answer to this multiplication must be an even number, because we are multiplying two even numbers together’, that is pure, simple logic. But where does the imagination come in? Well, if you speak to mathematicians who work on the research side, trying to map out parts of the universe of numbers that have not been fully explored, they all maintain that imagination is essential. They mean the imagination to ask ‘What if…?’ and follow a train of thought onto new ground. Or the imagination to conceive of shapes and forms that lesser brains simply boggle at.

The same is true of philosophy. In philosophy, the illogical is not allowed. There are, of course, schools of philosophy which claim that the illogical is a necessary part of thinking. But even this discussion over whether logic is the be-all-and-end-all still puts logic at the heart of things. And as for imagination, yes, the great philosophers have all been hypothetical thinkers, able to picture the world in a multitude of ways.

This is important for the study of maths. Every single school child studies it. To get the maximum from each one, we need to make sure that the imaginative, curious children have the chance to explore maths in that way. Yes, they too need to be drilled and practised on calculation methods. But they need more if they are going to take maths to their hearts.

In the UK, and the US too, taking maths to your heart is quite a comical notion for many. But that’s not the case elsewhere. Many children in East Asia, for example (China, Japan, Korea) claim to love maths. There is no social stigma to liking it, or being good at it. And that is a fact about the whole society, much more than its teaching methods.

Until we in the West take curiosity, imagination, wonder and mystery as essential parts of mathematics, we will lag behind.

We can do this by seeking out questions in maths that are difficult and starting to think about them. And the difficult questions are not only in the difficult areas of maths. Just asking yourself if zero is a number, and trying to prove your answer is enough.

Here are some others to get you started:

What happens if you divide a number by zero?
Does Pi go on for ever? How do we know?
Are there more fractions or more integers (whole numbers)?
How many shapes are there?
How many lines of symmetry does a circle have?

Some of these big questions we can answer. Some we can’t. Some no-one ever will but we don’t know which ones those are.

Philosophy is the missing link that makes maths meaningful, which is why philosophers are very good at sniffing out questions like this. But do you know what? They are not as good as children. Given the chance, children will bamboozle you with queries that strike right at the heart of what numbers actually are. And you won’t be able to answer them sometimes. And that’s great, because it keeps the flame of curiosity alive – for them and you.

**Check out my book The Numberverse: How Numbers Are Bursting Out Of Everything And Just Want To Have Fun.
You can ‘Look Inside’ on Amazon here:

You can also buy it here:
http://www.philosophy-foundation.org/resources/philosophy-foundation-publications/the-numberverse

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When Numbers Won’t Behave

When numbers won’t behave

Some people like Maths because it feels like a land of certainty. Where other subjects – indeed life in general – teem with doubts and contradictions, numbers are cool, hard and permanent. You know where you are with them.

But is this how numbers really are, or just how we want them to be?

Once we know that two plus two equals four it can be quite comforting. We feel confident that there will never be a time that teachers, the government, our parents or anyone else turn out to have misled us about this simple fact. George Orwell, in 1984, floated the idea that ‘freedom is the freedom to say that two plus two make four’. So for him, or the protagonist of his novel at least, it was the perfect example of objective truth.

That may well be so, and certainly I myself can’t think of a better example. But despite that, students of maths can find what they are being told vague, or illogical. And some of the most confusing moments come with the most basic concepts.

I once got into a discussion with a class about whether 7 was a number or a digit. One child said ‘both’. We then started to discuss whether a digit and a number are the same thing. Some children said ‘yes’, some ‘no’. Their teacher sighed and crinkled her brow, having gone to some pains to teach them recently that a digit and a number are not the same thing.

Except that sometimes they sort of are…

Think of it like this:
51 is a number made of two digits.
5 is a number made of one digit

In the first example, 51 is a number and I have used two digits to write it. A computer working in binary, on the other hand, might communicate it as 110011, using six digits to express the same number. So it is clear to me that one number can be expressed with different digits.

