Here's what the child has said in argument form (ie with premises and conclusion):

1. It’s a bird; (premise 1)
2. (All birds fly) (premise 2 – ‘hidden premise’)
3. So, it (must) fly. (Conclusion)

Next question: is this a good argument?

Standard answers:

1. No, because it’s wrong. Not all birds fly.
2. Yes, because she might not know that ‘not all birds fly’.

What do you think? Which of these answers do you find yourself agreeing with?

Being able to think about what people/children say in term of formal arguments is an important critical thinking tool for any teacher – or anyone! Indeed, it is the basis of critical thinking.

A little jargon

An argument is a series of statements (or claims) that are made in support of something thought to be true. The supporting claims, or reasons, are called premises, and the ‘something thought to be true’ that they support is called the conclusion. It is worth mentioning that a ‘hidden premise’ is a reason that is not stated explicitly, but that is held as an implicit belief. These are usually general claims (‘All Xs are F’).

There are two very important things to know about evaluating arguments. The first is to do with the structure of the argument and the second is to do with its truth. If an argument is structured well then it is valid; if an argument is both valid and true then it is sound. An argument is valid when the conclusion follows if the premises are true. And if it is established that the premises are in fact true, then the argument is sound.

A helpful technique

There is a simple way to tell whether an argument is valid (well-structured): you if the premises – I hope you’ll forgive my verbing the ‘if’ (and now my verbing of ‘verb’!) – to see if the conclusion follows. Here’s how you’d if the ‘bird’ argument:

1. If it’s a bird; (premise 1)
2. And if all birds fly; (premise 2 – ‘hidden premise’)
3. Would it follow that it must fly? (Conclusion)

Hopefully you can see that if it’s a bird and if it’s true that all birds fly then it would follow that it must fly.

This is the difficult bit – the ‘hump’ – in the lesson. Get past this and you’re home free! I suspect that many of you will be objecting, ‘But it’s not true that all birds fly!’ That’s why I have italicised the ‘if’s. Just for a second imagine that it is true that all birds fly. In that ‘imagined world’ it would follow that it must fly. It’s a little bit like ‘If x = 2 and y = 4, then x + y = 6’.

Back to the child

Now, let’s imagine two different scenarios.

1. The child believes that it is true that all birds fly. They are simply ignorant of ostrich, kiwi, emu etc or that they can’t fly. They did know about penguins, but didn’t know that they are birds.
2. The child had learnt about birds such as ostrich, kiwi, emu and penguins but had forgotten that they are birds or that they do not fly, or had simply not thought of them when they made the claim at the start of this piece.

Here’s the main point of the lesson. If it is the case that the child believes that all birds fly then the ‘bird’ argument above is a valid (well-structured) argument that just happens to be wrong. In as far as it is valid it is a good argument, just factually incorrect. And this presents an opportunity to the good teacher: to teach the class or child in question about birds that don’t fly, whether or not it is in the lesson plan or curriculum for that year! The second scenario presents another golden opportunity for the good teacher: to either:

1. Elicit more from the child to determine what exactly they might mean (for instance, it may turn out that they meant “It (probably) flies because it’s a bird” - a much more reasonable position which is only apparent when the ‘probably’ has been elicited from the child).
2. The teacher may question the child to reconsider the coherence of their reasoning (see below),
3. or engage the class critically by asking the class, “What do you think about that? Do you agree with… that…?”, perhaps writing up the argument said by the child (see above) on the board.

If questioning (see 2 above), the dialogue may run something like this:

Child: “It flies because it’s a bird, obviously!”
Teacher: “Does that mean that all birds fly?”
Child: “Errm… I don’t know.”
Teacher: “Can you think of a bird that doesn’t fly?”
(If the child says ‘no’ then the teacher knows to teach, or remind them of, this fact.)
Child: “Yes: a penguin. Is a penguin a bird?”
Teacher: “Yes, it is. So, if a penguin is a bird that doesn’t fly, do all birds fly?”

(If the child says ‘No’, then they would have successfully re-evaluated their position according to coherent logic – something that surely should be praised, according to Growth Mindset thinking, for instance.

If the child says ‘Yes’ then this tells the teacher something important about where that child is in terms of their logic or intransigence – after all, sometimes people refuse to re-evaluate not because they’ve failed to see the logic but because they are stubborn.)

Now, for the soundbite

So, now I hope it is clear how you might approach claims that are made by children in your class that may be wrong. The distinction I’ve introduced between validity and truth – between thinking and facts – affords us this invaluable insight: one may be wrong but thinking well; one may be right yet thinking poorly. Sensitivity to this can transform how you think about and tackle the thinking in your classroom.

To finish off…

Teacher asks: “What is 2 + 2?”
Boy says: “Four, Miss!”
Girl says: “Five.”
Teacher says: “Well done Johnny. Can you say why?”
Boy: “Because four is my lucky number.”
Teacher to girl: “Can you say why you think it’s five?”
Girl: “I held up two fingers and then counted two on.” (As she is demonstrating the teacher sees that she simply missed out ‘three’)

Question: Which answer should we prefer? Can you answer this question with an argument? Is it valid? Is it sound?

Do you allow pupils to be wrong in the right way? Let us know