I could, of course, communicate it another way altogether: ‘fifty-one’. That’s two words. Is it two digits? Maybe. What if I make up a single word to express the number… let’s say, ‘flimp’. If my new word caught on then people would be referring to the number 51 without using any digits. So this proves that numbers and digits are not the same thing. Doesn’t it?

But what about a single-digit number? The 5 in 51 was a digit, we said, but what about the 5 in the number 5? It’s a digit because it’s in a column where it means ‘5 units’. But isn’t it a number as well? And if it isn’t… what is a number?

Let’s widen this out a bit. Because ‘5’ (and I am talking about that bendy line on the page here) is also a numeral. A numeral is a mark, and can vary between languages. In Arabic, for example, 5 is written with a circle much like our sign for zero.

So 5 (European etc) and 0 (Arabic) are two different numerals, but they stand for the same digit. It helps to compare numbers with words here. The Arabic for ‘book’ is ‘kitab’, apparently. So ‘kitab’ and ‘book’ are two different words for one thing – a book.

The problem is that numbers aren’t quite like books. I have no doubt what both ‘book’ and ‘kitab’ stand for because there are some books on the shelf two metres away from me, and I could pick one up and drop it down on the table to illustrate. However, if I look at the numerals ‘5’ and ‘0’, there is nothing I can drop on the table to show what they refer to. So what do they refer to? If what they refer to is a number, how can I demonstrate what that number is without going back to the numerals all over again?

This may sound as if I am looking for a problem where there isn’t one – or at least not if you don’t go looking. But in my experience, people learning new concepts or procedures in maths come up against precisely these weird questions as they try to bend their brains around the new idea. This can happen when they are introduced to double-digit figures. Or decimal fractions.

Wittgenstein, a philosopher who was fascinated by the fundamentals of mathematics, wrote that as a philosopher he was trying to ‘show the fly the way out of the fly-bottle’. I always wondered what a fly bottle was but apparently it’s something they used to use to trap flies. Anyway, you can imagine the predicament of a fly inside a bottle. It buzzes around, ever more frantically, blocked by an invisible wall and unable to locate the exit.

That is a fitting metaphor for intellectual confusion. And you don’t have to be an intellectual to suffer from it. An ordinary 8-year-old can be unable to progress because a new concept is, basically, doing her head in. At that moment, numbers are doing things she thought they weren’t meant to do. They are behaving irrationally.

What can a teacher do? What a philosopher does. That is to:

• listen to the confusion
• try to understand the confusion rationally (i.e. how it stems naturally from the student’s current knowledge and beliefs)
• sympathise with the confusion (e.g. by saying ‘I see why you’re confused – that must be annoying’)
• consider why you the teacher believe what you believe instead, and try to explain it

Remember, we all have an upper limit of understanding in any subject, a point where the next stage doesn’t make sense to us. Reaching that point is anxious and frustrating. A guide who takes those feelings of ours seriously rather than brushing them aside is more likely to boost us up to that next level of understanding.

**Check out my book The Numberverse: How Numbers Are Bursting Out Of Everything And Just Want To Have Fun.
You can ‘Look Inside’ on Amazon here:

You can also buy it here:
http://www.philosophy-foundation.org/resources/philosophy-foundation-publications/the-numberverse

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The Philosophy Foundation Series Book Launch

On June 27th a crowd of teachers, philosophers, academics, friends and family gathered at Blackwell’s Bookshop at the Institute of Education to welcome The Numberverse and Provocations into the world.

book launch 3

Party go-ers at The Philosophy Foundation Series Launch Party.

These books are part of The Philosophy Foundation Book Series, a set of books published by Crown House, that challenge, engage and stimulate the imagination as well as being a practical resource for teachers/educators and parents to use. 

Andrew Day’s The Numberverse which was released on June 30th is a maths book designed to help teachers teach maths through enquiry, putting students at the heart of lessons and letting their curiosity drive it. 

What is in-between numbers?

What is in-between numbers?

At the launch Andy ran a session from his book where he puts a number line on the floor, and then asks, ‘Is there anything in-between the numbers?’. ‘Yes’, says one attendee, ‘Show us’ replies Andy. On pieces of paper in different colour they step forward and write 0.5, 1.5, 2.5, 3.5 and so on, placing them eqi distance between the whole (or as I would find out later that evening ‘natural’ numbers) numbers. ‘Is there anything else between the numbers?’ Andy asks, ‘Yes’, replies another and steps forward to show us. Through a series of comments, discussions and questions we soon find ourselves talking about infinity, ‘real’ numbers, and whether there are more numbers in-between the natural numbers than the natural numbers themselves. Andy does this session with Year 3 classes (aged 7/8) and above, and it is one of many activities on fractions, or the ‘in-betweeny-bits’, designed to make fractions more understandable.

Andy says in his introduction that “I’m putting The Numberverse out there now for two kinds of people: teachers looking for ways to get their more reluctant pupils into maths, and people who liked school generally but not maths (probably the latter group are the pupils from the first group but grown up).

“The evidence I have [that the book works] is anecdotal. Feedback from head teachers is very often positive. They want to instil a risk-taking, creative, exploratory attitude in all their classrooms. They want all their children to have high self-esteem and to believe they can improve at maths. But it’s hard. It’s also difficult to reconcile with the barrage of targets, levels, directives and schemes through which a teacher has to pick her way.

“One assumption I have made is that the teacher can get the class’s attention and manage behaviour to positive levels. I am as aware as anyone that those conditions are not always in place. I do know, however, that the material and techniques in this book can help win over a class, as part of an overall strategy for both ruling and entertaining the young.”

book launch 1

What order would you put these objects in?

Next up was David Birch, whose book Provocations: Philosophy for Secondary Schools has already received excellent reviews, including one from Michelle Sowey in Australia, having been released in February this year. David put the following objects on the floor: a banana, a mobile phone, Provocations and a chocolate bar, and then asked us to put them in order from the most to the least natural.

So, what order would you put them in? What do we mean by natural? Is something man-made natural? Are we natural? Is anything more natural than anything else? There was a fair amount of disagreement around these issues, and if you use David’s book his chapter on ‘Nature’ looks at the many varying ideas around nature, our relationship and responsibility (or not) towards it, including considering whether we should protect all natural things.

From Provocations:

“Smallpox has existed for at least 3,000 years and its rash can be seen on the faces of Egyptian mummies. In the 20th century alone an estimated 300 million people died from it. It is a disease caused by the variola virus; its most conspicuous symptom is blistering which develops all over the body, even in the mouth and throat, but mostly on the face and arms. It kills approximately a third of all those infected.

“Though there is no cure, smallpox was officially eradicated in 1979. The variola virus, however, still exists. It is preserved in two high-security facilities, one in Russia and the other in the US. The World Health Organisation (WHO), which was instrumental in its eradication, has been calling for its complete destruction for decades.

“The request by WHO has raised concern. It has been argued that if the virus were to be destroyed, it would be the first instance of humans intentionally acting with the explicit goal of eliminating another life form from the planet. It would constitute an unthinking disregard for nature. In arguing for the conservation of species, the biologist David Ehrenfeld has said, ‘they should be conserved because they exist and because this existence is itself but the present expression of a continuing historical process of immense antiquity and majesty.’

“The deliberate extinction of a species – the total annihilation of a life form – is perhaps an act worthy of moral scrutiny.”

Both of these books are available from all good booksellers and from The Philosophy Foundation Shop for £14.99. 

Win a copy of The Numberverse

Exterion Media (UK) have kindly provided The Philosophy Foundation with ad space on two bus routes in London and Wales and to mark the occasion we are giving away a copy of The Numberbervse. To find out which bus routes will be be carrying the ad, follow the hashtag #TPFBUS. To enter, simply take a photo and Tweet it to us @philosophyfound including the hashtag #TPFBUS and we will select a winner at random by the end of August.

If you would like a review copy of either of these books please email Rosalie Williams with the address you would like the book sent to, and details of where you will be publishing the review.

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UK’s First Primary Philosothon

On July 8th The Philosophy Foundation held the UK’s first primary Philosothon. It took place in Deptford Green Secondary School and involved five primary schools (seven classes, 200 students in total) all part of a collaborative of state schools in Deptford, they included Deptford Park, Sir Francis Drake, Grinling Gibbons, Lucas Vale and St Joseph’s.

Students from five primary schools in Deptford, at the start of the Philosothon

Students from five primary schools in Deptford, at the start of the Philosothon

For the past few years the schools have been conducting debating competitions for their Year 6 classes as part of the transition to secondary school – last year’s being run by The Philosophy Foundation, with a philosophical twist. At TPF we have an uncomfortable relationship with debates as they can become competitive rather than truth-seeking. The competitive edge of a debate, we observed, did not always – how shall we put this? – bring out the best in the students.

Earlier in the year Peter had been invited to act as a judge in the first Philosothon in this country at Kings College Taunton at which the originator of the Philosothon, Matthew Wills, was present having travelled from Australia. Peter was struck by the way in which the competitors were not only being marked on their intellectual contributions (their arguments and appropriate challenges etc.) but also on how well they facilitated each other towards a collaborative, group exploration of the issue.

We put it to the Deptford collaborative of schools that they might want to try a Philosothon instead of a traditional debate and the selling point was this idea of competitive collaboration. They decided to give it a go.

Students from Lucas Vale talk to Peter Worley about their philosophy classes.

Students from Lucas Vale talk to Peter Worley about their philosophy classes.

We invited seven Philosopher judges: Professor Simon Glendinning (LSE), Dr Catherine McCall (TPF Patron & Director of Epic International), Dr Marije Altorf (St Mary’s University), Dr Naomi Goulder (New College of Humanities), Dr Ellen Fridland (KCL), Dr Nathaniel Coleman (UCL) and Darren Chetty (IOE). We are grateful to all of them for giving their time, expertise and experience to help make this a memorable event for the young people involved.

The judges prepare for the event.

Some of the judges prepare for the event.

A Philosophical Enquiry from the competition, with the students discussing 'what is knowledge?'

A Philosophical Enquiry from the competition, with the students discussing ‘what is knowledge?’

All the classes underwent ten philosophy sessions around the two main topics of Knowledge and Freedom in the lead up to the competition. On the day, they were simply asked two direct questions: 1) How do you know that you know? (Knowledge) and 2) Are we in control of our lives? (Freedom) one for each of the two enquiries. Unlike other Philosothon’s where students are picked to represent their schools we had whole classes taking part. Each class were split into seven groups named after a philosopher and on the day the philosopher groups worked with each other all morning so that within each group there were 3-4 children from the same class.

Jenyd from Sir Francis Drake is awarded an 'Outstanding Contribution' prize.

Jenyd from Sir Francis Drake is awarded an ‘Outstanding Contribution’ prize.

Judges were given score sheets where they had to put a mark every time a student made a good philosophical contribution to the discussion – the students had different coloured badges on representing their class and the judge put a mark in the corresponding colour on their score sheet.

At the end the marks were all added up to find an overall class winner. Individual medals were also given to students for outstanding contributions, 14 were given out in total, and the winning class was ‘Opal’ from Deptford Park Primary School.

Opal Class from Deptford Park Primary School were the overall winners of the competition.

Opal Class from Deptford Park Primary School were the overall winners of the competition.

Everyone – judges and observers – thought that the level of co-operation and collaboration was outstanding. The synthesis of competition and collaboration that the Philosothon engendered is of particular importance because we think that philosophy (and the aim of gaining human knowledge in general) can be understood to be a synthesis between collaboration and opposition: people work together to solve a problem but in order to do so the process of gaining knowledge demands that they challenge each other in the right ways.

For more on Philosothon’s visit www.philosothon.org and for more on Philosothon’s in the UK visit www.philosothon.co.uk

 

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Book review: ‘Provocations: Philosophy for Secondary Schools’ by David Birch

Oddly, very few books exist to help teachers foster philosophical enquiry among high schoolers. Of these few, David Birch’s Provocations is a standout, distinguished by the originality, breadth and richness of its material. Any teacher who regards philosophy as a living, breathing practice will find in Provocations a vast reservoir of stimuli for thinking. It unlocks worlds of wonder and contemplation. Although wonderment may seem like a hard sell to a class of eye-rolling teens, this book is very likely to do the trick, reeling them in with tantalising vignettes and hooking them with contentious questions. “[A] question is an invitation,” Birch says –– and in class discussions, “the best questions are the questions that multiply.”

Hannah Arendt…believed that thinking is the quintessence of being alive.

Hannah Arendt…believed that thinking is the quintessence of being alive. Illustration by Tamar Levi.

Not once underestimating the maturity of high schoolers, Birch broaches sophisticated ethical, logical, political and social topics with characteristic pith and earnestness. He believes in students “speaking to find out what they believe”. Accordingly, he suggests that teachers reinvent themselves, shrugging off the mantle of the expert (and the fluency and assurance that go along with it) in favour of listening generously as their students think aloud.

When young people are free to experiment with ideas –– to propose, evaluate, reject or concede arguments as they see fit, rather than swallow readymade conclusions –– philosophy becomes something to do rather than something merely to learn about. It becomes a conscious practice of rationality, balancing open-mindedness and scepticism. Provocations offers prompt after prompt for young people to be curious and receptive learners.

The book opens with a foreword by A. C. Grayling, reminding us that in philosophy we tend not to find clear-cut answers, just more or less convincing (and always contestable) reasons for our views. Birch’s preface sets out his thoughts on the place of philosophy in education. His introduction offers teachers hints on how to encourage meaningful participation in classroom discussion. Much hinges on patient, uninterrupted listening while students explore familiar concepts made strange by their contexts: “Philosophy is a way of relearning language.”

The substance of the book is a diverse selection of engaging short texts, each followed by a thoughtful series of “catalytic questions”. More than 50 philosophical topics feature within themed sections about the World (It), Self (I), Society (We) and Others (You). Included are such intriguing topics as ‘Imperialism and Magic’, ‘Language and Originality’, ‘Perfectibility’ and ‘The Sacred’.

The author doesn’t shy away from raising confronting subjects like gender, suicide and torture, nor does he overlook classic tropes like the nature of time, freedom and autonomy, all presented in fresh and surprising ways.It’s easy to see why the questions of tradition and change, desire and boredom, and belief in God may be especially gripping for students in their adolescent years. Additionally, the inclusion of topics like mass surveillance, consumer marketing and the ethics of eating animals makes Provocations acutely relevant to our contemporary world.

Cerebral but never stuffy, the book introduces complex themes in unpredictable ways. It taps rich veins of cultural and scientific history, ranging freely across historical periods. It interweaves ancient and modern perspectives, philosophies and mythologies of the West and East, events from pivotal moments in world history and recent case studies.

To help students begin to understand death, for instance, Birch marshals contemporary ethnological observations; ideas distilled from the Buddha’s teachings and from Seneca’s writings; modern European philosophies from the idealist, psychoanalytic and existentialist traditions; and even a quote from Hamlet.

The book pulses with interest. Psychiatric reports, a Wagnerian opera narrative, futurologists’ predictions, logic puzzles, boundary-pushing poetry and invented dialogues all rub shoulders with accounts of disputes over workers’ strikes, prisoners’ voting rights, eugenics experiments and the enactment of secularity laws in French schools.

Provocations asks you to “suspend your certainties” and to celebrate the spontaneity and confusion that follows. A sorely-needed antidote to an increasingly results-orientated education system, this book offers much of value not only to philosophy teachers but also to teachers of English, humanities and the arts. Beyond the school gates, this book will find a wider audience among reflective adults. Parents, book clubbers and Philosophy Café enthusiasts are all in for a treat.

Provocations –– so fittingly titled –– will inspire fresh conversations that “crack things wide open”. I expect it will push many young people (and adults, too) to challenge and refine their intuitions, identities and worldviews.

Written by Michelle Sowey runs philosophy programs for children in Australia through her social enterprise, The Philosophy Club. You can follow her thoughts on The Philosophy Club blog and on facebook.

Buy your copy of Provocations in our online shop for only £14.99

Illustrations by Tamar Levi

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